We propose an approximate inference algorithm for continuous time Gaussian-Markov process models with both discrete and continuous time likelihoods. We show that the continuous time limit of the expectation propagation algorithm exists and results in a hybrid fixed point iteration consisting of (1) expectation propagation updates for the discrete time terms and (2) variational updates for the continuous time term. We introduce corrections methods that improve on the marginals of the approximation. This approach extends the classical Kalman-Bucy smoothing procedure to non-Gaussian observations, enabling continuous-time inference in a variety of models, including spiking neuronal models (state-space models with point process observations) and box likelihood models. Experimental results on real and simulated data demonstrate high distributional accuracy and significant computational savings compared to discrete-time approaches in a neural application.

For spiking neurons, the entropy rate places an upper bound on the rate at which the spike train can convey stimulus information, and a large literature has focused on the problem of estimating entropy rate from spike train data. Our estimator leverages the fact that the entropy rate of an ergodic Markov Chain with known transition probabilities can be calculated analytically, and many stochastic processes that are non-Markovian can still be well approximated by Markov processes of sufficient depth. Choosing an appropriate depth of Markov model presents challenges due to possibly long time dependencies and short data sequences: a deeper model can better account for long time-dependencies, but is more difficult to infer from limited data. Our approach mitigates this difficulty by using a hierarchical prior to share statistical power across Markov chains of different depths. We present both a fully Bayesian and empirical Bayes entropy rate estimator based on this model, and demonstrate their performance on simulated and real neural spike train data.

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.

Relational data--like graphs, networks, and matrices--is often dynamic, where the relational structure evolves over time. A fundamental problem in the analysis of time-varying network data is to extract a summary of the common structure and the dynamics of underlying relations between entities. Here we build on the intuition that changes in the network structure are driven by the dynamics at the level of groups of nodes. We propose a nonparametric multi-group membership model for dynamic networks. Our model contains three main components.

Small-variance asymptotics provide an emerging technique for obtaining scalable combinatorial algorithms from rich probabilistic models. We present a small-variance asymptotic analysis of the Hidden Markov Model and its infinite-state Bayesian nonparametric extension. Starting with the standard HMM, we first derive a "hard" inference algorithm analogous to k-means that arises when particular variances in the model tend to zero. This analysis is then extended to the Bayesian nonparametric case, yielding a simple, scalable, and flexible algorithm for discrete-state sequence data with a non-fixed number of states. We also derive the corresponding combinatorial objective functions arising from our analysis, which involve a k-means-like term along with penalties based on state transitions and the number of states. A key property of such algorithms is that -- particularly in the nonparametric setting -- standard probabilistic inference algorithms lack scalability and are heavily dependent on good initialization. A number of results on synthetic and real data sets demonstrate the advantages of the proposed framework.

We study the problem of online learning Markov Decision Processes (MDPs) when both the transition distributions and loss functions are chosen by an adversary. We present an algorithm that, under a mixing assumption, achieves O(\sqrt{T\log \Pi } \log \Pi) regret with respect to a comparison set of policies \Pi . The regret is independent of the size of the state and action spaces. When expectations over sample paths can be computed efficiently and the comparison set \Pi has polynomial size, this algorithm is efficient. We also consider the episodic adversarial online shortest path problem.

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. A convex quadratic program for approximate inference is employed for recovering those source signals. On a real-world energy disaggregation data set, we show that the use of SACs dramatically improves the original AFHMM, and significantly improves over a recent state-of-the art approach.

In this paper, we propose a learning approach for the Mixture of Hidden Markov Models (MHMM) based on the Method of Moments (MoM). Computational advantages of MoM make MHMM learning amenable for large data sets. It is not possible to directly learn an MHMM with existing learning approaches, mainly due to a permutation ambiguity in the estimation process. We show that it is possible to resolve this ambiguity using the spectral properties of a global transition matrix even in the presence of estimation noise. We demonstrate the validity of our approach on synthetic and real data.

Markov chain Monte Carlo (MCMC) algorithms are simple and extremely powerful techniques to sample from almost arbitrary distributions. The flaw in practice is that it can take a large and/or unknown amount of time to converge to the stationary distribution. This paper gives sufficient conditions to guarantee that univariate Gibbs sampling on Markov Random Fields (MRFs) will be fast mixing, in a precise sense. Further, an algorithm is given to project onto this set of fast-mixing parameters in the Euclidean norm. Following recent work, we give an example use of this to project in various divergence measures, comparing of univariate marginals obtained by sampling after projection to common variational methods and Gibbs sampling on the original parameters.

In this paper, we present a new approach for lifted MAP inference in Markov logic networks (MLNs). The key idea in our approach is to compactly encode the MAP inference problem as an Integer Polynomial Program (IPP) by schematically applying three lifted inference steps to the MLN: lifted decomposition, lifted conditioning, and partial grounding. Our IPP encoding is lifted in the sense that an integer assignment to a variable in the IPP may represent a truth-assignment to multiple indistinguishable ground atoms in the MLN. We show how to solve the IPP by first converting it to an Integer Linear Program (ILP) and then solving the latter using state-of-the-art ILP techniques. Experiments on several benchmark MLNs show that our new algorithm is substantially superior to ground inference and existing methods in terms of computational efficiency and solution quality.