Symmetry breaking is a technique for speeding up propositional satisfiability testing byadding constraints to the theory that restrict the search space while preserving satisfiability.In this work, we extend symmetry breaking to the problem of model finding in weighted and unweighted relational theories, a class of problems that includes MAP inference in Markov Logic and similar statistical-relational languages. We introduce term symmetries, which are induced by an evidence set and extend to symmetries over a relational theory. We provide the important special case of term equivalent symmetries, showing that such symmetries can be found in low-degree polynomial time. We show how to break an exponential number of these symmetries with added constraints whose number is linear in the size of the domain. We demonstrate the effectiveness of these techniques through experiments in two relational domains. We also discuss the connections between relational symmetry breaking and work on lifted inference in statistical-relational reasoning.

Monte Carlo sampling for Bayesian posterior inference is a common approach used in machine learning. The Markov Chain Monte Carlo procedures that are used are often discrete-time analogues of associated stochastic differential equations (SDEs). These SDEs are guaranteed to leave invariant the required posterior distribution. An area of current research addresses the computational benefits of stochastic gradient methods in this setting. Existing techniques rely on estimating the variance or covariance of the subsampling error, and typically assume constant variance. In this article, we propose a covariance-controlled adaptive Langevin thermostat that can effectively dissipate parameter-dependent noise while maintaining a desired target distribution. The proposed method achieves a substantial speedup over popular alternative schemes for large-scale machine learning applications.

We introduce Embed to Control (E2C), a method for model learning and control of non-linear dynamical systems from raw pixel images. E2C consists of a deep generative model, belonging to the family of variational autoencoders, that learns to generate image trajectories from a latent space in which the dynamics is constrained to be locally linear. Our model is derived directly from an optimal control formulation in latent space, supports long-term prediction of image sequences and exhibits strong performance on a variety of complex control problems.

This paper provides the first formalization of self-interested planning in multiagent settings using expectation-maximization (EM). Our formalization in the context of infinite-horizon and finitely-nested interactive POMDPs (I-POMDP) is distinct from EM formulations for POMDPs and cooperative multiagent planning frameworks. We exploit the graphical model structure specific to I-POMDPs, and present a new approach based on block-coordinate descent for further speed up. Forward filtering-backward sampling -- a combination of exact filtering with sampling -- is explored to exploit problem structure.

Adaptive stochastic optimization optimizes an objective function adaptively under uncertainty. Adaptive stochastic optimization plays a crucial role in planning and learning under uncertainty, but is, unfortunately, computationally intractable in general. This paper introduces two conditions on the objective function, the marginal likelihood rate bound and the marginal likelihood bound, which enable efficient approximate solution of adaptive stochastic optimization. Several interesting classes of functions satisfy these conditions naturally, e.g., the version space reduction function for hypothesis learning. We describe Recursive Adaptive Coverage (RAC), a new adaptive stochastic optimization algorithm that exploits these conditions, and apply it to two planning tasks under uncertainty. In constrast to the earlier submodular optimization approach, our algorithm applies to adaptive stochastic optimization algorithm over both sets and paths.

Many practical modeling problems involve discrete data that are best represented as draws from multinomial or categorical distributions. For example, nucleotides in a DNA sequence, children's names in a given state and year, and text documents are all commonly modeled with multinomial distributions. In all of these cases, we expect some form of dependency between the draws: the nucleotide at one position in the DNA strand may depend on the preceding nucleotides, children's names are highly correlated from year to year, and topics in text may be correlated anddynamic. These dependencies are not naturally captured by the typical Dirichlet-multinomial formulation. Here, we leverage a logistic stick-breaking representation and recent innovations in Pólya-gamma augmentation to reformulate themultinomial distribution in terms of latent variables with jointly Gaussian likelihoods, enabling us to take advantage of a host of Bayesian inference techniques forGaussian models with minimal overhead.

The Continuous-Time Hidden Markov Model (CT-HMM) is an attractive approach to modeling disease progression due to its ability to describe noisy observations arriving irregularly in time. However, the lack of an efficient parameter learning algorithm for CT-HMM restricts its use to very small models or requires unrealistic constraints on the state transitions. In this paper, we present the first complete characterization of efficient EM-based learning methods for CT-HMM models. We demonstrate that the learning problem consists of two challenges: the estimation of posterior state probabilities and the computation of end-state conditioned statistics. We solve the first challenge by reformulating the estimation problem in terms of an equivalent discrete time-inhomogeneous hidden Markov model. The second challenge is addressed by adapting three approaches from the continuous time Markov chain literature to the CT-HMM domain. We demonstrate the use of CT-HMMs with more than 100 states to visualize and predict disease progression using a glaucoma dataset and an Alzheimer's disease dataset.

Bayesian networks are a popular representation of asymmetric (for example causal) relationships between random variables. Markov random fields (MRFs) are a complementary model of symmetric relationships used in computer vision, spatial modeling, and social and gene expression networks. A chain graph model under the Lauritzen-Wermuth-Frydenberg interpretation (hereafter a chain graph model) generalizes both Bayesian networks and MRFs, and can represent asymmetric and symmetric relationships together.As in other graphical models, the set of marginals from distributions in a chain graph model induced by the presence of hidden variables forms a complex model. One recent approach to the study of marginal graphical models is to consider a well-behaved supermodel. Such a supermodel of marginals of Bayesian networks, defined only by conditional independences, and termed the ordinary Markov model, was studied at length in (Evans and Richardson, 2014).In this paper, we show that special mixed graphs which we call segregated graphs can be associated, via a Markov property, with supermodels of a marginal of chain graphs defined only by conditional independences. Special features of segregated graphs imply the existence of a very natural factorization for these supermodels, and imply many existing results on the chain graph model, and ordinary Markov model carry over. Our results suggest that segregated graphs define an analogue of the ordinary Markov model for marginals of chain graph models.

To improve the efficiency of Monte Carlo estimation, practitioners are turning to biased Markov chain Monte Carlo procedures that trade off asymptotic exactness for computational speed. The reasoning is sound: a reduction in variance due to more rapid sampling can outweigh the bias introduced. However, the inexactness creates new challenges for sampler and parameter selection, since standard measures of sample quality like effective sample size do not account for asymptotic bias. To address these challenges, we introduce a new computable quality measure based on Stein's method that bounds the discrepancy between sample and target expectations over a large class of test functions. We use our tool to compare exact, biased, and deterministic sample sequences and illustrate applications to hyperparameter selection, convergence rate assessment, and quantifying bias-variance tradeoffs in posterior inference.

In this paper, we explore the inclusion of latent random variables into the hidden state of a recurrent neural network (RNN) by combining the elements of the variational autoencoder. We argue that through the use of high-level latent random variables, the variational RNN (VRNN) can model the kind of variability observed in highly structured sequential data such as natural speech. We empirically evaluate the proposed model against other related sequential models on four speech datasets and one handwriting dataset. Our results show the important roles that latent random variables can play in the RNN dynamics.