We consider the problem of aggregating models learned from sequestered, possibly heterogeneous datasets. Exploiting tools from Bayesian nonparametrics, we develop a general meta-modeling framework that learns shared global latent structures by identifying correspondences among local model parameterizations. Our proposed framework is model-independent and is applicable to a wide range of model types. After verifying our approach on simulated data, we demonstrate its utility in aggregating Gaussian topic models, hierarchical Dirichlet process based hidden Markov models, and sparse Gaussian processes with applications spanning text summarization, motion capture analysis, and temperature forecasting.

Sampling from posterior distributions using Markov chain Monte Carlo (MCMC) methods can require an exhaustive number of iterations, particularly when the posterior is multi-modal as the MCMC sampler can become trapped in a local mode for a large number of iterations. In this paper, we introduce the pseudo-extended MCMC method as a simple approach for improving the mixing of the MCMC sampler for multi-modal posterior distributions.

Tensor-network techniques have recently proven useful in machine learning, both as a tool for the formulation of new learning algorithms and for enhancing the mathematical understanding of existing methods. Inspired by these developments, and the natural correspondence between tensor networks and probabilistic graphical models, we provide a rigorous analysis of the expressive power of various tensor-network factorizations of discrete multivariate probability distributions. These factorizations include non-negative tensor-trains/MPS, which are in correspondence with hidden Markov models, and Born machines, which are naturally related to the probabilistic interpretation of quantum circuits. When used to model probability distributions, they exhibit tractable likelihoods and admit efficient learning algorithms. Interestingly, we prove that there exist probability distributions for which there are unbounded separations between the resource requirements of some of these tensor-network factorizations. Of particular interest, using complex instead of real tensors can lead to an arbitrarily large reduction in the number of parameters of the network. Additionally, we introduce locally purified states (LPS), a new factorization inspired by techniques for the simulation of quantum systems, with provably better expressive power than all other representations considered. The ramifications of this result are explored through numerical experiments.

A graphical model is a structured representation of the data generating process. The traditional method to reason over random variables is to perform inference in this graphical model. However, in many cases the generating process is only a poor approximation of the much more complex true data generating process, leading to suboptimal estimation. The subtleties of the generative process are however captured in the data itself and we can ``learn to infer'', that is, learn a direct mapping from observations to explanatory latent variables. In this work we propose a hybrid model that combines graphical inference with a learned inverse model, which we structure as in a graph neural network, while the iterative algorithm as a whole is formulated as a recurrent neural network. By using cross-validation we can automatically balance the amount of work performed by graphical inference versus learned inference. We apply our ideas to the Kalman filter, a Gaussian hidden Markov model for time sequences, and show, among other things, that our model can estimate the trajectory of a noisy chaotic Lorenz Attractor much more accurately than either the learned or graphical inference run in isolation.

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.

We consider the problem of online reinforcement learning when several state representations (mapping histories to a discrete state space) are available to the learning agent. At least one of these representations is assumed to induce a Markov decision process (MDP), and the performance of the agent is measured in terms of cumulative regret against the optimal policy giving the highest average reward in this MDP representation. We propose an algorithm (UCB-MS) with O(sqrt(T)) regret in any communicating Markov decision process. The regret bound shows that UCB-MS automatically adapts to the Markov model. This improves over the currently known best results in the literature that gave regret bounds of order O(T^(2/3)).

Recently there is a large amount of work devoted to the study of Markov chain stochastic gradient methods (MC-SGMs) which mainly focus on their convergence analysis for solving minimization problems. In this paper, we provide a comprehensive generalization analysis of MC-SGMs for both minimization and minimax problems through the lens of algorithmic stability in the framework of statistical learning theory. For empirical risk minimization (ERM) problems, we establish the optimal excess population risk bounds for both smooth and non-smooth cases by introducing on-average argument stability. For minimax problems, we develop a quantitative connection between on-average argument stability and generalization error which extends the existing results for uniform stability (Lei et al., 2021). We further develop the first nearly optimal convergence rates for convex-concave problems both in expectation and with high probability, which, combined with our stability results, show that the optimal generalization bounds can be attained for both smooth and non-smooth cases. To the best of our knowledge, this is the first generalization analysis of SGMs when the gradients are sampled from a Markov process.

The paper introduces a new algorithm for planning in partially observable Markov decision processes (POMDP) based on the idea of aggregate simulation. The algorithm uses product distributions to approximate the belief state and shows how to build a representation graph of an approximate action-value function over belief space.

This paper is concerned with multi-view reinforcement learning (MVRL), which allows for decision making when agents share common dynamics but adhere to different observation models. We define the MVRL framework by extending partially observable Markov decision processes (POMDPs) to support more than one observation model and propose two solution methods through observation augmentation and cross-view policy transfer. We empirically evaluate our method and demonstrate its effectiveness in a variety of environments. Specifically, we show reductions in sample complexities and computational time for acquiring policies that handle multi-view environments.

Bayesian inference in state-space models is challenging due to high-dimensional state trajectories. A viable approach is particle Markov chain Monte Carlo (PMCMC), combining MCMC and sequential Monte Carlo to form ``exact approximations'' to otherwise-intractable MCMC methods. The performance of the approximation is limited to that of the exact method. We focus on particle Gibbs (PG) and particle Gibbs with ancestor sampling (PGAS), improving their performance beyond that of the ideal Gibbs sampler (which they approximate) by marginalizing out one or more parameters. This is possible when the parameter(s) has a conjugate prior relationship with the complete data likelihood. Marginalization yields a non-Markov model for inference, but we show that, in contrast to the general case, the methods still scale linearly in time. While marginalization can be cumbersome to implement, recent advances in probabilistic programming have enabled its automation. We demonstrate how the marginalized methods are viable as efficient inference backends in probabilistic programming, and demonstrate with examples in ecology and epidemiology.