Structured distributions, i.e. distributions over combinatorial spaces, are commonly used to learn latent probabilistic representations from observed data. However, scaling these models is bottlenecked by the high computational and memory complexity with respect to the size of the latent representations. Common models such as Hidden Markov Models (HMMs) and Probabilistic Context-Free Grammars (PCFGs) require time and space quadratic and cubic in the number of hidden states respectively. This work demonstrates a simple approach to reduce the computational and memory complexity of a large class of structured models. We show that by viewing the central inference step as a matrix-vector product and using a low-rank constraint, we can trade off model expressivity and speed via the rank. Experiments with neural parameterized structured models for language modeling, polyphonic music modeling, unsupervised grammar induction, and video modeling show that our approach matches the accuracy of standard models at large state spaces while providing practical speedups.

Developing computational models of neural response is crucial for understanding sensory processing and neural computations. Current state-of-the-art neural network methods use temporal filters to handle temporal dependencies, resulting in an unrealistic and inflexible processing paradigm. Meanwhile, these methods target trial-averaged firing rates and fail to capture important features in spike trains. This work presents the temporal conditioning spiking latent variable models (TeCoS-LVM) to simulate the neural response to natural visual stimuli. We use spiking neurons to produce spike outputs that directly match the recorded trains.

Many decision-making problems naturally exhibit pronounced structures inherited from the characteristics of the underlying environment. In a Markov decision process model, for example, two distinct states can have inherently related semantics or encode resembling physical state configurations. This often implies locally correlated transition dynamics among the states. In order to complete a certain task in such environments, the operating agent usually needs to execute a series of temporally and spatially correlated actions. Though there exists a variety of approaches to capture these correlations in continuous state-action domains, a principled solution for discrete environments is missing.

We propose to jointly analyze experts' eye movements and verbal narrations to discover important and interpretable knowledge patterns to better understand their decision-making processes. The discovered patterns can further enhance data-driven statistical models by fusing experts' domain knowledge to support complex human-machine collaborative decision-making. Our key contribution is a novel dynamic Bayesian nonparametric model that assigns latent knowledge patterns into key phases involved in complex decision-making. Each phase is characterized by a unique distribution of word topics discovered from verbal narrations and their dynamic interactions with eye movement patterns, indicating experts' special perceptual behavior within a given decision-making stage. A new split-merge-switch sampler is developed to efficiently explore the posterior state space with an improved mixing rate.

We propose a new sparse Granger-causal learning framework for temporal event data. We focus on a specific class of point processes called the Hawkes process. We begin by pointing out that most of the existing sparse causal learning algorithms for the Hawkes process suffer from a singularity in maximum likelihood estimation. As a result, their sparse solutions can appear only as numerical artifacts. In this paper, we propose a mathematically well-defined sparse causal learning framework based on a cardinality-regularized Hawkes process, which remedies the pathological issues of existing approaches.

In this paper, we provide a method to learn the directed structure of a Bayesian network using data. The data is accessed by making conditional probability queries to a black-box model. We introduce a notion of simplicity of representation of conditional probability tables for the nodes in the Bayesian network, that we call low rankness''. We connect this notion to the Fourier transformation of real valued set functions and propose a method which learns the exact directed structure of alow rank Bayesian network using very few queries. We formally prove that our method correctly recovers the true directed structure, runs in polynomial time and only needs polynomial samples with respect to the number of nodes.

We consider learning the structures of Gaussian latent tree models with vector observations when a subset of them are arbitrarily corrupted. First, we present the sample complexities of Recursive Grouping (RG) and Chow-Liu Recursive Grouping (CLRG) without the assumption that the effective depth is bounded in the number of observed nodes, significantly generalizing the results in Choi et al. (2011). We show that Chow-Liu initialization in CLRG greatly reduces the sample complexity of RG from being exponential in the diameter of the tree to only logarithmic in the diameter for the hidden Markov model (HMM). These robustified algorithms can tolerate a number of corruptions up to the square root of the number of clean samples. Finally, we derive the first known instance-dependent impossibility result for structure learning of latent trees.

Knowledge graph reasoning, which aims at predicting missing facts through reasoning with observed facts, is critical for many applications. Such a problem has been widely explored by traditional logic rule-based approaches and recent knowledge graph embedding methods. A principled logic rule-based approach is the Markov Logic Network (MLN), which is able to leverage domain knowledge with first-order logic and meanwhile handle uncertainty. However, the inference in MLNs is usually very difficult due to the complicated graph structures. TransE, DistMult) learn effective entity and relation embeddings for reasoning, which are much more effective and efficient. However, they are unable to leverage domain knowledge.

Much of reinforcement learning theory is built on top of oracles that are computationally hard to implement. Specifically for learning near-optimal policies in Partially Observable Markov Decision Processes (POMDPs), existing algorithms either need to make strong assumptions about the model dynamics (e.g. In this work we develop the first oracle-free learning algorithm for POMDPs under reasonable assumptions. Specifically, we give a quasipolynomial-time end-to-end algorithm for learning in observable'' POMDPs, where observability is the assumption that well-separated distributions over states induce well-separated distributions over observations. Our techniques circumvent the more traditional approach of using the principle of optimism under uncertainty to promote exploration, and instead give a novel application of barycentric spanners to constructing policy covers.

We study the problem of Safe Policy Improvement (SPI) under constraints in the offline Reinforcement Learning (RL) setting. We consider the scenario where: (i) we have a dataset collected under a known baseline policy, (ii) multiple reward signals are received from the environment inducing as many objectives to optimize. We present an SPI formulation for this RL setting that takes into account the preferences of the algorithm's user for handling the trade-offs for different reward signals while ensuring that the new policy performs at least as well as the baseline policy along each individual objective. We build on traditional SPI algorithms and propose a novel method based on Safe Policy Iteration with Baseline Bootstrapping (SPIBB, Laroche et al., 2019) that provides high probability guarantees on the performance of the agent in the true environment. We show the effectiveness of our method on a synthetic grid-world safety task as well as in a real-world critical care context to learn a policy for the administration of IV fluids and vasopressors to treat sepsis.