Long-distance language modeling is important not only in speech recognition and machine translation, but also in high-dimensional discrete sequence modeling in general. However, the problem of context length has almost been neglected so far and a naïve bag-of-words history has been employed in natural language processing. In contrast, in this paper we view topic shifts within a text as a latent stochastic process to give an explicit probabilistic generative model that has partial exchangeability. We propose an online inference algorithm using particle filters to recognize topic shifts to employ the most appropriate length of context automatically. Experiments on the BNC corpus showed consistent improvement over previous methods involving no chronological order.

Predictive state representations (PSRs) are a method of modeling dynamical systems using only observable data, such as actions and observations, to describe their model. PSRs use predictions about the outcome of future tests to summarize the system state. The best existing techniques for discovery and learning of PSRs use a Monte Carlo approach to explicitly estimate these outcome probabilities. In this paper, we present a new algorithm for discovery and learning of PSRs that uses a gradient descent approach to compute the predictions for the current state. The algorithm takes advantage of the large amount of structure inherent in a valid prediction matrix to constrain its predictions. Furthermore, the algorithm can be used online by an agent to constantly improve its prediction quality; something that current state of the art discovery and learning algorithms are unable to do. We give empirical results to show that our constrained gradient algorithm is able to discover core tests using very small amounts of data, and with larger amounts of data can compute accurate predictions of the system dynamics.

We investigate the problem of automatically constructing efficient representations or basis functions for approximating value functions based on analyzing the structure and topology of the state space. In particular, two novel approaches to value function approximation are explored based on automatically constructing basis functions on state spaces that can be represented as graphs or manifolds: one approach uses the eigenfunctions of the Laplacian, in effect performing a global Fourier analysis on the graph; the second approach is based on diffusion wavelets, which generalize classical wavelets to graphs using multiscale dilations induced by powers of a diffusion operator or random walk on the graph. Together, these approaches form the foundation of a new generation of methods for solving large Markov decision processes, in which the underlying representation and policies are simultaneously learned.

We study the statistical convergence and consistency of regularized Boosting methods, where the samples are not independent and identically distributed (i.i.d.) but come from empirical processes of stationary β-mixing sequences. Utilizing a technique that constructs a sequence of independent blocks close in distribution to the original samples, we prove the consistency of the composite classifiers resulting from a regularization achieved by restricting the 1-norm of the base classifiers' weights. When compared to the i.i.d.

A standard method to obtain stochastic models for symbolic time series is to train state-emitting hidden Markov models (SE-HMMs) with the Baum-Welch algorithm. Based on observable operator models (OOMs), in the last few months a number of novel learning algorithms for similar purposes have been developed: (1,2) two versions of an "efficiency sharpening" (ES) algorithm, which iteratively improves the statistical efficiency of a sequence of OOM estimators, (3) a constrained gradient descent ML estimator for transition-emitting HMMs (TE-HMMs). We give an overview on these algorithms and compare them with SE-HMM/EM learning on synthetic and real-life data.

We develop an approach for estimation with Gaussian Markov processes that imposes a smoothness prior while allowing for discontinuities. Instead of propagating information laterally between neighboring nodes in a graph, we study the posterior distribution of the hidden nodes as a whole--how it is perturbed by invoking discontinuities, or weakening the edges, in the graph. We show that the resulting computation amounts to feed-forward fan-in operations reminiscent of V1 neurons. Moreover, using suitable matrix preconditioners, the incurred matrix inverse and determinant can be approximated, without iteration, in the same computational style. Simulation results illustrate the merits of this approach.

This paper presents a new sampling algorithm for approximating functions of variables representable as undirected graphical models of arbitrary connectivity with pairwise potentials, as well as for estimating the notoriously difficult partition function of the graph. The algorithm fits into the framework of sequential Monte Carlo methods rather than the more widely used MCMC, and relies on constructing a sequence of intermediate distributions which get closer to the desired one. While the idea of using "tempered" proposals is known, we construct a novel sequence of target distributions where, rather than dropping a global temperature parameter, we sequentially couple individual pairs of variables that are, initially, sampled exactly from a spanning tree of the variables.

We introduce a method to automatically improve character models for a handwritten script without the use of transcriptions and using a minimum of document specific training data. We show that we can use searches for the words in a dictionary to identify portions of the document whose transcriptions are unambiguous. Using templates extracted from those regions, we retrain our character prediction model to drastically improve our search retrieval performance for words in the document.

This paper describes a highly successful application of MRFs to the problem of generating high-resolution range images. A new generation of range sensors combines the capture of low-resolution range images with the acquisition of registered high-resolution camera images. The MRF in this paper exploits the fact that discontinuities in range and coloring tend to co-align. This enables it to generate high-resolution, low-noise range images by integrating regular camera images into the range data. We show that by using such an MRF, we can substantially improve over existing range imaging technology.

Neurons can have rapidly changing spike train statistics dictated by the underlying network excitability or behavioural state of an animal. To estimate the time course of such state dynamics from single-or multiple neuron recordings, we have developed an algorithm that maximizes the likelihood of observed spike trains by optimizing the state lifetimes and the state-conditional interspike-interval (ISI) distributions. Our nonparametric algorithm is free of time-binning and spike-counting problems and has the computational complexity of a Mixed-state Markov Model operating on a state sequence of length equal to the total number of recorded spikes. As an example, we fit a two-state model to paired recordings of premotor neurons in the sleeping songbird. We find that the two state-conditional ISI functions are highly similar to the ones measured during waking and singing, respectively.