A core goal in systems neuroscience and neuroethology is to understand how neural circuits generate naturalistic behavior. One foundational idea is that complex naturalistic behavior may be composed of sequences of stereotyped behavioral syllables, which combine to generate rich sequences of actions. To investigate this, a common approach is to use autoregressive hidden Markov models (ARHMMs) to segment video into discrete behavioral syllables. While these approaches have been successful in extracting syllables that are interpretable, they fail to account for other forms of behavioral variability, such as differences in speed, which may be better described as continuous in nature. To overcome these limitations, we introduce a class of warped ARHMMs (WARHMM). As is the case in the ARHMM, behavior is modeled as a mixture of autoregressive dynamics. However, the dynamics under each discrete latent state (i.e. each behavioral syllable) are additionally modulated by a continuous latent ``warping variable.'' We present two versions of warped ARHMM in which the warping variable affects the dynamics of each syllable either linearly or nonlinearly. Using depth-camera recordings of freely moving mice, we demonstrate that the failure of ARHMMs to account for continuous behavioral variability results in duplicate cluster assignments. WARHMM achieves similar performance to the standard ARHMM while using fewer behavioral syllables. Further analysis of behavioral measurements in mice demonstrates that WARHMM identifies structure relating to response vigor.

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. We then use an autoregressive hidden Markov model (ARHMM) to segment the CAE representation into discrete "behavioral syllables." The resulting generative model can be used to simulate behavioral video data. Finally, based on this generative model, we develop a novel Bayesian decoding approach that takes in neural activity and outputs probabilistic estimates of the full-resolution behavioral video. We demonstrate this framework on two different experimental paradigms using distinct behavioral and neural recording technologies.

A major difficulty in studying the neural mechanisms underlying olfactory perception is the lack of obvious structure in the relationship between odorants and the neural activity patterns they elicit. Here we use odor-evoked responses in piriform cortex to identify a latent manifold specifying latent distance relationships between olfactory stimuli. Our approach is based on the Gaussian process latent variable model, and seeks to map odorants to points in a low-dimensional embedding space, where distances between points in the embedding space relate to the similarity of population responses they elicit. The model is specified by an explicit continuous mapping from a latent embedding space to the space of high-dimensional neural population firing rates via nonlinear tuning curves, each parametrized by a Gaussian process. Population responses are then generated by the addition of correlated, odor-dependent Gaussian noise. We fit this model to large-scale calcium fluorescence imaging measurements of population activity in layers 2 and 3 of mouse piriform cortex following the presentation of a diverse set of odorants. The model identifies a low-dimensional embedding of each odor, and a smooth tuning curve over the latent embedding space that accurately captures each neuron's response to different odorants. The model captures both signal and noise correlations across more than 500 neurons. We validate the model using a cross-validation analysis known as co-smoothing to show that the model can accurately predict the responses of a population of held-out neurons to test odorants.

We propose a general modeling and inference framework that combines the complementary strengths of probabilistic graphical models and deep learning methods. Our model family composes latent graphical models with neural network observation likelihoods. For inference, we use recognition networks to produce local evidence potentials, then combine them with the model distribution using efficient message-passing algorithms. All components are trained simultaneously with a single stochastic variational inference objective. We illustrate this framework by automatically segmenting and categorizing mouse behavior from raw depth video, and demonstrate several other example models.