Beyond GLMs: a generative mixture modeling approach to neural system identification

Exact Analysis of the Subthreshold Variability for Conductance-Based Neuronal Models with Synchronous Synaptic Inputs

The spiking activity of neocortical neurons exhibits a striking level of variability, even when these networks are driven by identical stimuli. The approximately Poisson firing of neurons has led to the hypothesis that these neural networks operate in the asynchronous state. In the asynchronous state, neurons fire independently from one another, so that the probability that a neuron experience synchronous synaptic inputs is exceedingly low. While the models of asynchronous neurons lead to observed spiking variability, it is not clear whether the asynchronous state can also account for the level of subthreshold membrane potential variability. We propose a new analytical framework to rigorously quantify the subthreshold variability of a single conductance-based neuron in response to synaptic inputs with prescribed degrees of synchrony. Technically, we leverage the theory of exchangeability to model input synchrony via jump-process-based synaptic drives; we then perform a moment analysis of the stationary response of a neuronal model with all-or-none conductances that neglects postspiking reset. As a result, we produce exact, interpretable closed forms for the first two stationary moments of the membrane voltage, with explicit dependence on the input synaptic numbers, strengths, and synchrony. For biophysically relevant parameters, we find that the asynchronous regime yields realistic subthreshold variability (voltage variance ≃4-9 mV2) only when driven by a restricted number of large synapses, compatible with strong thalamic drive. By contrast, we find that achieving realistic subthreshold variability with dense cortico-cortical inputs requires including weak but nonzero input synchrony, consistent with measured pairwise spiking correlations. We also show that, without synchrony, the neural variability averages out to zero for all scaling limits with vanishing synaptic weights, independent of any balanced state hypothesis. This result challenges the theoretical basis for mean-field theories of the asynchronous state.

Exact analysis of the subthreshold variability for conductance-based neuronal models with synchronous synaptic inputs

The spiking activity of neocortical neurons exhibits a striking level of variability, even when these networks are driven by identical stimuli. The approximately Poisson firing of neurons has led to the hypothesis that these neural networks operate in the asynchronous state. In the asynchronous state neurons fire independently from one another, so that the probability that a neuron experience synchronous synaptic inputs is exceedingly low. While the models of asynchronous neurons lead to observed spiking variability, it is not clear whether the asynchronous state can also account for the level of subthreshold membrane potential variability. We propose a new analytical framework to rigorously quantify the subthreshold variability of a single conductance-based neuron in response to synaptic inputs with prescribed degrees of synchrony. Technically we leverage the theory of exchangeability to model input synchrony via jump-process-based synaptic drives; we then perform a moment analysis of the stationary response of a neuronal model with all-or-none conductances that neglects post-spiking reset. As a result, we produce exact, interpretable closed forms for the first two stationary moments of the membrane voltage, with explicit dependence on the input synaptic numbers, strengths, and synchrony. For biophysically relevant parameters, we find that the asynchronous regime only yields realistic subthreshold variability (voltage variance ≃ 4 - 9 m V 2 ) when driven by a restricted number of large synapses, compatible with strong thalamic drive. By contrast, we find that achieving realistic subthreshold variability with dense cortico-cortical inputs requires including weak but nonzero input synchrony, consistent with measured pairwise spiking correlations. We also show that without synchrony, the neural variability averages out to zero for all scaling limits with vanishing synaptic weights, independent of any balanced state hypothesis. This result challenges the theoretical basis for mean-field theories of the asynchronous state.

Exact analysis of the subthreshold variability for conductance-based neuronal models with synchronous synaptic inputs

The spiking activity of neocortical neurons exhibits a striking level of variability, even when these networks are driven by identical stimuli. The approximately Poisson firing of neurons has led to the hypothesis that these neural networks operate in the asynchronous state. In the asynchronous state neurons fire independently from one another, so that the probability that a neuron experience synchronous synaptic inputs is exceedingly low. While the models of asynchronous neurons lead to observed spiking variability, it is not clear whether the asynchronous state can also account for the level of subthreshold membrane potential variability. We propose a new analytical framework to rigorously quantify the subthreshold variability of a single conductance-based neuron in response to synaptic inputs with prescribed degrees of synchrony. Technically we leverage the theory of exchangeability to model input synchrony via jump-process-based synaptic drives; we then perform a moment analysis of the stationary response of a neuronal model with all-or-none conductances that neglects post-spiking reset. As a result, we produce exact, interpretable closed forms for the first two stationary moments of the membrane voltage, with explicit dependence on the input synaptic numbers, strengths, and synchrony. For biophysically relevant parameters, we find that the asynchronous regime only yields realistic subthreshold variability (voltage variance ≅ 4-9mV 2 ) when driven by a restricted number of large synapses, compatible with strong thalamic drive. By contrast, we find that achieving realistic subthreshold variability with dense cortico-cortical inputs requires including weak but nonzero input synchrony, consistent with measured pairwise spiking correlations. We also show that without synchrony, the neural variability averages out to zero for all scaling limits with vanishing synaptic weights, independent of any balanced state hypothesis. This result challenges the theoretical basis for mean-field theories of the asynchronous state.

Artificial intelligence techniques for retinal prostheses: a comprehensive review and future direction

Objective. Retinal prostheses are promising devices to restore vision for patients with severe age-related macular degeneration or retinitis pigmentosa disease. The visual processing mechanism embodied in retinal prostheses play an important role in the restoration effect. Its performance depends on our understanding of the retina's working mechanism and the evolvement of computer vision models. Recently, remarkable progress has been made in the field of processing algorithm for retinal prostheses where the new discovery of the retina's working principle and state-of-the-arts computer vision models are combined together.Approach. We investigated the related research on artificial intelligence techniques for retinal prostheses. The processing algorithm in these studies could be attributed to three types: computer vision-related methods, biophysical models, and deep learning models.Main results. In this review, we first illustrate the structure and function of the normal and degenerated retina, then demonstrate the vision rehabilitation mechanism of three representative retinal prostheses. It is necessary to summarize the computational frameworks abstracted from the normal retina. In addition, the development and feature of three types of different processing algorithms are summarized. Finally, we analyze the bottleneck in existing algorithms and propose our prospect about the future directions to improve the restoration effect.Significance. This review systematically summarizes existing processing models for predicting the response of the retina to external stimuli. What's more, the suggestions for future direction may inspire researchers in this field to design better algorithms for retinal prostheses.

Continuous, multidimensional coding of 3D complex tactile stimuli by primary sensory neurons of the vibrissal system

Across all sensory modalities, first-stage sensory neurons are an information bottleneck: they must convey all information available for an animal to perceive and act in its environment. Our understanding of coding properties of primary sensory neurons in the auditory and visual systems has been aided by the use of increasingly complex, naturalistic stimulus sets. By comparison, encoding properties of primary somatosensory afferents are poorly understood. Here, we use the rodent whisker system to examine how tactile information is represented in primary sensory neurons of the trigeminal ganglion (Vg). Vg neurons have long been thought to segregate into functional classes associated with separate streams of information processing. However, this view is based on Vg responses to restricted stimulus sets which potentially underreport the coding capabilities of these neurons. In contrast, the current study records Vg responses to complex three-dimensional (3D) stimulation while quantifying the complete 3D whisker shape and mechanics, thereby beginning to reveal their full representational capabilities. The results show that individual Vg neurons simultaneously represent multiple mechanical features of a stimulus, do not preferentially encode principal components of the stimuli, and represent continuous and tiled variations of all available mechanical information. These results directly contrast with proposed codes in which subpopulations of Vg neurons encode select stimulus features. Instead, individual Vg neurons likely overcome the information bottleneck by encoding large regions of a complex sensory space. This proposed tiled and multidimensional representation at the Vg directly constrains the computations performed by more central neurons of the vibrissotrigeminal pathway.

Functional analysis of information rates conveyed by rat whisker-related trigeminal nuclei neurons

The rat whisker system connects the tactile environment with the somatosensory thalamocortical system using only two synaptic stages. Encoding properties of the first stage, the primary afferents with somas in the trigeminal ganglion (TG), has been well studied, whereas much less is known from the second stage, the brainstem trigeminal nuclei (TN). The TN are a computational hub giving rise to parallel ascending tactile pathways and receiving feedback from many brain sites. We asked the question, whether encoding properties of TG neurons are kept by two trigeminal nuclei, the principalis (Pr5) and the spinalis interpolaris (Sp5i), respectively giving rise to two "lemniscal" and two "nonlemniscal" pathways. Single units were recorded in anesthetized rats while a single whisker was deflected on a band-limited white noise trajectory. Using information theoretic methods and spike-triggered mixture models (STM), we found that both nuclei encode the stimulus locally in time, i.e., stimulus features more than 10 ms in the past do not significantly influence spike generation. They further encode stimulus kinematics in multiple, distinct response fields, indicating encoding characteristics beyond previously described directional responses. Compared with TG, Pr5 and Sp5i gave rise to lower spike and information rates, but information rate per spike was on par with TG. Importantly, both brainstem nuclei were found to largely keep encoding properties of primary afferents, i.e. local encoding and kinematic response fields. The preservation of encoding properties in channels assumed to serve different functions seems surprising. We discuss the possibility that it might reflect specific constraints of frictional whisker contact with object surfaces.NEW & NOTEWORTHY We studied two trigeminal nuclei containing the second neuron on the tactile pathway of whisker-related tactile information in rats. We found that the subnuclei, traditionally assumed to give rise to functional tactile channels, nevertheless transfer primary afferent information with quite similar properties in terms of integration time and kinematic profile. We discuss whether such commonality may be due the requirement to adapt to physical constraints of frictional whisker contact.

Signal-to-signal neural networks for improved spike estimation from calcium imaging data

Spiking information of individual neurons is essential for functional and behavioral analysis in neuroscience research. Calcium imaging techniques are generally employed to obtain activities of neuronal populations. However, these techniques result in slowly-varying fluorescence signals with low temporal resolution. Estimating the temporal positions of the neuronal action potentials from these signals is a challenging problem. In the literature, several generative model-based and data-driven algorithms have been studied with varied levels of success. This article proposes a neural network-based signal-to-signal conversion approach, where it takes as input raw-fluorescence signal and learns to estimate the spike information in an end-to-end fashion. Theoretically, the proposed approach formulates the spike estimation as a single channel source separation problem with unknown mixing conditions. The source corresponding to the action potentials at a lower resolution is estimated at the output. Experimental studies on the spikefinder challenge dataset show that the proposed signal-to-signal conversion approach significantly outperforms state-of-the-art-methods in terms of Pearson's correlation coefficient, Spearman's rank correlation coefficient and yields comparable performance for the area under the receiver operating characteristics measure. We also show that the resulting system: (a) has low complexity with respect to existing supervised approaches and is reproducible; (b) is layer-wise interpretable, and (c) has the capability to generalize across different calcium indicators.

A Survey on Probabilistic Models in Human Perception and Machines

Extracting information from noisy signals is of fundamental importance for both biological and artificial perceptual systems. To provide tractable solutions to this challenge, the fields of human perception and machine signal processing (SP) have developed powerful computational models, including Bayesian probabilistic models. However, little true integration between these fields exists in their applications of the probabilistic models for solving analogous problems, such as noise reduction, signal enhancement, and source separation. In this mini review, we briefly introduce and compare selective applications of probabilistic models in machine SP and human psychophysics. We focus on audio and audio-visual processing, using examples of speech enhancement, automatic speech recognition, audio-visual cue integration, source separation, and causal inference to illustrate the basic principles of the probabilistic approach. Our goal is to identify commonalities between probabilistic models addressing brain processes and those aiming at building intelligent machines. These commonalities could constitute the closest points for interdisciplinary convergence.

Inference of nonlinear receptive field subunits with spike-triggered clustering

Responses of sensory neurons are often modeled using a weighted combination of rectified linear subunits. Since these subunits often cannot be measured directly, a flexible method is needed to infer their properties from the responses of downstream neurons. We present a method for maximum likelihood estimation of subunits by soft-clustering spike-triggered stimuli, and demonstrate its effectiveness in visual neurons. For parasol retinal ganglion cells in macaque retina, estimated subunits partitioned the receptive field into compact regions, likely representing aggregated bipolar cell inputs. Joint clustering revealed shared subunits between neighboring cells, producing a parsimonious population model. Closed-loop validation, using stimuli lying in the null space of the linear receptive field, revealed stronger nonlinearities in OFF cells than ON cells. Responses to natural images, jittered to emulate fixational eye movements, were accurately predicted by the subunit model. Finally, the generality of the approach was demonstrated in macaque V1 neurons.

Inferring synaptic inputs from spikes with a conductance-based neural encoding model

Descriptive statistical models of neural responses generally aim to characterize the mapping from stimuli to spike responses while ignoring biophysical details of the encoding process. Here, we introduce an alternative approach, the conductance-based encoding model (CBEM), which describes a mapping from stimuli to excitatory and inhibitory synaptic conductances governing the dynamics of sub-threshold membrane potential. Remarkably, we show that the CBEM can be fit to extracellular spike train data and then used to predict excitatory and inhibitory synaptic currents. We validate these predictions with intracellular recordings from macaque retinal ganglion cells. Moreover, we offer a novel quasi-biophysical interpretation of the Poisson generalized linear model (GLM) as a special case of the CBEM in which excitation and inhibition are perfectly balanced. This work forges a new link between statistical and biophysical models of neural encoding and sheds new light on the biophysical variables that underlie spiking in the early visual pathway.

Spike Estimation from Fluorescence Signals Using High-Resolution Property of Group Delay

Spike estimation from calcium (Ca²⁺) fluorescence signals is a fundamental and challenging problem in neuroscience. Several models and algorithms have been proposed for this task over the past decade. Nevertheless, it is still hard to achieve accurate spike positions from the Ca²⁺ fluorescence signals. While existing methods rely on data-driven methods and the physiology of neurons for modelling the spiking process, this work exploits the nature of the fluorescence responses to spikes using signal processing. We first motivate the problem by a novel analysis of the high-resolution property of minimum-phase group delay (GD) functions for multi-pole resonators. The resonators could be connected either in series or in parallel. The Ca²⁺ indicator responds to a spike with a sudden rise, that is followed by an exponential decay. We interpret the Ca²⁺ signal as the response of an impulse train to the change in Ca²⁺ concentration, where the Ca²⁺ response corresponds to a resonator. We perform minimum-phase group delay-based filtering of the Ca²⁺ signal for resolving spike locations. The performance of the proposed algorithm is evaluated on nine datasets spanning various indicators, sampling rates and, mouse brain regions. The proposed approach: GDspike, is compared with other spike estimation methods including MLspike, Vogelstein de-convolution algorithm, and data-driven Spike Triggered Mixture (STM) model. The performance of GDSpike is superior to that of the Vogelstein algorithm and is comparable to that of MLSpike. It can also be used to post-process the output of MLSpike, which further enhances the performance.

Multi-Input, Multi-Output Neuronal Mode Network Approach to Modeling the Encoding Dynamics and Functional Connectivity of Neural Systems

This letter proposes a novel method, multi-input, multi-output neuronal mode network (MIMO-NMN), for modeling encoding dynamics and functional connectivity in neural ensembles such as the hippocampus. Compared with conventional approaches such as the Volterra-Wiener model, linear-nonlinear-cascade (LNC) model, and generalized linear model (GLM), the NMN has several advantages in terms of estimation accuracy, model interpretation, and functional connectivity analysis. We point out the limitations of current neural spike modeling methods, especially the estimation biases caused by the imbalanced class problem when the number of zeros is significantly larger than ones in the spike data. We use synthetic data to test the performance of NMN with a comparison of the traditional methods, and the results indicate the NMN approach could reduce the imbalanced class problem and achieve better predictions. Subsequently, we apply the MIMO-NMN method to analyze data from the human hippocampus. The results indicate that the MIMO-NMN method is a promising approach to modeling neural dynamics and analyzing functional connectivity of multi-neuronal data.

Modern Machine Learning as a Benchmark for Fitting Neural Responses

Neuroscience has long focused on finding encoding models that effectively ask "what predicts neural spiking?" and generalized linear models (GLMs) are a typical approach. It is often unknown how much of explainable neural activity is captured, or missed, when fitting a model. Here we compared the predictive performance of simple models to three leading machine learning methods: feedforward neural networks, gradient boosted trees (using XGBoost), and stacked ensembles that combine the predictions of several methods. We predicted spike counts in macaque motor (M1) and somatosensory (S1) cortices from standard representations of reaching kinematics, and in rat hippocampal cells from open field location and orientation. Of these methods, XGBoost and the ensemble consistently produced more accurate spike rate predictions and were less sensitive to the preprocessing of features. These methods can thus be applied quickly to detect if feature sets relate to neural activity in a manner not captured by simpler methods. Encoding models built with a machine learning approach accurately predict spike rates and can offer meaningful benchmarks for simpler models.

Organization of sensory feature selectivity in the whisker system

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Neurons in the whisker system are selective to spatial and dynamical properties – features – of sensory stimuli.

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At each stage of the pathway, different neurons encode distinct features, generating a rich population representation.

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Whisker touch is robustly represented; neurons respond to touch-driven fast fluctuations in forces at the whisker base.

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Cortical neurons have more complex and context-dependent selectivity than subcortical, e.g., to collective whisker motion.

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Understanding how these signals are integrated to construct whisker-mediated percepts requires further research.

Our sensory receptors are faced with an onslaught of different environmental inputs. Each sensory event or encounter with an object involves a distinct combination of physical energy sources impinging upon receptors. In the rodent whisker system, each primary afferent neuron located in the trigeminal ganglion innervates and responds to a single whisker and encodes a distinct set of physical stimulus properties – features – corresponding to changes in whisker angle and shape and the consequent forces acting on the whisker follicle. Here we review the nature of the features encoded by successive stages of processing along the whisker pathway. At each stage different neurons respond to distinct features, such that the population as a whole represents diverse properties. Different neuronal types also have distinct feature selectivity. Thus, neurons at the same stage of processing and responding to the same whisker nevertheless play different roles in representing objects contacted by the whisker. This diversity, combined with the precise timing and high reliability of responses, enables populations at each stage to represent a wide range of stimuli. Cortical neurons respond to more complex stimulus properties – such as correlated motion across whiskers – than those at early subcortical stages. Temporal integration along the pathway is comparatively weak: neurons up to barrel cortex (BC) are sensitive mainly to fast (tens of milliseconds) fluctuations in whisker motion. The topographic organization of whisker sensitivity is paralleled by systematic organization of neuronal selectivity to certain other physical features, but selectivity to touch and to dynamic stimulus properties is distributed in “salt-and-pepper” fashion.

Benchmarking Spike Rate Inference in Population Calcium Imaging

A fundamental challenge in calcium imaging has been to infer spike rates of neurons from the measured noisy fluorescence traces. We systematically evaluate different spike inference algorithms on a large benchmark dataset (>100,000 spikes) recorded from varying neural tissue (V1 and retina) using different calcium indicators (OGB-1 and GCaMP6). In addition, we introduce a new algorithm based on supervised learning in flexible probabilistic models and find that it performs better than other published techniques. Importantly, it outperforms other algorithms even when applied to entirely new datasets for which no simultaneously recorded data is available. Future data acquired in new experimental conditions can be used to further improve the spike prediction accuracy and generalization performance of the model. Finally, we show that comparing algorithms on artificial data is not informative about performance on real data, suggesting that benchmarking different methods with real-world datasets may greatly facilitate future algorithmic developments in neuroscience.

Inference of neuronal functional circuitry with spike-triggered non-negative matrix factorization

Neurons in sensory systems often pool inputs over arrays of presynaptic cells, giving rise to functional subunits inside a neuron’s receptive field. The organization of these subunits provides a signature of the neuron’s presynaptic functional connectivity and determines how the neuron integrates sensory stimuli. Here we introduce the method of spike-triggered non-negative matrix factorization for detecting the layout of subunits within a neuron’s receptive field. The method only requires the neuron’s spiking responses under finely structured sensory stimulation and is therefore applicable to large populations of simultaneously recorded neurons. Applied to recordings from ganglion cells in the salamander retina, the method retrieves the receptive fields of presynaptic bipolar cells, as verified by simultaneous bipolar and ganglion cell recordings. The identified subunit layouts allow improved predictions of ganglion cell responses to natural stimuli and reveal shared bipolar cell input into distinct types of ganglion cells.

How a neuron integrates sensory information requires knowledge about its functional presynaptic connections. Here the authors report a new method using non-negative matrix factorization to identify the layout of presynaptic bipolar cell inputs onto retinal ganglion cells and predict their responses to natural stimuli.

Artificial spatiotemporal touch inputs reveal complementary decoding in neocortical neurons

Investigations of the mechanisms of touch perception and decoding has been hampered by difficulties in achieving invariant patterns of skin sensor activation. To obtain reproducible spatiotemporal patterns of activation of sensory afferents, we used an artificial fingertip equipped with an array of neuromorphic sensors. The artificial fingertip was used to transduce real-world haptic stimuli into spatiotemporal patterns of spikes. These spike patterns were delivered to the skin afferents of the second digit of rats via an array of stimulation electrodes. Combined with low-noise intra- and extracellular recordings from neocortical neurons in vivo, this approach provided a previously inaccessible high resolution analysis of the representation of tactile information in the neocortical neuronal circuitry. The results indicate high information content in individual neurons and reveal multiple novel neuronal tactile coding features such as heterogeneous and complementary spatiotemporal input selectivity also between neighboring neurons. Such neuronal heterogeneity and complementariness can potentially support a very high decoding capacity in a limited population of neurons. Our results also indicate a potential neuroprosthetic approach to communicate with the brain at a very high resolution and provide a potential novel solution for evaluating the degree or state of neurological disease in animal models.

Models of Neuronal Stimulus-Response Functions: Elaboration, Estimation, and Evaluation

Rich, dynamic, and dense sensory stimuli are encoded within the nervous system by the time-varying activity of many individual neurons. A fundamental approach to understanding the nature of the encoded representation is to characterize the function that relates the moment-by-moment firing of a neuron to the recent history of a complex sensory input. This review provides a unifying and critical survey of the techniques that have been brought to bear on this effort thus far—ranging from the classical linear receptive field model to modern approaches incorporating normalization and other nonlinearities. We address separately the structure of the models; the criteria and algorithms used to identify the model parameters; and the role of regularizing terms or “priors.” In each case we consider benefits or drawbacks of various proposals, providing examples for when these methods work and when they may fail. Emphasis is placed on key concepts rather than mathematical details, so as to make the discussion accessible to readers from outside the field. Finally, we review ways in which the agreement between an assumed model and the neuron's response may be quantified. Re-implemented and unified code for many of the methods are made freely available.

A Novel Nonparametric Approach for Neural Encoding and Decoding Models of Multimodal Receptive Fields

Pyramidal neurons recorded from the rat hippocampus and entorhinal cortex, such as place and grid cells, have diverse receptive fields, which are either unimodal or multimodal. Spiking activity from these cells encodes information about the spatial position of a freely foraging rat. At fine timescales, a neuron's spike activity also depends significantly on its own spike history. However, due to limitations of current parametric modeling approaches, it remains a challenge to estimate complex, multimodal neuronal receptive fields while incorporating spike history dependence. Furthermore, efforts to decode the rat's trajectory in one- or two-dimensional space from hippocampal ensemble spiking activity have mainly focused on spike history-independent neuronal encoding models. In this letter, we address these two important issues by extending a recently introduced nonparametric neural encoding framework that allows modeling both complex spatial receptive fields and spike history dependencies. Using this extended nonparametric approach, we develop novel algorithms for decoding a rat's trajectory based on recordings of hippocampal place cells and entorhinal grid cells. Results show that both encoding and decoding models derived from our new method performed significantly better than state-of-the-art encoding and decoding models on 6 minutes of test data. In addition, our model's performance remains invariant to the apparent modality of the neuron's receptive field.

The Essential Complexity of Auditory Receptive Fields

Encoding properties of sensory neurons are commonly modeled using linear finite impulse response (FIR) filters. For the auditory system, the FIR filter is instantiated in the spectro-temporal receptive field (STRF), often in the framework of the generalized linear model. Despite widespread use of the FIR STRF, numerous formulations for linear filters are possible that require many fewer parameters, potentially permitting more efficient and accurate model estimates. To explore these alternative STRF architectures, we recorded single-unit neural activity from auditory cortex of awake ferrets during presentation of natural sound stimuli. We compared performance of > 1000 linear STRF architectures, evaluating their ability to predict neural responses to a novel natural stimulus. Many were able to outperform the FIR filter. Two basic constraints on the architecture lead to the improved performance: (1) factorization of the STRF matrix into a small number of spectral and temporal filters and (2) low-dimensional parameterization of the factorized filters. The best parameterized model was able to outperform the full FIR filter in both primary and secondary auditory cortex, despite requiring fewer than 30 parameters, about 10% of the number required by the FIR filter. After accounting for noise from finite data sampling, these STRFs were able to explain an average of 40% of A1 response variance. The simpler models permitted more straightforward interpretation of sensory tuning properties. They also showed greater benefit from incorporating nonlinear terms, such as short term plasticity, that provide theoretical advances over the linear model. Architectures that minimize parameter count while maintaining maximum predictive power provide insight into the essential degrees of freedom governing auditory cortical function. They also maximize statistical power available for characterizing additional nonlinear properties that limit current auditory models.

Understanding how the brain solves sensory problems can provide useful insight for the development of automated systems such as speech recognizers and image classifiers. Recent developments in nonlinear regression and machine learning have produced powerful algorithms for characterizing the input-output relationship of complex systems. However, the complexity of sensory neural systems, combined with practical limitations on experimental data, make it difficult to apply arbitrarily complex analyses to neural data. In this study we pushed analysis in the opposite direction, toward simpler models. We asked how simple a model can be while still capturing the essential sensory properties of neurons in auditory cortex. We found that substantially simpler formulations of the widely-used spectro-temporal receptive field are able to perform as well as the best current models. These simpler formulations define new basis sets that can be incorporated into state-of-the-art machine learning algorithms for a more exhaustive exploration of sensory processing.

The equivalence of information-theoretic and likelihood-based methods for neural dimensionality reduction

Stimulus dimensionality-reduction methods in neuroscience seek to identify a low-dimensional space of stimulus features that affect a neuron's probability of spiking. One popular method, known as maximally informative dimensions (MID), uses an information-theoretic quantity known as "single-spike information" to identify this space. Here we examine MID from a model-based perspective. We show that MID is a maximum-likelihood estimator for the parameters of a linear-nonlinear-Poisson (LNP) model, and that the empirical single-spike information corresponds to the normalized log-likelihood under a Poisson model. This equivalence implies that MID does not necessarily find maximally informative stimulus dimensions when spiking is not well described as Poisson. We provide several examples to illustrate this shortcoming, and derive a lower bound on the information lost when spiking is Bernoulli in discrete time bins. To overcome this limitation, we introduce model-based dimensionality reduction methods for neurons with non-Poisson firing statistics, and show that they can be framed equivalently in likelihood-based or information-theoretic terms. Finally, we show how to overcome practical limitations on the number of stimulus dimensions that MID can estimate by constraining the form of the non-parametric nonlinearity in an LNP model. We illustrate these methods with simulations and data from primate visual cortex.

Circuit motifs for contrast-adaptive differentiation in early sensory systems: the role of presynaptic inhibition and short-term plasticity

In natural signals, such as the luminance value across of a visual scene, abrupt changes in intensity value are often more relevant to an organism than intensity values at other positions and times. Thus to reduce redundancy, sensory systems are specialized to detect the times and amplitudes of informative abrupt changes in the input stream rather than coding the intensity values at all times. In theory, a system that responds transiently to fast changes is called a differentiator. In principle, several different neural circuit mechanisms exist that are capable of responding transiently to abrupt input changes. However, it is unclear which circuit would be best suited for early sensory systems, where the dynamic range of the natural input signals can be very wide. We here compare the properties of different simple neural circuit motifs for implementing signal differentiation. We found that a circuit motif based on presynaptic inhibition (PI) is unique in a sense that the vesicle resources in the presynaptic site can be stably maintained over a wide range of stimulus intensities, making PI a biophysically plausible mechanism to implement a differentiator with a very wide dynamical range. Moreover, by additionally considering short-term plasticity (STP), differentiation becomes contrast adaptive in the PI-circuit but not in other potential neural circuit motifs. Numerical simulations show that the behavior of the adaptive PI-circuit is consistent with experimental observations suggesting that adaptive presynaptic inhibition might be a good candidate neural mechanism to achieve differentiation in early sensory systems.

Dynamic alignment models for neural coding

Recently, there have been remarkable advances in modeling the relationships between the sensory environment, neuronal responses, and behavior. However, most models cannot encompass variable stimulus-response relationships such as varying response latencies and state or context dependence of the neural code. Here, we consider response modeling as a dynamic alignment problem and model stimulus and response jointly by a mixed pair hidden Markov model (MPH). In MPHs, multiple stimulus-response relationships (e.g., receptive fields) are represented by different states or groups of states in a Markov chain. Each stimulus-response relationship features temporal flexibility, allowing modeling of variable response latencies, including noisy ones. We derive algorithms for learning of MPH parameters and for inference of spike response probabilities. We show that some linear-nonlinear Poisson cascade (LNP) models are a special case of MPHs. We demonstrate the efficiency and usefulness of MPHs in simulations of both jittered and switching spike responses to white noise and natural stimuli. Furthermore, we apply MPHs to extracellular single and multi-unit data recorded in cortical brain areas of singing birds to showcase a novel method for estimating response lag distributions. MPHs allow simultaneous estimation of receptive fields, latency statistics, and hidden state dynamics and so can help to uncover complex stimulus response relationships that are subject to variable timing and involve diverse neural codes.

The brain computes using electrical discharges of nerve cells, so called spikes. Specific sensory stimuli, for instance, tones, often lead to specific spiking patterns. The same is true for behavior: specific motor actions are generated by specific spiking patterns. The relationship between neural activity and stimuli or motor actions can be difficult to infer, because of dynamic dependencies and hidden nonlinearities. For instance, in a freely behaving animal a neuron could exhibit variable levels of sensory and motor involvements depending on the state of the animal and on current motor plans—a situation that cannot be accounted for by many existing models. Here we present a new type of model that is specifically designed to cope with such changing regularities. We outline the mathematical framework and show, through computer simulations and application to recorded neural data, how MPHs can advance our understanding of stimulus-response relationships.

Algorithms of whisker-mediated touch perception

Comparison of the functional organization of sensory modalities can reveal the specialized mechanisms unique to each modality as well as processing algorithms that are common across modalities. Here we examine the rodent whisker system. The whisker's mechanical properties shape the forces transmitted to specialized receptors. The sensory and motor systems are intimately interconnected, giving rise to two forms of sensation: generative and receptive. The sensory pathway is a test bed for fundamental concepts in computation and coding: hierarchical feature detection, sparseness, adaptive representations, and population coding. The central processing of signals can be considered a sequence of filters. At the level of cortex, neurons represent object features by a coordinated population code which encompasses cells with heterogeneous properties.

Functional analysis of ultra high information rates conveyed by rat vibrissal primary afferents

Sensory receptors determine the type and the quantity of information available for perception. Here, we quantified and characterized the information transferred by primary afferents in the rat whisker system using neural system identification. Quantification of "how much" information is conveyed by primary afferents, using the direct method (DM), a classical information theoretic tool, revealed that primary afferents transfer huge amounts of information (up to 529 bits/s). Information theoretic analysis of instantaneous spike-triggered kinematic stimulus features was used to gain functional insight on "what" is coded by primary afferents. Amongst the kinematic variables tested--position, velocity, and acceleration--primary afferent spikes encoded velocity best. The other two variables contributed to information transfer, but only if combined with velocity. We further revealed three additional characteristics that play a role in information transfer by primary afferents. Firstly, primary afferent spikes show preference for well separated multiple stimuli (i.e., well separated sets of combinations of the three instantaneous kinematic variables). Secondly, neurons are sensitive to short strips of the stimulus trajectory (up to 10 ms pre-spike time), and thirdly, they show spike patterns (precise doublet and triplet spiking). In order to deal with these complexities, we used a flexible probabilistic neuron model fitting mixtures of Gaussians to the spike triggered stimulus distributions, which quantitatively captured the contribution of the mentioned features and allowed us to achieve a full functional analysis of the total information rate indicated by the DM. We found that instantaneous position, velocity, and acceleration explained about 50% of the total information rate. Adding a 10 ms pre-spike interval of stimulus trajectory achieved 80-90%. The final 10-20% were found to be due to non-linear coding by spike bursts.