Time-varying generalized linear models: characterizing and decoding neuronal dynamics in higher visual areas

To create a behaviorally relevant representation of the visual world, neurons in higher visual areas exhibit dynamic response changes to account for the time-varying interactions between external (e.g., visual input) and internal (e.g., reward value) factors. The resulting high-dimensional representational space poses challenges for precisely quantifying individual factors' contributions to the representation and readout of sensory information during a behavior. The widely used point process generalized linear model (GLM) approach provides a powerful framework for a quantitative description of neuronal processing as a function of various sensory and non-sensory inputs (encoding) as well as linking particular response components to particular behaviors (decoding), at the level of single trials and individual neurons. However, most existing variations of GLMs assume the neural systems to be time-invariant, making them inadequate for modeling nonstationary characteristics of neuronal sensitivity in higher visual areas. In this review, we summarize some of the existing GLM variations, with a focus on time-varying extensions. We highlight their applications to understanding neural representations in higher visual areas and decoding transient neuronal sensitivity as well as linking physiology to behavior through manipulation of model components. This time-varying class of statistical models provide valuable insights into the neural basis of various visual behaviors in higher visual areas and hold significant potential for uncovering the fundamental computational principles that govern neuronal processing underlying various behaviors in different regions of the brain.

Reconstructing computational system dynamics from neural data with recurrent neural networks

Computational models in neuroscience usually take the form of systems of differential equations. The behaviour of such systems is the subject of dynamical systems theory. Dynamical systems theory provides a powerful mathematical toolbox for analysing neurobiological processes and has been a mainstay of computational neuroscience for decades. Recently, recurrent neural networks (RNNs) have become a popular machine learning tool for studying the non-linear dynamics of neural and behavioural processes by emulating an underlying system of differential equations. RNNs have been routinely trained on similar behavioural tasks to those used for animal subjects to generate hypotheses about the underlying computational mechanisms. By contrast, RNNs can also be trained on the measured physiological and behavioural data, thereby directly inheriting their temporal and geometrical properties. In this way they become a formal surrogate for the experimentally probed system that can be further analysed, perturbed and simulated. This powerful approach is called dynamical system reconstruction. In this Perspective, we focus on recent trends in artificial intelligence and machine learning in this exciting and rapidly expanding field, which may be less well known in neuroscience. We discuss formal prerequisites, different model architectures and training approaches for RNN-based dynamical system reconstructions, ways to evaluate and validate model performance, how to interpret trained models in a neuroscience context, and current challenges.

Adult-born granule cells improve stimulus encoding and discrimination in the dentate gyrus

Heterogeneity plays an important role in diversifying neural responses to support brain function. Adult neurogenesis provides the dentate gyrus with a heterogeneous population of granule cells (GCs) that were born and developed their properties at different times. Immature GCs have distinct intrinsic and synaptic properties than mature GCs and are needed for correct encoding and discrimination in spatial tasks. How immature GCs enhance the encoding of information to support these functions is not well understood. Here, we record the responses to fluctuating current injections of GCs of different ages in mouse hippocampal slices to study how they encode stimuli. Immature GCs produce unreliable responses compared to mature GCs, exhibiting imprecise spike timings across repeated stimulation. We use a statistical model to describe the stimulus-response transformation performed by GCs of different ages. We fit this model to the data and obtain parameters that capture GCs' encoding properties. Parameter values from this fit reflect the maturational differences of the population and indicate that immature GCs perform a differential encoding of stimuli. To study how this age heterogeneity influences encoding by a population, we perform stimulus decoding using populations that contain GCs of different ages. We find that, despite their individual unreliability, immature GCs enhance the fidelity of the signal encoded by the population and improve the discrimination of similar time-dependent stimuli. Thus, the observed heterogeneity confers the population with enhanced encoding capabilities.

Quantifying uncertainty in spikes estimated from calcium imaging data

In recent years, a number of methods have been proposed to estimate the times at which a neuron spikes on the basis of calcium imaging data. However, quantifying the uncertainty associated with these estimated spikes remains an open problem. We consider a simple and well-studied model for calcium imaging data, which states that calcium decays exponentially in the absence of a spike, and instantaneously increases when a spike occurs. We wish to test the null hypothesis that the neuron did not spike-i.e., that there was no increase in calcium-at a particular timepoint at which a spike was estimated. In this setting, classical hypothesis tests lead to inflated Type I error, because the spike was estimated on the same data used for testing. To overcome this problem, we propose a selective inference approach. We describe an efficient algorithm to compute finite-sample $p$-values that control selective Type I error, and confidence intervals with correct selective coverage, for spikes estimated using a recent proposal from the literature. We apply our proposal in simulation and on calcium imaging data from the $\texttt{spikefinder}$ challenge.

Opponent control of behavior by dorsomedial striatal pathways depends on task demands and internal state

A classic view of the striatum holds that activity in direct and indirect pathways oppositely modulates motor output. Whether this involves direct control of movement, or reflects a cognitive process underlying movement, remains unresolved. Here we find that strong, opponent control of behavior by the two pathways of the dorsomedial striatum depends on the cognitive requirements of a task. Furthermore, a latent state model (a hidden Markov model with generalized linear model observations) reveals that-even within a single task-the contribution of the two pathways to behavior is state dependent. Specifically, the two pathways have large contributions in one of two states associated with a strategy of evidence accumulation, compared to a state associated with a strategy of repeating previous choices. Thus, both the demands imposed by a task, as well as the internal state of mice when performing a task, determine whether dorsomedial striatum pathways provide strong and opponent control of behavior.

Modelling the neural code in large populations of correlated neurons

Neurons respond selectively to stimuli, and thereby define a code that associates stimuli with population response patterns. Certain correlations within population responses (noise correlations) significantly impact the information content of the code, especially in large populations. Understanding the neural code thus necessitates response models that quantify the coding properties of modelled populations, while fitting large-scale neural recordings and capturing noise correlations. In this paper, we propose a class of response model based on mixture models and exponential families. We show how to fit our models with expectation-maximization, and that they capture diverse variability and covariability in recordings of macaque primary visual cortex. We also show how they facilitate accurate Bayesian decoding, provide a closed-form expression for the Fisher information, and are compatible with theories of probabilistic population coding. Our framework could allow researchers to quantitatively validate the predictions of neural coding theories against both large-scale neural recordings and cognitive performance.

Differences in olfactory bulb mitral cell spiking with ortho- and retronasal stimulation revealed by data-driven models

The majority of olfaction studies focus on orthonasal stimulation where odors enter via the front nasal cavity, while retronasal olfaction, where odors enter the rear of the nasal cavity during feeding, is understudied. The coding of retronasal odors via coordinated spiking of neurons in the olfactory bulb (OB) is largely unknown despite evidence that higher level processing is different than orthonasal. To this end, we use multi-electrode array in vivo recordings of rat OB mitral cells (MC) in response to a food odor with both modes of stimulation, and find significant differences in evoked firing rates and spike count covariances (i.e., noise correlations). Differences in spiking activity often have implications for sensory coding, thus we develop a single-compartment biophysical OB model that is able to reproduce key properties of important OB cell types. Prior experiments in olfactory receptor neurons (ORN) showed retro stimulation yields slower and spatially smaller ORN inputs than with ortho, yet whether this is consequential for OB activity remains unknown. Indeed with these specifications for ORN inputs, our OB model captures the salient trends in our OB data. We also analyze how first and second order ORN input statistics dynamically transfer to MC spiking statistics with a phenomenological linear-nonlinear filter model, and find that retro inputs result in larger linear filters than ortho inputs. Finally, our models show that the temporal profile of ORN is crucial for capturing our data and is thus a distinguishing feature between ortho and retro stimulation, even at the OB. Using data-driven modeling, we detail how ORN inputs result in differences in OB dynamics and MC spiking statistics. These differences may ultimately shape how ortho and retro odors are coded.

Olfaction is a key sense for many cognitive and behavioral tasks, and is particularly unique because odors can naturally enter the nasal cavity from the front or rear, i.e., ortho- and retro-nasal, respectively. Yet little is known about the differences in coordinated spiking in the olfactory bulb with ortho versus retro stimulation, let alone how these different modes of olfaction may alter coding of odors. We simultaneously record many cells in rat olfactory bulb to assess the differences in spiking statistics, and develop a biophysical olfactory bulb network model to study the reasons for these differences. Using theoretical and computational methods, we find that the olfactory bulb transfers input statistics differently for retro stimulation relative to ortho stimulation. Furthermore, our models show that the temporal profile of inputs is crucial for capturing our data and is thus a distinguishing feature between ortho and retro stimulation, even at the olfactory bulb. Understanding the spiking dynamics of the olfactory bulb with both ortho and retro stimulation is a key step for ultimately understanding how the brain codes odors with different modes of olfaction.

Uncovering structured responses of neural populations recorded from macaque monkeys with linear support vector machines

When a mammal, such as a macaque monkey, sees a complex natural image, many neurons in its visual cortex respond simultaneously. Here, we provide a protocol for studying the structure of population responses in laminar recordings with a machine learning model, the linear support vector machine. To unravel the role of single neurons in population responses and the structure of noise correlations, we use a multivariate decoding technique on time-averaged responses.

For complete details on the use and execution of this protocol, please refer to Koren et al. (2020a).

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Linear support vector machine (SVM) is an efficient model for decoding from neural data

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Permutation test is a rigorous method for testing the significance of results

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Neural responses along the cortical depth are heterogeneous

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Decoding weights and noise correlations share a similar structure

Building population models for large-scale neural recordings: Opportunities and pitfalls

Modern recording technologies now enable simultaneous recording from large numbers of neurons. This has driven the development of new statistical models for analyzing and interpreting neural population activity. Here, we provide a broad overview of recent developments in this area. We compare and contrast different approaches, highlight strengths and limitations, and discuss biological and mechanistic insights that these methods provide.

An unbiased, efficient sleep-wake detection algorithm for a population with sleep disorders: change point decoder

STUDY OBJECTIVES

The usage of wrist-worn wearables to detect sleep-wake states remains a formidable challenge, particularly among individuals with disordered sleep. We developed a novel and unbiased data-driven method for the detection of sleep-wake and compared its performance with the well-established Oakley algorithm (OA) relative to polysomnography (PSG) in elderly men with disordered sleep.

METHODS

Overnight in-lab PSG from 102 participants was compared with accelerometry and photoplethysmography simultaneously collected with a wearable device (Empatica E4). A binary segmentation algorithm was used to detect change points in these signals. A model that estimates sleep or wake states given the changes in these signals was established (change point decoder, CPD). The CPD's performance was compared with the performance of the OA in relation to PSG.

RESULTS

On the testing set, OA provided sleep accuracy of 0.85, wake accuracy of 0.54, AUC of 0.67, and Kappa of 0.39. Comparable values for CPD were 0.70, 0.74, 0.78, and 0.40. The CPD method had sleep onset latency error of -22.9 min, sleep efficiency error of 2.09%, and underestimated the number of sleep-wake transitions with an error of 64.4. The OA method's performance was 28.6 min, -0.03%, and -17.2, respectively.

CONCLUSIONS

The CPD aggregates information from both cardiac and motion signals for state determination as well as the cross-dimensional influences from these domains. Therefore, CPD classification achieved balanced performance and higher AUC, despite underestimating sleep-wake transitions. The CPD could be used as an alternate framework to investigate sleep-wake dynamics within the conventional time frame of 30-s epochs.

Statistical Analysis of Decoding Performances of Diverse Populations of Neurons

A central theme in computational neuroscience is determining the neural correlates of efficient and accurate coding of sensory signals. Diversity, or heterogeneity, of intrinsic neural attributes is known to exist in many brain areas and is thought to significantly affect neural coding. Recent theoretical and experimental work has argued that in uncoupled networks, coding is most accurate at intermediate levels of heterogeneity. Here we consider this question with data from in vivo recordings of neurons in the electrosensory system of weakly electric fish subject to the same realization of noisy stimuli; we use a generalized linear model (GLM) to assess the accuracy of (Bayesian) decoding of stimulus given a population spiking response. The long recordings enable us to consider many uncoupled networks and a relatively wide range of heterogeneity, as well as many instances of the stimuli, thus enabling us to address this question with statistical power. The GLM decoding is performed on a single long time series of data to mimic realistic conditions rather than using trial-averaged data for better model fits. For a variety of fixed network sizes, we generally find that the optimal levels of heterogeneity are at intermediate values, and this holds in all core components of GLM. These results are robust to several measures of decoding performance, including the absolute value of the error, error weighted by the uncertainty of the estimated stimulus, and the correlation between the actual and estimated stimulus. Although a quadratic fit to decoding performance as a function of heterogeneity is statistically significant, the result is highly variable with low R2 values. Taken together, intermediate levels of neural heterogeneity are indeed a prominent attribute for efficient coding even within a single time series, but the performance is highly variable.

Information processing in the LGN: a comparison of neural codes and cell types

To understand how anatomy and physiology allow an organism to perform its function, it is important to know how information that is transmitted by spikes in the brain is received and encoded. A natural question is whether the spike rate alone encodes the information about a stimulus (rate code), or additional information is contained in the temporal pattern of the spikes (temporal code). Here we address this question using data from the cat Lateral Geniculate Nucleus (LGN), which is the visual portion of the thalamus, through which visual information from the retina is communicated to the visual cortex. We analyzed the responses of LGN neurons to spatially homogeneous spots of various sizes with temporally random luminance modulation. We compared the Firing Rate with the Shannon Information Transmission Rate , which quantifies the information contained in the temporal relationships between spikes. We found that the behavior of these two rates can differ quantitatively. This suggests that the energy used for spiking does not translate directly into the information to be transmitted. We also compared Firing Rates with Information Rates for X-ON and X-OFF cells. We found that, for X-ON cells the Firing Rate and Information Rate often behave in a completely different way, while for X-OFF cells these rates are much more highly correlated. Our results suggest that for X-ON cells a more efficient "temporal code" is employed, while for X-OFF cells a straightforward "rate code" is used, which is more reliable and is correlated with energy consumption.

In vitro validation of in silico identified inhibitory interactions

BACKGROUND

Understanding how neuronal signals propagate in local network is an important step in understanding information processing. As a result, spike trains recorded with multi-electrode arrays (MEAs) have been widely used to study the function of neural networks. Studying the dynamics of neuronal networks requires the identification of both excitatory and inhibitory connections. The detection of excitatory relationships can robustly be inferred by characterizing the statistical relationships of neural spike trains. However, the identification of inhibitory relationships is more difficult: distinguishing endogenous low firing rates from active inhibition is not obvious.

NEW METHOD

In this paper, we propose an in silico interventional procedure that makes predictions about the effect of stimulating or inhibiting single neurons on other neurons, and thereby gives the ability to accurately identify inhibitory effects.

COMPARISON

To experimentally test these predictions, we have developed a Neural Circuit Probe (NCP) that delivers drugs transiently and reversibly on individually identified neurons to assess their contributions to the neural circuit behavior.

RESULTS

Using the NCP, putative inhibitory connections identified by the in silico procedure were validated through in vitro interventional experiments.

CONCLUSIONS

Together, these results demonstrate how detailed microcircuitry can be inferred from statistical models derived from neurophysiology data.

A Matrix Information-Geometric Method for Change-Point Detection of Rigid Body Motion

A matrix information-geometric method was developed to detect the change-points of rigid body motions. Note that the set of all rigid body motions is the special Euclidean group S E ( 3 ) , so the Riemannian mean based on the Lie group structures of S E ( 3 ) reflects the characteristics of change-points. Once a change-point occurs, the distance between the current point and the Riemannian mean of its neighbor points should be a local maximum. A gradient descent algorithm is proposed to calculate the Riemannian mean. Using the Baker-Campbell-Hausdorff formula, the first-order approximation of the Riemannian mean is taken as the initial value of the iterative procedure. The performance of our method was evaluated by numerical examples and manipulator experiments.

Neural decoding with visual attention using sequential Monte Carlo for leaky integrate-and-fire neurons

How the brain makes sense of a complicated environment is an important question, and a first step is to be able to reconstruct the stimulus that give rise to an observed brain response. Neural coding relates neurobiological observations to external stimuli using computational methods. Encoding refers to how a stimulus affects the neuronal output, and entails constructing a neural model and parameter estimation. Decoding refers to reconstruction of the stimulus that led to a given neuronal output. Existing decoding methods rarely explain neuronal responses to complicated stimuli in a principled way. Here we perform neural decoding for a mixture of multiple stimuli using the leaky integrate-and-fire model describing neural spike trains, under the visual attention hypothesis of probability mixing in which the neuron only attends to a single stimulus at any given time. We assume either a parallel or serial processing visual search mechanism when decoding multiple simultaneous neurons. We consider one or multiple stochastic stimuli following Ornstein-Uhlenbeck processes, and dynamic neuronal attention that switches following discrete Markov processes. To decode stimuli in such situations, we develop various sequential Monte Carlo particle methods in different settings. The likelihood of the observed spike trains is obtained through the first-passage time probabilities obtained by solving the Fokker-Planck equations. We show that the stochastic stimuli can be successfully decoded by sequential Monte Carlo, and different particle methods perform differently considering the number of observed spike trains, the number of stimuli, model complexity, etc. The proposed novel decoding methods, which analyze the neural data through psychological visual attention theories, provide new perspectives to understand the brain.

Adaptive stimulus selection for multi-alternative psychometric functions with lapses

Psychometric functions (PFs) quantify how external stimuli affect behavior, and they play an important role in building models of sensory and cognitive processes. Adaptive stimulus-selection methods seek to select stimuli that are maximally informative about the PF given data observed so far in an experiment and thereby reduce the number of trials required to estimate the PF. Here we develop new adaptive stimulus-selection methods for flexible PF models in tasks with two or more alternatives. We model the PF with a multinomial logistic regression mixture model that incorporates realistic aspects of psychophysical behavior, including lapses and multiple alternatives for the response. We propose an information-theoretic criterion for stimulus selection and develop computationally efficient methods for inference and stimulus selection based on adaptive Markov-chain Monte Carlo sampling. We apply these methods to data from macaque monkeys performing a multi-alternative motion-discrimination task and show in simulated experiments that our method can achieve a substantial speed-up over random designs. These advances will reduce the amount of data needed to build accurate models of multi-alternative PFs and can be extended to high-dimensional PFs that would be infeasible to characterize with standard methods.

Interpreting encoding and decoding models

Encoding and decoding models are widely used in systems, cognitive, and computational neuroscience to make sense of brain-activity data. However, the interpretation of their results requires care. Decoding models can help reveal whether particular information is present in a brain region in a format the decoder can exploit. Encoding models make comprehensive predictions about representational spaces. In the context of sensory experiments, where stimuli are experimentally controlled, encoding models enable us to test and compare brain-computational theories. Encoding and decoding models typically include fitted linear-model components. Sometimes the weights of the fitted linear combinations are interpreted as reflecting, in an encoding model, the contribution of different sensory features to the representation or, in a decoding model, the contribution of different measured brain responses to a decoded feature. Such interpretations can be problematic when the predictor variables or their noise components are correlated and when priors (or penalties) are used to regularize the fit. Encoding and decoding models are evaluated in terms of their generalization performance. The correct interpretation depends on the level of generalization a model achieves (e.g. to new response measurements for the same stimuli, to new stimuli from the same population, or to stimuli from a different population). Significant decoding or encoding performance of a single model (at whatever level of generality) does not provide strong constraints for theory. Many models must be tested and inferentially compared for analyses to drive theoretical progress.

High-resolution directed human connectomes and the Consensus Connectome Dynamics

Here we show a method of directing the edges of the connectomes, prepared from HARDI datasets from the human brain. Before the present work, no high-definition directed braingraphs were published, because the tractography methods in use are not capable of assigning directions to the neural tracts discovered. Previous work on the functional connectomes applied low-resolution functional MRI-detected statistical causality for the assignment of directions of connectomes of typically several dozens of vertices. Our method is based on the phenomenon of the “Consensus Connectome Dynamics”, described earlier by our research group. In this contribution, we apply the method to the 423 braingraphs, each with 1015 vertices, computed from the public release of the Human Connectome Project, and we also made the directed connectomes publicly available at the site http://braingraph.org. We also show the robustness of our edge directing method in four independently chosen connectome datasets: we have found that 86% of the edges, which were present in all four datasets, get the same directions in all datasets; therefore the direction method is robust. While our new edge-directing method still needs more empirical validation, we think that our present contribution opens up new possibilities in the analysis of the high-definition human connectome.

Axonal Anatomy Optimizes Spatial Encoding in the Rat Entorhinal-Dentate System: A Computational Study

OBJECTIVE

The network architecture connecting neural regions is defined by the organization and anatomical properties of the projecting axons, but its contributions to neural encoding and system function are difficult to study experimentally.

METHODS

Using a large-scale, spiking neuronal network model of rat dentate gyrus, the role of the anatomy of the entorhinal-dentate axonal projection was evaluated in the context of spatial encoding by incorporating grid cell activity to provide physiological, spatially-correlated input. The dorso-ventral extents of the entorhinal axon terminal fields were varied to generate different feedforward architectures, and the resulting spatial representations and spatial information scores of the network were evaluated. Position was decoded from the population activity using a point process filter to investigate the contributions of network architecture on spatial encoding.

RESULTS

The model predicted the emergence of anatomical gradients within the dentate gyrus for place field size and spatial information along its dorso-ventral axis, which were dependent on the extents of the entorhinal axon terminal fields. The decoding results revealed an optimal performance at an axon terminal field extent of 2 mm that lies within the biological range.

CONCLUSION

The axonal anatomy mediates a tradeoff between encoding multiple place field sizes or achieving a high spatial information score, and the combination of both properties is necessary to maximize spatial encoding by a network.

SIGNIFICANCE

In total, this paper establishes a mechanistic neuronal network model that, in concert with information-theoretic and statistical methods, can be used to investigate how lower level properties contribute to higher level function.

Identification of Retinal Ganglion Cell Firing Patterns Using Clustering Analysis Supplied with Failure Diagnosis

An important goal in visual neuroscience is to understand how neuronal population coding in vertebrate retina mediates the broad range of visual functions. Microelectrode arrays interface on isolated retina registers a collective measure of the spiking dynamics of retinal ganglion cells (RGCs) by probing them simultaneously and in large numbers. The recorded data stream is then processed to identify spike trains of individual RGCs by efficient and scalable spike detection and sorting routines. Most spike sorting software packages, available either commercially or as freeware, combine automated steps with judgment calls by the investigator to verify the quality of sorted spikes. This work focused on sorting spikes of RGCs into clusters using an integrated analytical platform for the data recorded during visual stimulation of wild-type mice retinas with whole field stimuli. After spike train detection, we projected each spike onto two feature spaces: a parametric space and a principal components space. We then applied clustering algorithms to sort spikes into separate clusters. To eliminate the need for human intervention, the initial clustering results were submitted to diagnostic tests that evaluated the results to detect the sources of failure in cluster assignment. This failure diagnosis formed a decision logic for diagnosable electrodes to enhance the clustering quality iteratively through rerunning the clustering algorithms. The new clustering results showed that the spike sorting accuracy was improved. Subsequently, the number of active RGCs during each whole field stimulation was found, and the light responsiveness of each RGC was identified. Our approach led to error-resilient spike sorting in both feature extraction methods; however, using parametric features led to less erroneous spike sorting compared to principal components, particularly for low signal-to-noise ratios. As our approach is reliable for retinal signal processing in response to simple visual stimuli, it could be applied to the evaluation of disrupted physiological signaling in retinal neurodegenerative diseases.

Ensembles of change-point detectors: implications for real-time BMI applications

Brain-machine interfaces (BMIs) have been widely used to study basic and translational neuroscience questions. In real-time closed-loop neuroscience experiments, many practical issues arise, such as trial-by-trial variability, and spike sorting noise or multi-unit activity. In this paper, we propose a new framework for change-point detection based on ensembles of independent detectors in the context of BMI application for detecting acute pain signals. Motivated from ensemble learning, our proposed "ensembles of change-point detectors" (ECPDs) integrate multiple decisions from independent detectors, which may be derived based on data recorded from different trials, data recorded from different brain regions, data of different modalities, or models derived from different learning methods. By integrating multiple sources of information, the ECPDs aim to improve detection accuracy (in terms of true positive and true negative rates) and achieve an optimal trade-off of sensitivity and specificity. We validate our method using computer simulations and experimental recordings from freely behaving rats. Our results have shown superior and robust performance of ECPDS in detecting the onset of acute pain signals based on neuronal population spike activity (or combined with local field potentials) recorded from single or multiple brain regions.

Nonlinear decoding of a complex movie from the mammalian retina

Retina is a paradigmatic system for studying sensory encoding: the transformation of light into spiking activity of ganglion cells. The inverse problem, where stimulus is reconstructed from spikes, has received less attention, especially for complex stimuli that should be reconstructed "pixel-by-pixel". We recorded around a hundred neurons from a dense patch in a rat retina and decoded movies of multiple small randomly-moving discs. We constructed nonlinear (kernelized and neural network) decoders that improved significantly over linear results. An important contribution to this was the ability of nonlinear decoders to reliably separate between neural responses driven by locally fluctuating light signals, and responses at locally constant light driven by spontaneous-like activity. This improvement crucially depended on the precise, non-Poisson temporal structure of individual spike trains, which originated in the spike-history dependence of neural responses. We propose a general principle by which downstream circuitry could discriminate between spontaneous and stimulus-driven activity based solely on higher-order statistical structure in the incoming spike trains.

Real-time particle filtering and smoothing algorithms for detecting abrupt changes in neural ensemble spike activity

Sequential change-point detection from time series data is a common problem in many neuroscience applications, such as seizure detection, anomaly detection, and pain detection. In our previous work (Chen Z, Zhang Q, Tong AP, Manders TR, Wang J. J Neural Eng 14: 036023, 2017), we developed a latent state-space model, known as the Poisson linear dynamical system, for detecting abrupt changes in neuronal ensemble spike activity. In online brain-machine interface (BMI) applications, a recursive filtering algorithm is used to track the changes in the latent variable. However, previous methods have been restricted to Gaussian dynamical noise and have used Gaussian approximation for the Poisson likelihood. To improve the detection speed, we introduce non-Gaussian dynamical noise for modeling a stochastic jump process in the latent state space. To efficiently estimate the state posterior that accommodates non-Gaussian noise and non-Gaussian likelihood, we propose particle filtering and smoothing algorithms for the change-point detection problem. To speed up the computation, we implement the proposed particle filtering algorithms using advanced graphics processing unit computing technology. We validate our algorithms, using both computer simulations and experimental data for acute pain detection. Finally, we discuss several important practical issues in the context of real-time closed-loop BMI applications. NEW & NOTEWORTHY Sequential change-point detection is an important problem in closed-loop neuroscience experiments. This study proposes novel sequential Monte Carlo methods to quickly detect the onset and offset of a stochastic jump process that drives the population spike activity. This new approach is robust with respect to spike sorting noise and varying levels of signal-to-noise ratio. The GPU implementation of the computational algorithm allows for parallel processing in real time.

Encoding and Decoding Models in Cognitive Electrophysiology

Cognitive neuroscience has seen rapid growth in the size and complexity of data recorded from the human brain as well as in the computational tools available to analyze this data. This data explosion has resulted in an increased use of multivariate, model-based methods for asking neuroscience questions, allowing scientists to investigate multiple hypotheses with a single dataset, to use complex, time-varying stimuli, and to study the human brain under more naturalistic conditions. These tools come in the form of "Encoding" models, in which stimulus features are used to model brain activity, and "Decoding" models, in which neural features are used to generated a stimulus output. Here we review the current state of encoding and decoding models in cognitive electrophysiology and provide a practical guide toward conducting experiments and analyses in this emerging field. Our examples focus on using linear models in the study of human language and audition. We show how to calculate auditory receptive fields from natural sounds as well as how to decode neural recordings to predict speech. The paper aims to be a useful tutorial to these approaches, and a practical introduction to using machine learning and applied statistics to build models of neural activity. The data analytic approaches we discuss may also be applied to other sensory modalities, motor systems, and cognitive systems, and we cover some examples in these areas. In addition, a collection of Jupyter notebooks is publicly available as a complement to the material covered in this paper, providing code examples and tutorials for predictive modeling in python. The aim is to provide a practical understanding of predictive modeling of human brain data and to propose best-practices in conducting these analyses.

A state space approach for piecewise-linear recurrent neural networks for identifying computational dynamics from neural measurements

The computational and cognitive properties of neural systems are often thought to be implemented in terms of their (stochastic) network dynamics. Hence, recovering the system dynamics from experimentally observed neuronal time series, like multiple single-unit recordings or neuroimaging data, is an important step toward understanding its computations. Ideally, one would not only seek a (lower-dimensional) state space representation of the dynamics, but would wish to have access to its statistical properties and their generative equations for in-depth analysis. Recurrent neural networks (RNNs) are a computationally powerful and dynamically universal formal framework which has been extensively studied from both the computational and the dynamical systems perspective. Here we develop a semi-analytical maximum-likelihood estimation scheme for piecewise-linear RNNs (PLRNNs) within the statistical framework of state space models, which accounts for noise in both the underlying latent dynamics and the observation process. The Expectation-Maximization algorithm is used to infer the latent state distribution, through a global Laplace approximation, and the PLRNN parameters iteratively. After validating the procedure on toy examples, and using inference through particle filters for comparison, the approach is applied to multiple single-unit recordings from the rodent anterior cingulate cortex (ACC) obtained during performance of a classical working memory task, delayed alternation. Models estimated from kernel-smoothed spike time data were able to capture the essential computational dynamics underlying task performance, including stimulus-selective delay activity. The estimated models were rarely multi-stable, however, but rather were tuned to exhibit slow dynamics in the vicinity of a bifurcation point. In summary, the present work advances a semi-analytical (thus reasonably fast) maximum-likelihood estimation framework for PLRNNs that may enable to recover relevant aspects of the nonlinear dynamics underlying observed neuronal time series, and directly link these to computational properties.

Optimizing for generalization in the decoding of internally generated activity in the hippocampus

The decoding of a sensory or motor variable from neural activity benefits from a known ground truth against which decoding performance can be compared. In contrast, the decoding of covert, cognitive neural activity, such as occurs in memory recall or planning, typically cannot be compared to a known ground truth. As a result, it is unclear how decoders of such internally generated activity should be configured in practice. We suggest that if the true code for covert activity is unknown, decoders should be optimized for generalization performance using cross-validation. Using ensemble recording data from hippocampal place cells, we show that this cross-validation approach results in different decoding error, different optimal decoding parameters, and different distributions of error across the decoded variable space. In addition, we show that a minor modification to the commonly used Bayesian decoding procedure, which enables the use of spike density functions, results in substantially lower decoding errors. These results have implications for the interpretation of covert neural activity, and suggest easy-to-implement changes to commonly used procedures across domains, with applications to hippocampal place cells in particular. © 2017 Wiley Periodicals, Inc.

Efficient sensory cortical coding optimizes pursuit eye movements

In the natural world, the statistics of sensory stimuli fluctuate across a wide range. In theory, the brain could maximize information recovery if sensory neurons adaptively rescale their sensitivity to the current range of inputs. Such adaptive coding has been observed in a variety of systems, but the premise that adaptation optimizes behaviour has not been tested. Here we show that adaptation in cortical sensory neurons maximizes information about visual motion in pursuit eye movements guided by that cortical activity. We find that gain adaptation drives a rapid (<100 ms) recovery of information after shifts in motion variance, because the neurons and behaviour rescale their sensitivity to motion fluctuations. Both neurons and pursuit rapidly adopt a response gain that maximizes motion information and minimizes tracking errors. Thus, efficient sensory coding is not simply an ideal standard but a description of real sensory computation that manifests in improved behavioural performance.

Uncovering representations of sleep-associated hippocampal ensemble spike activity

Pyramidal neurons in the rodent hippocampus exhibit spatial tuning during spatial navigation, and they are reactivated in specific temporal order during sharp-wave ripples observed in quiet wakefulness or slow wave sleep. However, analyzing representations of sleep-associated hippocampal ensemble spike activity remains a great challenge. In contrast to wake, during sleep there is a complete absence of animal behavior, and the ensemble spike activity is sparse (low occurrence) and fragmental in time. To examine important issues encountered in sleep data analysis, we constructed synthetic sleep-like hippocampal spike data (short epochs, sparse and sporadic firing, compressed timescale) for detailed investigations. Based upon two Bayesian population-decoding methods (one receptive field-based, and the other not), we systematically investigated their representation power and detection reliability. Notably, the receptive-field-free decoding method was found to be well-tuned for hippocampal ensemble spike data in slow wave sleep (SWS), even in the absence of prior behavioral measure or ground truth. Our results showed that in addition to the sample length, bin size, and firing rate, number of active hippocampal pyramidal neurons are critical for reliable representation of the space as well as for detection of spatiotemporal reactivated patterns in SWS or quiet wakefulness.

Eliciting naturalistic cortical responses with a sensory prosthesis via optimized microstimulation

OBJECTIVE

Lost sensations, such as touch, could one day be restored by electrical stimulation along the sensory neural pathways. Such stimulation, when informed by electronic sensors, could provide naturalistic cutaneous and proprioceptive feedback to the user. Perceptually, microstimulation of somatosensory brain regions produces localized, modality-specific sensations, and several spatiotemporal parameters have been studied for their discernibility. However, systematic methods for encoding a wide array of naturally occurring stimuli into biomimetic percepts via multi-channel microstimulation are lacking. More specifically, generating spatiotemporal patterns for explicitly evoking naturalistic neural activation has not yet been explored.

APPROACH

We address this problem by first modeling the dynamical input-output relationship between multichannel microstimulation and downstream neural responses, and then optimizing the input pattern to reproduce naturally occurring touch responses as closely as possible.

MAIN RESULTS

Here we show that such optimization produces responses in the S1 cortex of the anesthetized rat that are highly similar to natural, tactile-stimulus-evoked counterparts. Furthermore, information on both pressure and location of the touch stimulus was found to be highly preserved.

SIGNIFICANCE

Our results suggest that the currently presented stimulus optimization approach holds great promise for restoring naturalistic levels of sensation.

Empirical Bayesian significance measure of neuronal spike response

Background

Functional connectivity analyses of multiple neurons provide a powerful bottom-up approach to reveal functions of local neuronal circuits by using simultaneous recording of neuronal activity. A statistical methodology, generalized linear modeling (GLM) of the spike response function, is one of the most promising methodologies to reduce false link discoveries arising from pseudo-correlation based on common inputs. Although recent advancement of fluorescent imaging techniques has increased the number of simultaneously recoded neurons up to the hundreds or thousands, the amount of information per pair of neurons has not correspondingly increased, partly because of the instruments’ limitations, and partly because the number of neuron pairs increase in a quadratic manner. Consequently, the estimation of GLM suffers from large statistical uncertainty caused by the shortage in effective information.

Results

In this study, we propose a new combination of GLM and empirical Bayesian testing for the estimation of spike response functions that enables both conservative false discovery control and powerful functional connectivity detection. We compared our proposed method’s performance with those of sparse estimation of GLM and classical Granger causality testing. Our method achieved high detection performance of functional connectivity with conservative estimation of false discovery rate and q values in case of information shortage due to short observation time. We also showed that empirical Bayesian testing on arbitrary statistics in place of likelihood-ratio statistics reduce the computational cost without decreasing the detection performance. When our proposed method was applied to a functional multi-neuron calcium imaging dataset from the rat hippocampal region, we found significant functional connections that are possibly mediated by AMPA and NMDA receptors.

Conclusions

The proposed empirical Bayesian testing framework with GLM is promising especially when the amount of information per a neuron pair is small because of growing size of observed network.

Electronic supplementary material

The online version of this article (doi:10.1186/s12868-016-0255-x) contains supplementary material, which is available to authorized users.

Towards the design principles of neural population codes

The ability to record the joint activity of large groups of neurons would allow for direct study of information representation and computation at the level of whole circuits in the brain. The combinatorial space of potential population activity patterns and neural noise imply that it would be impossible to directly map the relations between stimuli and population responses. Understanding of large neural population codes therefore depends on identifying simplifying design principles. We review recent results showing that strongly correlated population codes can be explained using minimal models that rely on low order relations among cells. We discuss the implications for large populations, and how such models allow for mapping the semantic organization of the neural codebook and stimulus space, and decoding.

Estimation of Directed Effective Connectivity from fMRI Functional Connectivity Hints at Asymmetries of Cortical Connectome

The brain exhibits complex spatio-temporal patterns of activity. This phenomenon is governed by an interplay between the internal neural dynamics of cortical areas and their connectivity. Uncovering this complex relationship has raised much interest, both for theory and the interpretation of experimental data (e.g., fMRI recordings) using dynamical models. Here we focus on the so-called inverse problem: the inference of network parameters in a cortical model to reproduce empirically observed activity. Although it has received a lot of interest, recovering directed connectivity for large networks has been rather unsuccessful so far. The present study specifically addresses this point for a noise-diffusion network model. We develop a Lyapunov optimization that iteratively tunes the network connectivity in order to reproduce second-order moments of the node activity, or functional connectivity. We show theoretically and numerically that the use of covariances with both zero and non-zero time shifts is the key to infer directed connectivity. The first main theoretical finding is that an accurate estimation of the underlying network connectivity requires that the time shift for covariances is matched with the time constant of the dynamical system. In addition to the network connectivity, we also adjust the intrinsic noise received by each network node. The framework is applied to experimental fMRI data recorded for subjects at rest. Diffusion-weighted MRI data provide an estimate of anatomical connections, which is incorporated to constrain the cortical model. The empirical covariance structure is reproduced faithfully, especially its temporal component (i.e., time-shifted covariances) in addition to the spatial component that is usually the focus of studies. We find that the cortical interactions, referred to as effective connectivity, in the tuned model are not reciprocal. In particular, hubs are either receptors or feeders: they do not exhibit both strong incoming and outgoing connections. Our results sets a quantitative ground to explore the propagation of activity in the cortex.

The study of interactions between different cortical regions at rest or during a task has considerably developed in the past decades thanks to progress in non-invasive imaging techniques, such as fMRI, EEG and MEG. These techniques have revealed that distant cortical areas exhibit specific correlated activity during the resting state, also called functional connectivity (FC). Moreover, recent studies have highlighted the possible role of white-matter projections between cortical regions in shaping these activity patterns. This structural connectivity (SC) can be estimated using MRI, which measures the probability for two areas to be connected via the density of neural fibers. However, this does not provide the strengths of dynamical interactions. Many methods have thus been developed to estimate the connectivity between neural populations in the cortex that is hypothesized to shape FC. The strengths of these dynamical interactions are called effective connectivity (EC). We use a cortical model that combines information from Diffusion-weighted MRI (dwMRI) and fMRI in order to estimate EC. We demonstrate theoretically that directed C can be inferred using time-shifted covariances. The key point of our method is the use of temporal information from FC at the scale of the whole network. Applying our model on experimental fMRI data at rest, we estimate the asymmetry of intracortical connectivity. Obtaining an accurate EC estimate is essential to analyze its graph properties, such as hubs. In particular, directed connectivity links to the asymmetry between input and output EC strengths of each node, which characterizes feeder and receiver hubs in the cortical network.

Reconstruction of the input signal of the leaky integrate-and-fire neuronal model from its interspike intervals

Extracting the input signal of a neuron by analyzing its spike output is an important step toward understanding how external information is coded into discrete events of action potentials and how this information is exchanged between different neurons in the nervous system. Most of the existing methods analyze this decoding problem in a stochastic framework and use probabilistic metrics such as maximum-likelihood method to determine the parameters of the input signal assuming a leaky and integrate-and-fire (LIF) model. In this article, the input signal of the LIF model is considered as a combination of orthogonal basis functions. The coefficients of the basis functions are found by minimizing the norm of the observed spikes and those generated by the estimated signal. This approach gives rise to the deterministic reconstruction of the input signal and results in a simple matrix identity through which the coefficients of the basis functions and therefore the neuronal stimulus can be identified. The inherent noise of the neuron is considered as an additional factor in the membrane potential and is treated as the disturbance in the reconstruction algorithm. The performance of the proposed scheme is evaluated by numerical simulations, and it is shown that input signals with different characteristics can be well recovered by this algorithm.

Improving neural decoding in the central auditory system using bio-inspired spectro-temporal representations and a generalized bilinear model

We study the impact of different encoding models and spectro-temporal representations on the accuracy of Bayesian decoding of neural activity recorded from the central auditory system. Two encoding models, a generalized linear model (GLM) and a generalized bilinear model (GBM), are compared along with three different spectro-temporal representations of the input stimuli: a spectrogram and two bio-inspired representations, i.e. a gammatone filter bank (GFB) and a spikegram. Signal to noise ratios between the reconstructed and original representations are used to evaluate the decoding, or reconstruction accuracy. We experimentally show that the reconstruction accuracy is best with the spikegram representation and worst with the spectrogram representation and, furthermore, that using a GBM instead of a GLM significantly increases the reconstruction accuracy. In fact, our results show that the spikegram reconstruction accuracy with a GBM fitting yields an SNR that is 3.3 dB better than when using the standard decoding approach of reconstructing a spectrogram with GLM fitting.

Closed-loop and activity-guided optogenetic control

Advances in optical manipulation and observation of neural activity have set the stage for widespread implementation of closed-loop and activity-guided optical control of neural circuit dynamics. Closing the loop optogenetically (i.e., basing optogenetic stimulation on simultaneously observed dynamics in a principled way) is a powerful strategy for causal investigation of neural circuitry. In particular, observing and feeding back the effects of circuit interventions on physiologically relevant timescales is valuable for directly testing whether inferred models of dynamics, connectivity, and causation are accurate in vivo. Here we highlight technical and theoretical foundations as well as recent advances and opportunities in this area, and we review in detail the known caveats and limitations of optogenetic experimentation in the context of addressing these challenges with closed-loop optogenetic control in behaving animals.

Modulation depth estimation and variable selection in state-space models for neural interfaces

Rapid developments in neural interface technology are making it possible to record increasingly large signal sets of neural activity. Various factors such as asymmetrical information distribution and across-channel redundancy may, however, limit the benefit of high-dimensional signal sets, and the increased computational complexity may not yield corresponding improvement in system performance. High-dimensional system models may also lead to overfitting and lack of generalizability. To address these issues, we present a generalized modulation depth measure using the state-space framework that quantifies the tuning of a neural signal channel to relevant behavioral covariates. For a dynamical system, we develop computationally efficient procedures for estimating modulation depth from multivariate data. We show that this measure can be used to rank neural signals and select an optimal channel subset for inclusion in the neural decoding algorithm. We present a scheme for choosing the optimal subset based on model order selection criteria. We apply this method to neuronal ensemble spike-rate decoding in neural interfaces, using our framework to relate motor cortical activity with intended movement kinematics. With offline analysis of intracortical motor imagery data obtained from individuals with tetraplegia using the BrainGate neural interface, we demonstrate that our variable selection scheme is useful for identifying and ranking the most information-rich neural signals. We demonstrate that our approach offers several orders of magnitude lower complexity but virtually identical decoding performance compared to greedy search and other selection schemes. Our statistical analysis shows that the modulation depth of human motor cortical single-unit signals is well characterized by the generalized Pareto distribution. Our variable selection scheme has wide applicability in problems involving multisensor signal modeling and estimation in biomedical engineering systems.

Task-Independent Cognitive State Transition Detection From Cortical Neurons During 3-D Reach-to-Grasp Movements

Complex reach, grasp, and object manipulation tasks require sequential, temporal coordination of movements by neurons in the brain. Detecting cognitive state transitions associated with motor tasks from sequential neural data is pivotal in rehabilitation engineering. The cognitive state detectors proposed thus far rely on task-dependent (TD) models, i.e., the detection strategy exploits a priori knowledge of the movement tasks to determine the actual cognitive states, regardless of whether these cognitive states actually depend on the movement tasks or not. This approach, however, is not viable when the tasks are not known a priori (e.g., the subject performs many different tasks) or there is paucity of neural data for each task. Moreover, some cognitive states (e.g., holding) may be invariant to the movement tasks performed. Here we propose a real-time (online) task-independent (TI) framework to detect cognitive state transitions from spike trains and kinematic measurements. We constructed this detection framework using 452 single-unit neural spike recordings collected via multielectrode arrays in the premotor dorsal and ventral (PMd and PMv) cortical regions of two nonhuman primates performing 3-D multiobject reach-to-grasp tasks. We used the detection latency and accuracy of state transitions to measure the performance. We find that, in both online and offline detection modes: 1) TI models have significantly better performance than corresponding TD models when using neuronal data alone and 2) during movements, the addition of the kinematics history to the TI models further improves detection performance. These findings suggest that TI models may accurately detect cognitive state transitions. Our framework could pave the way for a TI control of neural prosthesis from cortical neurons.

Volterra dendritic stimulus processors and biophysical spike generators with intrinsic noise sources

We consider a class of neural circuit models with internal noise sources arising in sensory systems. The basic neuron model in these circuits consists of a dendritic stimulus processor (DSP) cascaded with a biophysical spike generator (BSG). The dendritic stimulus processor is modeled as a set of nonlinear operators that are assumed to have a Volterra series representation. Biophysical point neuron models, such as the Hodgkin-Huxley neuron, are used to model the spike generator. We address the question of how intrinsic noise sources affect the precision in encoding and decoding of sensory stimuli and the functional identification of its sensory circuits. We investigate two intrinsic noise sources arising (i) in the active dendritic trees underlying the DSPs, and (ii) in the ion channels of the BSGs. Noise in dendritic stimulus processing arises from a combined effect of variability in synaptic transmission and dendritic interactions. Channel noise arises in the BSGs due to the fluctuation of the number of the active ion channels. Using a stochastic differential equations formalism we show that encoding with a neuron model consisting of a nonlinear DSP cascaded with a BSG with intrinsic noise sources can be treated as generalized sampling with noisy measurements. For single-input multi-output neural circuit models with feedforward, feedback and cross-feedback DSPs cascaded with BSGs we theoretically analyze the effect of noise sources on stimulus decoding. Building on a key duality property, the effect of noise parameters on the precision of the functional identification of the complete neural circuit with DSP/BSG neuron models is given. We demonstrate through extensive simulations the effects of noise on encoding stimuli with circuits that include neuron models that are akin to those commonly seen in sensory systems, e.g., complex cells in V1.

Quantal Basis of Secretory Granule Biogenesis and Inventory Maintenance: the Surreptitious Nano-machine Behind It

Proteins are molecular machines with the capacity to perform diverse physical work as response to signals from the environment. Proteins may be found as monomers or polymers, two states that represent an important subset of protein interactions and generate considerable functional diversity, leading to regulatory mechanisms closely akin to decision-making in service systems. Polymerization is not unique to proteins. Other cell compartments (e.g. secretory granules) or tissue states (e.g. miniature end plate potential) are associated with polymerization of some sort, leading to information transport. This data-processing mechanism has similarities with (and led us to the investigation of) granule homotypic polymerization kinetics. Using information theory, we demonstrate the role played by the heterogeneity induced by polymerization: granule size distribution and the stealthy machine behind granule life cycle increase system entropy, which modulates the source/receiver potential that affects communication between the cell and its environment. The granule inventory management by the same nano-machine is discussed.

On Stationary Distributions of Stochastic Neural Networks

The paper deals with nonlinear Poisson neuron network models with bounded memory dynamics, which can include both Hebbian learning mechanisms and refractory periods. The state of the network is described by the times elapsed since its neurons fired within the post-synaptic transfer kernel memory span, and the current strengths of synaptic connections, the state spaces of our models being hierarchies of finite-dimensional components. We prove the ergodicity of the stochastic processes describing the behaviour of the networks, establish the existence of continuously differentiable stationary distribution densities (with respect to the Lebesgue measures of corresponding dimensionality) on the components of the state space, and find upper bounds for them. For the density components, we derive a system of differential equations that can be solved in a few simplest cases only. Approaches to approximate computation of the stationary density are discussed. One approach is to reduce the dimensionality of the problem by modifying the network so that each neuron cannot fire if the number of spikes it emitted within the post-synaptic transfer kernel memory span reaches a given threshold. We show that the stationary distribution of this ‘truncated’ network converges to that of the unrestricted network as the threshold increases, and that the convergence is at a superexponential rate. A complementary approach uses discrete Markov chain approximations to the network process.

On Stationary Distributions of Stochastic Neural Networks

The paper deals with nonlinear Poisson neuron network models with bounded memory dynamics, which can include both Hebbian learning mechanisms and refractory periods. The state of the network is described by the times elapsed since its neurons fired within the post-synaptic transfer kernel memory span, and the current strengths of synaptic connections, the state spaces of our models being hierarchies of finite-dimensional components. We prove the ergodicity of the stochastic processes describing the behaviour of the networks, establish the existence of continuously differentiable stationary distribution densities (with respect to the Lebesgue measures of corresponding dimensionality) on the components of the state space, and find upper bounds for them. For the density components, we derive a system of differential equations that can be solved in a few simplest cases only. Approaches to approximate computation of the stationary density are discussed. One approach is to reduce the dimensionality of the problem by modifying the network so that each neuron cannot fire if the number of spikes it emitted within the post-synaptic transfer kernel memory span reaches a given threshold. We show that the stationary distribution of this ‘truncated’ network converges to that of the unrestricted network as the threshold increases, and that the convergence is at a superexponential rate. A complementary approach uses discrete Markov chain approximations to the network process.

Likelihood Methods for Point Processes with Refractoriness

Likelihood-based encoding models founded on point processes have received significant attention in the literature because of their ability to reveal the information encoded by spiking neural populations. We propose an approximation to the likelihood of a point-process model of neurons that holds under assumptions about the continuous time process that are physiologically reasonable for neural spike trains: the presence of a refractory period, the predictability of the conditional intensity function, and its integrability. These are properties that apply to a large class of point processes arising in applications other than neuroscience. The proposed approach has several advantages over conventional ones. In particular, one can use standard fitting procedures for generalized linear models based on iteratively reweighted least squares while improving the accuracy of the approximation to the likelihood and reducing bias in the estimation of the parameters of the underlying continuous-time model. As a result, the proposed approach can use a larger bin size to achieve the same accuracy as conventional approaches would with a smaller bin size. This is particularly important when analyzing neural data with high mean and instantaneous firing rates. We demonstrate these claims on simulated and real neural spiking activity. By allowing a substantive increase in the required bin size, our algorithm has the potential to lower the barrier to the use of point-process methods in an increasing number of applications.

An overview of Bayesian methods for neural spike train analysis

Neural spike train analysis is an important task in computational neuroscience which aims to understand neural mechanisms and gain insights into neural circuits. With the advancement of multielectrode recording and imaging technologies, it has become increasingly demanding to develop statistical tools for analyzing large neuronal ensemble spike activity. Here we present a tutorial overview of Bayesian methods and their representative applications in neural spike train analysis, at both single neuron and population levels. On the theoretical side, we focus on various approximate Bayesian inference techniques as applied to latent state and parameter estimation. On the application side, the topics include spike sorting, tuning curve estimation, neural encoding and decoding, deconvolution of spike trains from calcium imaging signals, and inference of neuronal functional connectivity and synchrony. Some research challenges and opportunities for neural spike train analysis are discussed.

Motor circuit-specific burst patterns drive different muscle and behavior patterns

In the isolated CNS, different modulatory inputs can enable one motor network to generate multiple output patterns. Thus far, however, few studies have established whether different modulatory inputs also enable a defined network to drive distinct muscle and movement patterns in vivo, much as they enable these distinctions in behavioral studies. This possibility is not a foregone conclusion, because additional influences present in vivo (e.g., sensory feedback, hormonal modulation) could alter the motor patterns. Additionally, rhythmic neuronal activity can be transformed into sustained muscle contractions, particularly in systems with slow muscle dynamics, as in the crab (Cancer borealis) stomatogastric system used here. We assessed whether two different versions of the biphasic (protraction, retraction) gastric mill (chewing) rhythm, triggered in the isolated stomatogastric system by the modulatory ventral cardiac neurons (VCNs) and postoesophageal commissure (POC) neurons, drive different muscle and movement patterns. One distinction between these rhythms is that the lateral gastric (LG) protractor motor neuron generates tonic bursts during the VCN rhythm, whereas its POC-rhythm bursts are divided into fast, rhythmic burstlets. Intracellular muscle fiber recordings and tension measurements show that the LG-innervated muscles retain the distinct VCN-LG and POC-LG neuron burst structures. Moreover, endoscope video recordings in vivo, during VCN-triggered and POC-triggered chewing, show that the lateral teeth protraction movements exhibit the same, distinct protraction patterns generated by LG in the isolated nervous system. Thus, the multifunctional nature of an identified motor network in the isolated CNS can be preserved in vivo, where it drives different muscle activity and movement patterns.

Merits of random forests emerge in evaluation of chemometric classifiers by external validation

Real-world applications will inevitably entail divergence between samples on which chemometric classifiers are trained and the unknowns requiring classification. This has long been recognized, but there is a shortage of empirical studies on which classifiers perform best in 'external validation' (EV), where the unknown samples are subject to sources of variation relative to the population used to train the classifier. Survey of 286 classification studies in analytical chemistry found only 6.6% that stated elements of variance between training and test samples. Instead, most tested classifiers using hold-outs or resampling (usually cross-validation) from the same population used in training. The present study evaluated a wide range of classifiers on NMR and mass spectra of plant and food materials, from four projects with different data properties (e.g., different numbers and prevalence of classes) and classification objectives. Use of cross-validation was found to be optimistic relative to EV on samples of different provenance to the training set (e.g., different genotypes, different growth conditions, different seasons of crop harvest). For classifier evaluations across the diverse tasks, we used ranks-based non-parametric comparisons, and permutation-based significance tests. Although latent variable methods (e.g., PLSDA) were used in 64% of the surveyed papers, they were among the less successful classifiers in EV, and orthogonal signal correction was counterproductive. Instead, the best EV performances were obtained with machine learning schemes that coped with the high dimensionality (914-1898 features). Random forests confirmed their resilience to high dimensionality, as best overall performers on the full data, despite being used in only 4.5% of the surveyed papers. Most other machine learning classifiers were improved by a feature selection filter (ReliefF), but still did not out-perform random forests.

Transductive neural decoding for unsorted neuronal spikes of rat hippocampus

Neural decoding is an important approach for extracting information from population codes. We previously proposed a novel transductive neural decoding paradigm and applied it to reconstruct the rat's position during navigation based on unsorted rat hippocampal ensemble spiking activity. Here, we investigate several important technical issues of this new paradigm using one data set of one animal. Several extensions of our decoding method are discussed.

Intermediate intrinsic diversity enhances neural population coding

Cell-to-cell variability in molecular, genetic, and physiological features is increasingly recognized as a critical feature of complex biological systems, including the brain. Although such variability has potential advantages in robustness and reliability, how and why biological circuits assemble heterogeneous cells into functional groups is poorly understood. Here, we develop analytic approaches toward answering how neuron-level variation in intrinsic biophysical properties of olfactory bulb mitral cells influences population coding of fluctuating stimuli. We capture the intrinsic diversity of recorded populations of neurons through a statistical approach based on generalized linear models. These models are flexible enough to predict the diverse responses of individual neurons yet provide a common reference frame for comparing one neuron to the next. We then use Bayesian stimulus decoding to ask how effectively different populations of mitral cells, varying in their diversity, encode a common stimulus. We show that a key advantage provided by physiological levels of intrinsic diversity is more efficient and more robust encoding of stimuli by the population as a whole. However, we find that the populations that best encode stimulus features are not simply the most heterogeneous, but those that balance diversity with the benefits of neural similarity.