Markov random fields (MRFs), or undirected graphical models, provide a powerful framework for modeling complex dependencies among random variables. Maximum likelihood learning in MRFs is hard due to the presence of the global normalizing constant. In this paper we consider a class of stochastic approximation algorithms of Robbins-Monro type that uses Markov chain Monte Carlo to do approximate maximum likelihood learning. We show that using MCMC operators based on tempered transitions enables the stochastic approximation algorithm to better explore highly multimodal distributions, which considerably improves parameter estimates in large densely-connected MRFs. Our results on MNIST and NORB datasets demonstrate that we can successfully learn good generative models of high-dimensional, richly structured data and perform well on digit and object recognition tasks.

A score function induced by a generative model of the data can provide a feature vectorof a fixed dimension for each data sample. Data samples themselves may be of differing lengths (e.g., speech segments, or other sequence data), but as a score function is based on the properties of the data generation process, it produces a fixed-length vector in a highly informative space, typically referred to as a "score space". Discriminative classifiers have been shown to achieve higher performance in appropriately chosen score spaces than is achievable by either the corresponding generative likelihood-based classifiers, or the discriminative classifiers usingstandard feature extractors. In this paper, we present a novel score space that exploits the free energy associated with a generative model. The resulting freeenergy score space (FESS) takes into account latent structure of the data at various levels, and can be trivially shown to lead to classification performance that at least matches the performance of the free energy classifier based on the same generative model, and the same factorization of the posterior. We also show that in several typical vision and computational biology applications the classifiers optimized in FESS outperform the corresponding pure generative approaches, as well as a number of previous approaches to combining discriminating and generative models.

Pruning can massively accelerate the computation of feature expectations in large models. However, any single pruning mask will introduce bias. We present a novel approach which employs a randomized sequence of pruning masks. Formally, we apply auxiliary variable MCMC sampling to generate this sequence of masks, thereby gaining theoretical guarantees about convergence. Because each mask is generally able to skip large portions of an underlying dynamic program, our approach is particularly compelling for high-degree algorithms. Empirically, we demonstrate our method on bilingual parsing, showing decreasing bias as more masks are incorporated, and outperforming fixed tic-tac-toe pruning.

While many perceptual and cognitive phenomena are well described in terms of Bayesian inference, the necessary computations are intractable at the scale of real-world tasks, and it remains unclear how the human mind approximates Bayesian inference algorithmically. We explore the proposal that for some tasks, humans use a form of Markov Chain Monte Carlo to approximate the posterior distribution over hidden variables. As a case study, we show how several phenomena of perceptual multistability can be explained as MCMC inference in simple graphical models for low-level vision.

Offline handwriting recognition---the transcription of images of handwritten text---is an interesting task, in that it combines computer vision with sequence learning. In most systems the two elements are handled separately, with sophisticated preprocessing techniques used to extract the image features and sequential models such as HMMs used to provide the transcriptions. By combining two recent innovations in neural networks---multidimensional recurrent neural networks and connectionist temporal classification---this paper introduces a globally trained offline handwriting recogniser that takes raw pixel data as input. Unlike competing systems, it does not require any alphabet specific preprocessing, and can therefore be used unchanged for any language. Evidence of its generality and power is provided by data from a recent international Arabic recognition competition, where it outperformed all entries (91.4% accuracy compared to 87.2% for the competition winner) despite the fact that neither author understands a word of Arabic.

Learning graphical models with hidden variables can offer semantic insights to complex data and lead to salient structured predictors without relying on expensive, sometime unattainable fully annotated training data. While likelihood-based methods have been extensively explored, to our knowledge, learning structured prediction models with latent variables based on the max-margin principle remains largely an open problem. In this paper, we present a partially observed Maximum Entropy Discrimination Markov Network (PoMEN) model that attempts to combine the advantages of Bayesian and margin based paradigms for learning Markov networks from partially labeled data. PoMEN leads to an averaging prediction rule that resembles a Bayes predictor that is more robust to overfitting, but is also built on the desirable discriminative laws resemble those of the M$^3$N. We develop an EM-style algorithm utilizing existing convex optimization algorithms for M$^3$N as a subroutine. We demonstrate competent performance of PoMEN over existing methods on a real-world web data extraction task.

Working memory is a central topic of cognitive neuroscience because it is critical for solving real world problems in which information from multiple temporally distant sources must be combined to generate appropriate behavior. However, an often neglected fact is that learning to use working memory effectively is itself a difficult problem. The Gating" framework is a collection of psychological models that show how dopamine can train the basal ganglia and prefrontal cortex to form useful working memory representations in certain types of problems. We bring together gating with ideas from machine learning about using finite memory systems in more general problems. Thus we present a normative Gating model that learns, by online temporal difference methods, to use working memory to maximize discounted future rewards in general partially observable settings. The model successfully solves a benchmark working memory problem, and exhibits limitations similar to those observed in human experiments. Moreover, the model introduces a concise, normative definition of high level cognitive concepts such as working memory and cognitive control in terms of maximizing discounted future rewards."

Inspired by the hierarchical hidden Markov models (HHMM), we present the hierarchical semi-Markovconditional random field (HSCRF), a generalisation of embedded undirected Markov chains to model complex hierarchical, nested Markov processes. It is parameterised in a discriminative framework and has polynomial time algorithms for learning and inference. Importantly, we develop efficient algorithms forlearning and constrained inference in a partially-supervised setting, which is important issue in practice where labels can only be obtained sparsely. We demonstrate the HSCRF in two applications: (i) recognising human activities of daily living (ADLs) from indoor surveillance cameras, and (ii) noun-phrase chunking. We show that the HSCRF is capable of learning rich hierarchical models withreasonable accuracy in both fully and partially observed data cases.

We define a metric for measuring behavior similarity between states in a Markov decision process (MDP), which takes action similarity into account. We show that the kernel of our metric corresponds exactly to the classes of states defined by MDP homomorphisms (Ravindran & Barto, 2003). We prove that the difference inthe optimal value function of different states can be upper-bounded by the value of this metric, and that the bound is tighter than previous bounds provided bybisimulation metrics (Ferns et al. 2004, 2005). Our results hold both for discrete and for continuous actions. We provide an algorithm for constructing approximate homomorphisms, by using this metric to identify states that can be grouped together, as well as actions that can be matched. Previous research on this topic is based mainly on heuristics.

We present a novel mathematical formalism for the idea of a local model,'' a model of a potentially complex dynamical system that makes only certain predictions in only certain situations. As a result of its restricted responsibilities, a local model may be far simpler than a complete model of the system. We then show how one might combine several local models to produce a more detailed model. We demonstrate our ability to learn a collection of local models on a large-scale example and do a preliminary empirical comparison of learning a collection of local models and some other model learning methods."