A fundamental goal of systems neuroscience is to understand how neural activity gives rise to natural behavior. In order to achieve this goal, we must first build comprehensive models that offer quantitative descriptions of behavior. We develop a new class of probabilistic models to tackle this challenge in the study of larval zebrafish, an important model organism for neuroscience. Larval zebrafish locomote via sequences of punctate swim bouts--brief flicks of the tail--which are naturally modeled as a marked point process. However, these sequences of swim bouts belie a set of discrete and continuous internal states, latent variables that are not captured by standard point process models. We incorporate these variables as latent marks of a point process and explore various models for their dynamics. To infer the latent variables and fit the parameters of this model, we develop an amortized variational inference algorithm that targets the collapsed posterior distribution, analytically marginalizing out the discrete latent variables. With a dataset of over 120,000 swim bouts, we show that our models reveal interpretable discrete classes of swim bouts and continuous internal states like hunger that modulate their dynamics. These models are a major step toward understanding the natural behavioral program of the larval zebrafish and, ultimately, its neural underpinnings.

A fundamental goal of systems neuroscience is to understand the relationship between neural activity and behavior. Behavior has traditionally been characterized by low-dimensional, task-related variables such as movement speed or response times. More recently, there has been a growing interest in automated analysis of high-dimensional video data collected during experiments. Here we introduce a probabilistic framework for the analysis of behavioral video and neural activity. This framework provides tools for compression, segmentation, generation, and decoding of behavioral videos. Compression is performed using a convolutional autoencoder (CAE), which yields a low-dimensional continuous representation of behavior.

This paper presents the Poisson-randomized gamma dynamical system (PRGDS), a model for sequentially observed count tensors that encodes a strong inductive bias toward sparsity and burstiness. The PRGDS is based on a new motif in Bayesian latent variable modeling, an alternating chain of discrete Poisson and continuous gamma latent states that is analytically convenient and computationally tractable. This motif yields closed-form complete conditionals for all variables by way of the Bessel distribution and a novel discrete distribution that we call the shifted confluent hypergeometric distribution. We draw connections to closely related models and compare the PRGDS to these models in studies of real-world count data sets of text, international events, and neural spike trains. We find that a sparse variant of the PRGDS, which allows the continuous gamma latent states to take values of exactly zero, often obtains better predictive performance than other models and is uniquely capable of inferring latent structures that are highly localized in time.

Recent advances in optical voltage sensors have brought us closer to a critical goal in cellular neuroscience: imaging the full spatiotemporal voltage on a dendritic tree. However, current sensors and imaging approaches still face significant limitations in SNR and sampling frequency; therefore statistical denoising methods remain critical for understanding single-trial spatiotemporal dendritic voltage dynamics. Previous denoising approaches were either based on an inadequate linear voltage model or scaled poorly to large trees. Here we introduce a scalable fully Bayesian approach. We develop a generative nonlinear model that requires few parameters per dendritic compartment but is nonetheless flexible enough to sample realistic spatiotemporal data. The model captures potentially different dynamics in each compartment and leverages biophysical knowledge to constrain intra-and inter-compartmental dynamics. We obtain a full posterior distribution over spatiotemporal voltage via an efficient augmented block-Gibbs sampling algorithm. The nonlinear smoother model outperforms previously developed linear methods, and scales to much larger systems than previous methods based on sequential Monte Carlo approaches.

A fundamental goal of systems neuroscience is to understand the relationship between neural activity and behavior. Behavior has traditionally been characterized by low-dimensional, task-related variables such as movement speed or response times. More recently, there has been a growing interest in automated analysis of high-dimensional video data collected during experiments. Here we introduce a probabilistic framework for the analysis of behavioral video and neural activity. This framework provides tools for compression, segmentation, generation, and decoding of behavioral videos. Compression is performed using a convolutional autoencoder (CAE), which yields a low-dimensional continuous representation of behavior.

Many real-world data represent sequences of interdependent events unfolding over time. They can be modeled naturally as realizations of a point process. Despite many potential applications, existing point process models are limited in their ability to capture complex patterns of interaction. Hawkes processes admit many efficient inference algorithms, but are limited to mutually excitatory effects. Nonlinear Hawkes processes allow for more complex influence patterns, but for their estimation it is typically necessary to resort to discrete-time approximations that may yield poor generative models. In this paper, we introduce the first general class of Bayesian point process models extended with a nonlinear component that allows both excitatory and inhibitory relationships in continuous time. We derive a fully Bayesian inference algorithm for these processes using Pólya-Gamma augmentation and Poisson thinning. We evaluate the proposed model on single and multi-neuronal spike train recordings. Results demonstrate that the proposed model, unlike existing point process models, can generate biologically-plausible spike trains, while still achieving competitive predictive likelihoods.

This paper presents the Poisson-randomized gamma dynamical system (PRGDS), a model for sequentially observed count tensors that encodes a strong inductive bias toward sparsity and burstiness. The PRGDS is based on a new motif in Bayesian latent variable modeling, an alternating chain of discrete Poisson and continuous gamma latent states that is analytically convenient and computationally tractable. This motif yields closed-form complete conditionals for all variables by way of the Bessel distribution and a novel discrete distribution that we call the shifted confluent hypergeometric distribution. We draw connections to closely related models and compare the PRGDS to these models in studies of real-world count data sets of text, international events, and neural spike trains. We find that a sparse variant of the PRGDS, which allows the continuous gamma latent states to take values of exactly zero, often obtains better predictive performance than other models and is uniquely capable of inferring latent structures that are highly localized in time.

Neural circuits contain heterogeneous groups of neurons that differ in type, location, connectivity, and basic response properties. However, traditional methods for dimensionality reduction and clustering are ill-suited to recovering the structure underlying the organization of neural circuits. In particular, they do not take advantage of the rich temporal dependencies in multi-neuron recordings and fail to account for the noise in neural spike trains. Here we describe new tools for inferring latent structure from simultaneously recorded spike train data using a hierarchical extension of a multi-neuron point process model commonly known as the generalized linear model (GLM). Our approach combines the GLM with flexible graph-theoretic priors governing the relationship between latent features and neural connectivity patterns. Fully Bayesian inference via Pólya-gamma augmentation of the resulting model allows us to classify neurons and infer latent dimensions of circuit organization from correlated spike trains. We demonstrate the effectiveness of our method with applications to synthetic data and multi-neuron recordings in primate retina, revealing latent patterns of neural types and locations from spike trains alone.

A fundamental goal of systems neuroscience is to understand how neural activity gives rise to natural behavior. In order to achieve this goal, we must first build comprehensive models that offer quantitative descriptions of behavior. We develop a new class of probabilistic models to tackle this challenge in the study of larval zebrafish, an important model organism for neuroscience. Larval zebrafish locomote via sequences of punctate swim bouts--brief flicks of the tail--which are naturally modeled as a marked point process. However, these sequences of swim bouts belie a set of discrete and continuous internal states, latent variables that are not captured by standard point process models. We incorporate these variables as latent marks of a point process and explore various models for their dynamics. To infer the latent variables and fit the parameters of this model, we develop an amortized variational inference algorithm that targets the collapsed posterior distribution, analytically marginalizing out the discrete latent variables. With a dataset of over 120,000 swim bouts, we show that our models reveal interpretable discrete classes of swim bouts and continuous internal states like hunger that modulate their dynamics. These models are a major step toward understanding the natural behavioral program of the larval zebrafish and, ultimately, its neural underpinnings.

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