We introduce the Multi-Prediction Deep Boltzmann Machine (MP-DBM). The MP-DBM can be seen as a single probabilistic model trained to maximize a variational approximation to the generalized pseudolikelihood, or as a family of recurrent nets that share parameters and approximately solve different inference problems. Prior methods of training DBMs either do not perform well on classification tasks or require an initial learning pass that trains the DBM greedily, one layer at a time. The MP-DBM does not require greedy layerwise pretraining, and outperforms the standard DBM at classification, classification with missing inputs, and mean field prediction tasks. Papers published at the Neural Information Processing Systems Conference.

This paper considers a number of related inverse filtering problems for hidden Markov models (HMMs). In particular, given a sequence of state posteriors and the system dynamics; i) estimate the corresponding sequence of observations, ii) estimate the observation likelihoods, and iii) jointly estimate the observation likelihoods and the observation sequence. We show how to avoid a computationally expensive mixed integer linear program (MILP) by exploiting the algebraic structure of the HMM filter using simple linear algebra operations, and provide conditions for when the quantities can be uniquely reconstructed. We also propose a solution to the more general case where the posteriors are noisily observed. Finally, the proposed inverse filtering algorithms are evaluated on real-world polysomnographic data used for automatic sleep segmentation.

Boltzmann machines are able to learn highly complex, multimodal, structured and multiscale real-world data distributions. Parameters of the model are usually learned by minimizing the Kullback-Leibler (KL) divergence from training samples to the learned model. We propose in this work a novel approach for Boltzmann machine training which assumes that a meaningful metric between observations is known. This metric between observations can then be used to define the Wasserstein distance between the distribution induced by the Boltzmann machine on the one hand, and that given by the training sample on the other hand. We derive a gradient of that distance with respect to the model parameters.

Learning dynamic models from observed data has been a central issue in many scientific studies or engineering tasks. The usual setting is that data are collected sequentially from trajectories of some dynamical system operation. In quite a few modern scientific modeling tasks, however, it turns out that reliable sequential data are rather difficult to gather, whereas out-of-order snapshots are much easier to obtain. Examples include the modeling of galaxies, chronic diseases such Alzheimer's, or certain biological processes. Existing methods for learning dynamic model from non-sequence data are mostly based on Expectation-Maximization, which involves non-convex optimization and is thus hard to analyze.

Recently, there has been growing interest in lifting MAP inference algorithms for Markov logic networks (MLNs). A key advantage of these lifted algorithms is that they have much smaller computational complexity than propositional algorithms when symmetries are present in the MLN and these symmetries can be detected using lifted inference rules. Unfortunately, lifted inference rules are sound but not complete and can often miss many symmetries. This is problematic because when symmetries cannot be exploited, lifted inference algorithms ground the MLN, and search for solutions in the much larger propositional space. In this paper, we present a novel approach, which cleverly introduces new symmetries at the time of grounding.

We study the problem of reconstructing a mixture of Markov chains from the trajectories generated by random walks through the state space. Under mild non-degeneracy conditions, we show that we can uniquely reconstruct the underlying chains by only considering trajectories of length three, which represent triples of states. Our algorithm is spectral in nature, and is easy to implement. Papers published at the Neural Information Processing Systems Conference.

This paper presents four major results towards solving decentralized partially observable Markov decision problems (DecPOMDPs) culminating in an algorithm that outperforms all existing algorithms on all but one standard infinite-horizon benchmark problems. The program is notable because its linear relaxation is very often integral. These actions correspond to strategies of a CBG. We choose one such algorithm, point-based valued iteration, and modify it to produce the first tractable value iteration method for DecPOMDPs which outperforms existing algorithms. Papers published at the Neural Information Processing Systems Conference.

As datasets capturing human choices grow in richness and scale, particularly in online domains, there is an increasing need for choice models flexible enough to handle data that violate traditional choice-theoretic axioms such as regularity, stochastic transitivity, or Luce's choice axiom. In this work we introduce the Pairwise Choice Markov Chain (PCMC) model of discrete choice, an inferentially tractable model that does not assume these traditional axioms while still satisfying the foundational axiom of uniform expansion, which can be viewed as a weaker version of Luce's axiom. We show that the PCMC model significantly outperforms the Multinomial Logit (MNL) model in prediction tasks on two empirical data sets known to exhibit violations of Luce's axiom. Our analysis also synthesizes several recent observations connecting the Multinomial Logit model and Markov chains; the PCMC model retains the Multinomial Logit model as a special case. Papers published at the Neural Information Processing Systems Conference.

Variational inference algorithms have proven successful for Bayesian analysis in large data settings, with recent advances using stochastic variational inference (SVI). However, such methods have largely been studied in independent or exchangeable data settings. We develop an SVI algorithm to learn the parameters of hidden Markov models (HMMs) in a time-dependent data setting. The challenge in applying stochastic optimization in this setting arises from dependencies in the chain, which must be broken to consider minibatches of observations. We propose an algorithm that harnesses the memory decay of the chain to adaptively bound errors arising from edge effects.

Blind source separation problems are difficult because they are inherently unidentifiable, yet the entire goal is to identify meaningful sources. We introduce a way of incorporating domain knowledge into this problem, called signal aggregate constraints (SACs). SACs encourage the total signal for each of the unknown sources to be close to a specified value. This is based on the observation that the total signal often varies widely across the unknown sources, and we often have a good idea of what total values to expect. We incorporate SACs into an additive factorial hidden Markov model (AFHMM) to formulate the energy disaggregation problems where only one mixture signal is assumed to be observed.