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.

We describe a framework for defining high-order image models that can be used in a variety of applications. The approach involves modeling local patterns in a multiscale representation of an image. Local properties of a coarsened image reflect non-local properties of the original image. In the case of binary images local properties are defined by the binary patterns observed over small neighborhoods around each pixel. With the multiscale representation we capture the frequency of patterns observed at different scales of resolution. This framework leads to expressive priors that depend on a relatively small number of parameters. For inference and learning we use an MCMC method for block sampling with very large blocks. We evaluate the approach with two example applications.

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, comparingunivariatemarginals obtained by sampling after projection to common variational methodsandGibbs sampling on the original parameters.

We consider the problem of learning the canonical parameters specifying an undirected graphical model (Markov random field) from the mean parameters. For graphical models representing a minimal exponential family, the canonical parameters are uniquely determined by the mean parameters, so the problem is feasible in principle. The goal of this paper is to investigate the computational feasibility of this statistical task. Our main result shows that parameter estimation is in general intractable: no algorithm can learn the canonical parameters of a generic pair-wise binary graphical model from the mean parameters in time bounded by a polynomial in the number of variables (unless RP = NP). Indeed, such a result has been believed to be true (see [1]) but no proof was known. Our proof gives a polynomial time reduction from approximating the partition function of the hard-core model, known to be hard, to learning approximate parameters. Our reduction entails showing that the marginal polytope boundary has an inherent repulsive property, which validates an optimization procedure over the polytope that does not use any knowledge of its structure (as required by the ellipsoid method and others).

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.

Neural population activity in cortical circuits is not solely driven by external inputs, but is also modulated by endogenous states which vary on multiple time-scales. To understand information processing in cortical circuits, we need to understand the statistical structure of internal states and their interaction with sensory inputs. Here, we present a statistical model for extracting hierarchically organised neural population states from multi-channel recordings of neural spiking activity. Population states are modelled using a hidden Markov decision tree with state-dependent tuning parameters and a generalised linear observation model. We present a variational Bayesian inference algorithm for estimating the posterior distribution over parameters from neural population recordings. On simulated data, we show that we can identify the underlying sequence of population states and reconstruct the ground truth parameters. Using population recordings from visual cortex, we find that a model with two levels of population states outperforms both a one-state and a two-state generalised linear model. Finally, we find that modelling of state-dependence also improves the accuracy with which sensory stimuli can be decoded from the population response.

We show that the usual score function for conditional Markov networks can be written as the expectation over the scores of their spanning trees. We also show that a small random sample of these output trees can attain a significant fraction of the margin obtained by the complete graph and we provide conditions under which we can perform tractable inference. The experimental results confirm that practical learning is scalable to realistic datasets using this approach.

We develop a sampling technique for Hierarchical Dirichlet process models. The parallel algorithm builds upon [1] by proposing large split and merge moves based on learned sub-clusters. The additional global split and merge moves drastically improve convergence in the experimental results. Furthermore, we discover that cross-validation techniques do not adequately determine convergence, and that previous sampling methods converge slower than were previously expected.

State-space models have been successfully used for more than fifty years in different areas of science and engineering. We present a procedure for efficient variational Bayesian learning of nonlinear state-space models based on sparse Gaussian processes. The result of learning is a tractable posterior over nonlinear dynamical systems. In comparison to conventional parametric models, we offer the possibility to straightforwardly trade off model capacity and computational cost whilst avoiding overfitting. Our main algorithm uses a hybrid inference approach combining variational Bayes and sequential Monte Carlo.