Latent dynamical systems have been widely used to characterize the dynamics of neural population activity in the brain. However, these models typically ignore the fact that the brain contains multiple cell types. This limits their ability to capture the functional roles of distinct cell classes, and to predict the effects of cell-specific perturbations on neural activity or behavior. To overcome these limitations, we introduce the `"cell-type dynamical systems" (CTDS) model. This model extends latent linear dynamical systems to contain distinct latent variables for each cell class, with biologically inspired constraints on both dynamics and emissions. To illustrate our approach, we consider neural recordings with distinct excitatory (E) and inhibitory (I) populations. The CTDS model defines separate latents for both cell types, and constrains the dynamics so that E (I) latents have a strictly positive (negative) effects on other latents. We applied CTDS to recordings from rat frontal orienting fields (FOF) and anterior dorsal striatum (ADS) during an auditory decision-making task. The model achieved higher accuracy than a standard linear dynamical system (LDS), and revealed that the animal's choice can be decoded from both E and I latents and thus is not restricted to a single cell-class. We also performed in-silico optogenetic perturbation experiments in the FOF and ADS, and found that CTDS was able to replicate the experimentally observed effects of different perturbations on behavior, whereas a standard LDS model---which does not differentiate between cell types---did not. Crucially, our model allowed us to understand the effects of these perturbations by revealing the dynamics of different cell-specific latents. Finally, CTDS can also be used to identify cell types for neurons whose class labels are unknown in electrophysiological recordings. These results illustrate the power of the CTDS model to provide more accurate and more biologically interpretable descriptions of neural population dynamics and their relationship to behavior.

Active learning seeks to reduce the amount of data required to fit the parameters of a model, thus forming an important class of techniques in modern machine learning. However, past work on active learning has largely overlooked latent variable models, which play a vital role in neuroscience, psychology, and a variety of other engineering and scientific disciplines. Here we address this gap by proposing a novel framework for maximum-mutual-information input selection for discrete latent variable regression models. We first apply our method to a class of models known as mixtures of linear regressions (MLR). While it is well known that active learning confers no advantage for linear-gaussian regression models, we use Fisher information to show analytically that active learning can nevertheless achieve large gains for mixtures of such models, and we validate this improvement using both simulations and real-world data. We then consider a powerful class of temporally structured latent variable models given by a hidden Markov model (HMM) with generalized linear model (GLM) observations, which has recently been used to identify discrete states from animal decision-making data. We show that our method substantially reduces the amount of data needed to fit GLM-HMMs and outperforms a variety of approximate methods based on variational and amortized inference. Infomax learning for latent variable models thus offers a powerful approach for characterizing temporally structured latent states, with a wide variety of applications in neuroscience and beyond.

Understanding decision-making is a core goal in both neuroscience and psychology, and computational models have often been helpful in the pursuit of this goal. While many models have been developed for characterizing behavior in binary decision-making and bandit tasks, comparatively little work has focused on animal decision-making in more complex tasks, such as navigation through a maze. Inverse reinforcement learning (IRL) is a promising approach for understanding such behavior, as it aims to infer the unknown reward function of an agent from its observed trajectories through state space. However, IRL has yet to be widely applied in neuroscience. One potential reason for this is that existing IRL frameworks assume that an agent's reward function is fixed over time. To address this shortcoming, we introduce dynamic inverse reinforcement learning (DIRL), a novel IRL framework that allows for time-varying intrinsic rewards. Our method parametrizes the unknown reward function as a time-varying linear combination of spatial reward maps (which we refer to as "goal maps"). We develop an efficient inference method for recovering this dynamic reward function from behavioral data. We demonstrate DIRL in simulated experiments and then apply it to a dataset of mice exploring a labyrinth. Our method returns interpretable reward functions for two separate cohorts of mice, and provides a novel characterization of exploratory behavior. We expect DIRL to have broad applicability in neuroscience, and to facilitate the design of biologically-inspired reward functions for training artificial agents.

Sufficient dimension reduction (SDR) methods are a family of supervised methods for dimensionality reduction that seek to reduce dimensionality while preserving information about a target variable of interest. However, existing SDR methods typically require more observations than the number of dimensions ($N > p$). To overcome this limitation, we propose Class-conditional Factor Analytic Dimensions (CFAD), a model-based dimensionality reduction method for high-dimensional, small-sample data. We show that CFAD substantially outperforms existing SDR methods in the small-sample regime, and can be extended to incorporate prior information such as smoothness in the projection axes. We demonstrate the effectiveness of CFAD with an application to functional magnetic resonance imaging (fMRI) measurements during visual object recognition and working memory tasks, where it outperforms existing SDR and a variety of other dimensionality-reduction methods.