Event detection and classification from multimodal time series with application to neural data

The detection of events in time-series data is a common signal-processing problem. When the data can be modeled as a known template signal with an unknown delay in Gaussian noise, detection of the template signal can be done with a traditional matched filter. However, in many applications, the event of interest is represented in multimodal data consisting of both Gaussian and point-process time series. Neuroscience experiments, for example, can simultaneously record multimodal neural signals such as local field potentials (LFPs), which can be modeled as Gaussian, and neuronal spikes, which can be modeled as point processes. Currently, no method exists for event detection from such multimodal data, and as such our objective in this work is to develop a method to meet this need. Here we address this challenge by developing the multimodal event detector (MED) algorithm which simultaneously estimates event times and classes. To do this, we write a multimodal likelihood function for Gaussian and point-process observations and derive the associated maximum likelihood estimator of simultaneous event times and classes. We additionally introduce a cross-modal scaling parameter to account for model mismatch in real datasets. We validate this method in extensive simulations as well as in a neural spike-LFP dataset recorded during an eye-movement task, where the events of interest are eye movements with unknown times and directions. We show that the MED can successfully detect eye movement onset and classify eye movement direction. Further, the MED successfully combines information across data modalities, with multimodal performance exceeding unimodal performance. This method can facilitate applications such as the discovery of latent events in multimodal neural population activity and the development of brain-computer interfaces for naturalistic settings without constrained tasks or prior knowledge of event times.

Multimodal subspace identification for modeling discrete-continuous spiking and field potential population activity

Objective.Learning dynamical latent state models for multimodal spiking and field potential activity can reveal their collective low-dimensional dynamics and enable better decoding of behavior through multimodal fusion. Toward this goal, developing unsupervised learning methods that are computationally efficient is important, especially for real-time learning applications such as brain-machine interfaces (BMIs). However, efficient learning remains elusive for multimodal spike-field data due to their heterogeneous discrete-continuous distributions and different timescales.Approach.Here, we develop a multiscale subspace identification (multiscale SID) algorithm that enables computationally efficient learning for modeling and dimensionality reduction for multimodal discrete-continuous spike-field data. We describe the spike-field activity as combined Poisson and Gaussian observations, for which we derive a new analytical SID method. Importantly, we also introduce a novel constrained optimization approach to learn valid noise statistics, which is critical for multimodal statistical inference of the latent state, neural activity, and behavior. We validate the method using numerical simulations and with spiking and local field potential population activity recorded during a naturalistic reach and grasp behavior.Main results.We find that multiscale SID accurately learned dynamical models of spike-field signals and extracted low-dimensional dynamics from these multimodal signals. Further, it fused multimodal information, thus better identifying the dynamical modes and predicting behavior compared to using a single modality. Finally, compared to existing multiscale expectation-maximization learning for Poisson-Gaussian observations, multiscale SID had a much lower training time while being better in identifying the dynamical modes and having a better or similar accuracy in predicting neural activity and behavior.Significance.Overall, multiscale SID is an accurate learning method that is particularly beneficial when efficient learning is of interest, such as for online adaptive BMIs to track non-stationary dynamics or for reducing offline training time in neuroscience investigations.

Modeling and dissociation of intrinsic and input-driven neural population dynamics underlying behavior

Neural dynamics can reflect intrinsic dynamics or dynamic inputs, such as sensory inputs or inputs from other brain regions. To avoid misinterpreting temporally structured inputs as intrinsic dynamics, dynamical models of neural activity should account for measured inputs. However, incorporating measured inputs remains elusive in joint dynamical modeling of neural-behavioral data, which is important for studying neural computations of behavior. We first show how training dynamical models of neural activity while considering behavior but not input or input but not behavior may lead to misinterpretations. We then develop an analytical learning method for linear dynamical models that simultaneously accounts for neural activity, behavior, and measured inputs. The method provides the capability to prioritize the learning of intrinsic behaviorally relevant neural dynamics and dissociate them from both other intrinsic dynamics and measured input dynamics. In data from a simulated brain with fixed intrinsic dynamics that performs different tasks, the method correctly finds the same intrinsic dynamics regardless of the task while other methods can be influenced by the task. In neural datasets from three subjects performing two different motor tasks with task instruction sensory inputs, the method reveals low-dimensional intrinsic neural dynamics that are missed by other methods and are more predictive of behavior and/or neural activity. The method also uniquely finds that the intrinsic behaviorally relevant neural dynamics are largely similar across the different subjects and tasks, whereas the overall neural dynamics are not. These input-driven dynamical models of neural-behavioral data can uncover intrinsic dynamics that may otherwise be missed.

Dynamical flexible inference of nonlinear latent factors and structures in neural population activity

Modelling the spatiotemporal dynamics in the activity of neural populations while also enabling their flexible inference is hindered by the complexity and noisiness of neural observations. Here we show that the lower-dimensional nonlinear latent factors and latent structures can be computationally modelled in a manner that allows for flexible inference causally, non-causally and in the presence of missing neural observations. To enable flexible inference, we developed a neural network that separates the model into jointly trained manifold and dynamic latent factors such that nonlinearity is captured through the manifold factors and the dynamics can be modelled in tractable linear form on this nonlinear manifold. We show that the model, which we named 'DFINE' (for 'dynamical flexible inference for nonlinear embeddings') achieves flexible inference in simulations of nonlinear dynamics and across neural datasets representing a diversity of brain regions and behaviours. Compared with earlier neural-network models, DFINE enables flexible inference, better predicts neural activity and behaviour, and better captures the latent neural manifold structure. DFINE may advance the development of neurotechnology and investigations in neuroscience.

Unsupervised learning of stationary and switching dynamical system models from Poisson observations

Objective. Investigating neural population dynamics underlying behavior requires learning accurate models of the recorded spiking activity, which can be modeled with a Poisson observation distribution. Switching dynamical system models can offer both explanatory power and interpretability by piecing together successive regimes of simpler dynamics to capture more complex ones. However, in many cases, reliable regime labels are not available, thus demanding accurate unsupervised learning methods for Poisson observations. Existing learning methods, however, rely on inference of latent states in neural activity using the Laplace approximation, which may not capture the broader properties of densities and may lead to inaccurate learning. Thus, there is a need for new inference methods that can enable accurate model learning.Approach. To achieve accurate model learning, we derive a novel inference method based on deterministic sampling for Poisson observations called the Poisson Cubature Filter (PCF) and embed it in an unsupervised learning framework. This method takes a minimum mean squared error approach to estimation. Terms that are difficult to find analytically for Poisson observations are approximated in a novel way with deterministic sampling based on numerical integration and cubature rules.Main results. PCF enabled accurate unsupervised learning in both stationary and switching dynamical systems and largely outperformed prior Laplace approximation-based learning methods in both simulations and motor cortical spiking data recorded during a reaching task. These improvements were larger for smaller data sizes, showing that PCF-based learning was more data efficient and enabled more reliable regime identification. In experimental data and unsupervised with respect to behavior, PCF-based learning uncovered interpretable behavior-relevant regimes unlike prior learning methods.Significance. The developed unsupervised learning methods for switching dynamical systems can accurately uncover latent regimes and states in population spiking activity, with important applications in both basic neuroscience and neurotechnology.

Multimodal subspace identification for modeling discrete-continuous spiking and field potential population activity

Learning dynamical latent state models for multimodal spiking and field potential activity can reveal their collective low-dimensional dynamics and enable better decoding of behavior through multimodal fusion. Toward this goal, developing unsupervised learning methods that are computationally efficient is important, especially for real-time learning applications such as brain-machine interfaces (BMIs). However, efficient learning remains elusive for multimodal spike-field data due to their heterogeneous discrete-continuous distributions and different timescales. Here, we develop a multiscale subspace identification (multiscale SID) algorithm that enables computationally efficient modeling and dimensionality reduction for multimodal discrete-continuous spike-field data. We describe the spike-field activity as combined Poisson and Gaussian observations, for which we derive a new analytical subspace identification method. Importantly, we also introduce a novel constrained optimization approach to learn valid noise statistics, which is critical for multimodal statistical inference of the latent state, neural activity, and behavior. We validate the method using numerical simulations and spike-LFP population activity recorded during a naturalistic reach and grasp behavior. We find that multiscale SID accurately learned dynamical models of spike-field signals and extracted low-dimensional dynamics from these multimodal signals. Further, it fused multimodal information, thus better identifying the dynamical modes and predicting behavior compared to using a single modality. Finally, compared to existing multiscale expectation-maximization learning for Poisson-Gaussian observations, multiscale SID had a much lower computational cost while being better in identifying the dynamical modes and having a better or similar accuracy in predicting neural activity. Overall, multiscale SID is an accurate learning method that is particularly beneficial when efficient learning is of interest.

Dynamical flexible inference of nonlinear latent structures in neural population activity

Inferring complex spatiotemporal dynamics in neural population activity is critical for investigating neural mechanisms and developing neurotechnology. These activity patterns are noisy observations of lower-dimensional latent factors and their nonlinear dynamical structure. A major unaddressed challenge is to model this nonlinear structure, but in a manner that allows for flexible inference, whether causally, non-causally, or in the presence of missing neural observations. We address this challenge by developing DFINE, a new neural network that separates the model into dynamic and manifold latent factors, such that the dynamics can be modeled in tractable form. We show that DFINE achieves flexible nonlinear inference across diverse behaviors and brain regions. Further, despite enabling flexible inference unlike prior neural network models of population activity, DFINE also better predicts the behavior and neural activity, and better captures the latent neural manifold structure. DFINE can both enhance future neurotechnology and facilitate investigations across diverse domains of neuroscience.

Modeling and dissociation of intrinsic and input-driven neural population dynamics underlying behavior

Neural dynamics can reflect intrinsic dynamics or dynamic inputs, such as sensory inputs or inputs from other regions. To avoid misinterpreting temporally-structured inputs as intrinsic dynamics, dynamical models of neural activity should account for measured inputs. However, incorporating measured inputs remains elusive in joint dynamical modeling of neural-behavioral data, which is important for studying neural computations of a specific behavior. We first show how training dynamical models of neural activity while considering behavior but not input, or input but not behavior may lead to misinterpretations. We then develop a novel analytical learning method that simultaneously accounts for neural activity, behavior, and measured inputs. The method provides the new capability to prioritize the learning of intrinsic behaviorally relevant neural dynamics and dissociate them from both other intrinsic dynamics and measured input dynamics. In data from a simulated brain with fixed intrinsic dynamics that performs different tasks, the method correctly finds the same intrinsic dynamics regardless of task while other methods can be influenced by the change in task. In neural datasets from three subjects performing two different motor tasks with task instruction sensory inputs, the method reveals low-dimensional intrinsic neural dynamics that are missed by other methods and are more predictive of behavior and/or neural activity. The method also uniquely finds that the intrinsic behaviorally relevant neural dynamics are largely similar across the three subjects and two tasks whereas the overall neural dynamics are not. These input-driven dynamical models of neural-behavioral data can uncover intrinsic dynamics that may otherwise be missed.

Modeling and inference methods for switching regime-dependent dynamical systems with multiscale neural observations

Objective.Realizing neurotechnologies that enable long-term neural recordings across multiple spatial-temporal scales during naturalistic behaviors requires new modeling and inference methods that can simultaneously address two challenges. First, the methods should aggregate information across all activity scales from multiple recording sources such as spiking and field potentials. Second, the methods should detect changes in the regimes of behavior and/or neural dynamics during naturalistic scenarios and long-term recordings. Prior regime detection methods are developed for a single scale of activity rather than multiscale activity, and prior multiscale methods have not considered regime switching and are for stationary cases.Approach.Here, we address both challenges by developing a switching multiscale dynamical system model and the associated filtering and smoothing methods. This model describes the encoding of an unobserved brain state in multiscale spike-field activity. It also allows for regime-switching dynamics using an unobserved regime state that dictates the dynamical and encoding parameters at every time-step. We also design the associated switching multiscale inference methods that estimate both the unobserved regime and brain states from simultaneous spike-field activity.Main results.We validate the methods in both extensive numerical simulations and prefrontal spike-field data recorded in a monkey performing saccades for fluid rewards. We show that these methods can successfully combine the spiking and field potential observations to simultaneously track the regime and brain states accurately. Doing so, these methods lead to better state estimation compared with single-scale switching methods or stationary multiscale methods. Also, for single-scale linear Gaussian observations, the new switching smoother can better generalize to diverse system settings compared to prior switching smoothers.Significance.These modeling and inference methods effectively incorporate both regime-detection and multiscale observations. As such, they could facilitate investigation of latent switching neural population dynamics and improve future brain-machine interfaces by enabling inference in naturalistic scenarios where regime-dependent multiscale activity and behavior arise.

Modeling multiscale causal interactions between spiking and field potential signals during behavior

Objective. Brain recordings exhibit dynamics at multiple spatiotemporal scales, which are measured with spike trains and larger-scale field potential signals. To study neural processes, it is important to identify and model causal interactions not only at a single scale of activity, but also across multiple scales, i.e. between spike trains and field potential signals. Standard causality measures are not directly applicable here because spike trains are binary-valued but field potentials are continuous-valued. It is thus important to develop computational tools to recover multiscale neural causality during behavior, assess their performance on neural datasets, and study whether modeling multiscale causalities can improve the prediction of neural signals beyond what is possible with single-scale causality. Approach. We design a multiscale model-based Granger-like causality method based on directed information and evaluate its success both in realistic biophysical spike-field simulations and in motor cortical datasets from two non-human primates (NHP) performing a motor behavior. To compute multiscale causality, we learn point-process generalized linear models that predict the spike events at a given time based on the history of both spike trains and field potential signals. We also learn linear Gaussian models that predict the field potential signals at a given time based on their own history as well as either the history of binary spike events or that of latent firing rates. Main results. We find that our method reveals the true multiscale causality network structure in biophysical simulations despite the presence of model mismatch. Further, models with the identified multiscale causalities in the NHP neural datasets lead to better prediction of both spike trains and field potential signals compared to just modeling single-scale causalities. Finally, we find that latent firing rates are better predictors of field potential signals compared with the binary spike events in the NHP datasets. Significance. This multiscale causality method can reveal the directed functional interactions across spatiotemporal scales of brain activity to inform basic science investigations and neurotechnologies.

Multi-scale neural decoding and analysis

Objective.

Complex spatiotemporal neural activity encodes rich information related to behavior and cognition. Conventional research has focused on neural activity acquired using one of many different measurement modalities, each of which provides useful but incomplete assessment of the neural code. Multi-modal techniques can overcome tradeoffs in the spatial and temporal resolution of a single modality to reveal deeper and more comprehensive understanding of system-level neural mechanisms. Uncovering multi-scale dynamics is essential for a mechanistic understanding of brain function and for harnessing neuroscientific insights to develop more effective clinical treatment.

Approach.

We discuss conventional methodologies used for characterizing neural activity at different scales and review contemporary examples of how these approaches have been combined. Then we present our case for integrating activity across multiple scales to benefit from the combined strengths of each approach and elucidate a more holistic understanding of neural processes.

Main results.

We examine various combinations of neural activity at different scales and analytical techniques that can be used to integrate or illuminate information across scales, as well the technologies that enable such exciting studies. We conclude with challenges facing future multi-scale studies, and a discussion of the power and potential of these approaches.

Significance.

This roadmap will lead the readers toward a broad range of multi-scale neural decoding techniques and their benefits over single-modality analyses. This Review article highlights the importance of multi-scale analyses for systematically interrogating complex spatiotemporal mechanisms underlying cognition and behavior.

Adaptive latent state modeling of brain network dynamics with real-time learning rate optimization

Objective. Dynamic latent state models are widely used to characterize the dynamics of brain network activity for various neural signal types. To date, dynamic latent state models have largely been developed for stationary brain network dynamics. However, brain network dynamics can be non-stationary for example due to learning, plasticity or recording instability. To enable modeling these non-stationarities, two problems need to be resolved. First, novel methods should be developed that can adaptively update the parameters of latent state models, which is difficult due to the state being latent. Second, new methods are needed to optimize the adaptation learning rate, which specifies how fast new neural observations update the model parameters and can significantly influence adaptation accuracy.Approach. We develop a Rate Optimized-adaptive Linear State-Space Modeling (RO-adaptive LSSM) algorithm that solves these two problems. First, to enable adaptation, we derive a computation- and memory-efficient adaptive LSSM fitting algorithm that updates the LSSM parameters recursively and in real time in the presence of the latent state. Second, we develop a real-time learning rate optimization algorithm. We use comprehensive simulations of a broad range of non-stationary brain network dynamics to validate both algorithms, which together constitute the RO-adaptive LSSM.Main results. We show that the adaptive LSSM fitting algorithm can accurately track the broad simulated non-stationary brain network dynamics. We also find that the learning rate significantly affects the LSSM fitting accuracy. Finally, we show that the real-time learning rate optimization algorithm can run in parallel with the adaptive LSSM fitting algorithm. Doing so, the combined RO-adaptive LSSM algorithm rapidly converges to the optimal learning rate and accurately tracks non-stationarities.Significance. These algorithms can be used to study time-varying neural dynamics underlying various brain functions and enhance future neurotechnologies such as brain-machine interfaces and closed-loop brain stimulation systems.

Modelling and prediction of the dynamic responses of large-scale brain networks during direct electrical stimulation

Direct electrical stimulation can modulate the activity of brain networks for the treatment of several neurological and neuropsychiatric disorders and for restoring lost function. However, precise neuromodulation in an individual requires the accurate modelling and prediction of the effects of stimulation on the activity of their large-scale brain networks. Here, we report the development of dynamic input-output models that predict multiregional dynamics of brain networks in response to temporally varying patterns of ongoing microstimulation. In experiments with two awake rhesus macaques, we show that the activities of brain networks are modulated by changes in both stimulation amplitude and frequency, that they exhibit damping and oscillatory response dynamics, and that variabilities in prediction accuracy and in estimated response strength across brain regions can be explained by an at-rest functional connectivity measure computed without stimulation. Input-output models of brain dynamics may enable precise neuromodulation for the treatment of disease and facilitate the investigation of the functional organization of large-scale brain networks.

Multiscale low-dimensional motor cortical state dynamics predict naturalistic reach-and-grasp behavior

Motor function depends on neural dynamics spanning multiple spatiotemporal scales of population activity, from spiking of neurons to larger-scale local field potentials (LFP). How multiple scales of low-dimensional population dynamics are related in control of movements remains unknown. Multiscale neural dynamics are especially important to study in naturalistic reach-and-grasp movements, which are relatively under-explored. We learn novel multiscale dynamical models for spike-LFP network activity in monkeys performing naturalistic reach-and-grasps. We show low-dimensional dynamics of spiking and LFP activity exhibited several principal modes, each with a unique decay-frequency characteristic. One principal mode dominantly predicted movements. Despite distinct principal modes existing at the two scales, this predictive mode was multiscale and shared between scales, and was shared across sessions and monkeys, yet did not simply replicate behavioral modes. Further, this multiscale mode's decay-frequency explained behavior. We propose that multiscale, low-dimensional motor cortical state dynamics reflect the neural control of naturalistic reach-and-grasp behaviors.

Modeling behaviorally relevant neural dynamics enabled by preferential subspace identification

Neural activity exhibits complex dynamics related to various brain functions, internal states and behaviors. Understanding how neural dynamics explain specific measured behaviors requires dissociating behaviorally relevant and irrelevant dynamics, which is not achieved with current neural dynamic models as they are learned without considering behavior. We develop preferential subspace identification (PSID), which is an algorithm that models neural activity while dissociating and prioritizing its behaviorally relevant dynamics. Modeling data in two monkeys performing three-dimensional reach and grasp tasks, PSID revealed that the behaviorally relevant dynamics are significantly lower-dimensional than otherwise implied. Moreover, PSID discovered distinct rotational dynamics that were more predictive of behavior. Furthermore, PSID more accurately learned behaviorally relevant dynamics for each joint and recording channel. Finally, modeling data in two monkeys performing saccades demonstrated the generalization of PSID across behaviors, brain regions and neural signal types. PSID provides a general new tool to reveal behaviorally relevant neural dynamics that can otherwise go unnoticed.

A point-process matched filter for event detection and decoding from population spike trains

OBJECTIVE

Information encoding in neurons can be described through their response fields. The spatial response field of a neuron is the region of space in which a sensory stimulus or a behavioral event causes that neuron to fire. Neurons can also exhibit temporal response fields (TRFs), which characterize a transient response to stimulus or behavioral event onsets. These neurons can thus be described by a spatio-temporal response field (STRF). The activity of neurons with STRFs can be well-described with point process models that characterize binary spike trains with an instantaneous firing rate that is a function of both time and space. However, developing decoders for point process models of neurons that exhibit TRFs is challenging because it requires prior knowledge of event onset times, which are unknown. Indeed, point process filters (PPF) to date have largely focused on decoding neuronal activity without considering TRFs. Also, neural classifiers have required data to be behavior- or stimulus-aligned, i.e. event times to be known, which is often not possible in real-world applications. Our objective in this work is to develop a viable decoder for neurons with STRFs when event times are unknown.

APPROACH

To enable decoding of neurons with STRFs, we develop a novel point-process matched filter (PPMF) that can detect events and estimate their onset times from population spike trains. We also devise a PPF for neurons with transient responses as characterized by STRFs. When neurons exhibit STRFs and event times are unknown, the PPMF can be combined with the PPF or with discrete classifiers for continuous and discrete brain state decoding, respectively.

MAIN RESULTS

We validate our algorithm on two datasets: simulated spikes from neurons that encode visual saliency in response to stimuli, and prefrontal spikes recorded in a monkey performing a delayed-saccade task. We show that the PPMF can estimate the stimulus times and saccade times accurately. Further, the PPMF combined with the PPF can decode visual saliency maps without knowing the stimulus times. Similarly, the PPMF combined with a point process classifier can decode the saccade direction without knowing the saccade times.

SIGNIFICANCE

These event detection and decoding algorithms can help develop neurotechnologies to decode cognitive states from neural responses that exhibit STRFs.