We demonstrate that log-linear grammars with latent variables can be practically trained using discriminative methods. Central to efficient discriminative training is a hierarchical pruning procedure which allows feature expectations to be efficiently approximatedin a gradient-based procedure.

Bayesian model averaging, model selection and their approximations such as BIC are generally statistically consistent, but sometimes achieve slower rates of convergence thanother methods such as AIC and leave-one-out cross-validation. On the other hand, these other methods can be inconsistent. We identify the catchup phenomenon as a novel explanation for the slow convergence of Bayesian methods. Basedon this analysis we define the switch-distribution, a modification of the Bayesian model averaging distribution. We prove that in many situations model selection and prediction based on the switch-distribution is both consistent and achieves optimal convergence rates, thereby resolving the AIC-BIC dilemma. The method is practical; we give an efficient algorithm.

In order to represent state in controlled, partially observable, stochastic dynamical systems, some sort of sufficient statistic for history is necessary. Predictive representations ofstate (PSRs) capture state as statistics of the future. We introduce a new model of such systems called the "Exponential family PSR," which defines as state the time-varying parameters of an exponential family distribution which models n sequential observations in the future. This choice of state representation explicitly connects PSRs to state-of-the-art probabilistic modeling, which allows us to take advantage of current efforts in high-dimensional density estimation, and in particular, graphical models and maximum entropy models. We present a parameter learningalgorithm based on maximum likelihood, and we show how a variety of current approximate inference methods apply. We evaluate the quality ofour model with reinforcement learning by directly evaluating the control performance of the model.

For infants, early word learning is a chicken-and-egg problem.

The model is based on a construction of tree-structured copulas -- multivariate distributions with uniform on [07 1] marginals.

When training and test samples follow different input distributions (i.e., the situation called \emph{covariate shift}), the maximum likelihood estimator is known to lose its consistency. For regaining consistency, the log-likelihood terms need to be weighted according to the \emph{importance} (i.e., the ratio of test and training input densities). Thus, accurately estimating the importance is one of the key tasks in covariate shift adaptation. A naive approach is to first estimate training and test input densities and then estimate the importance by the ratio of the density estimates. However, since density estimation is a hard problem, this approach tends to perform poorly especially in high dimensional cases. In this paper, we propose a direct importance estimation method that does not require the input density estimates. Our method is equipped with a natural model selection procedure so tuning parameters such as the kernel width can be objectively optimized. This is an advantage over a recently developed method of direct importance estimation. Simulations illustrate the usefulness of our approach.

We propose an extended probabilistic model for human perception. We argue that in many circumstances, human observers simultaneously evaluate sensory evidence under different hypotheses regarding the underlying physical process that might have generated the sensory information. Within this context, inference can be optimal if the observer weighs each hypothesis according to the correct belief in that hypothesis. But if the observer commits to a particular hypothesis, the belief in that hypothesis is converted into subjective certainty, and subsequent perceptual behavior is suboptimal, conditioned only on the chosen hypothesis. We demonstrate that this framework can explain psychophysical data of a recently reported decision-estimation experiment. The model well accounts for the data, predicting the same estimation bias as a consequence of the preceding decision step. The power of the framework is that it has no free parameters except the degree of the observer's uncertainty about its internal sensory representation. All other parameters are defined by the particular experiment which allows us to make quantitative predictions of human perception to two modifications of the original experiment.

Automatic relevance determination (ARD), and the closely-related sparse Bayesian learning (SBL) framework, are effective tools for pruning large numbers of irrelevant features. However, popular update rules used for this process are either prohibitively slow in practice and/or heuristic in nature without proven convergence properties. This paper furnishes an alternative means of optimizing a general ARD cost function using an auxiliary function that can naturally be solved using a series of re-weighted L1 problems. The result is an efficient algorithm that can be implemented using standard convex programming toolboxes and is guaranteed to converge to a stationary point unlike existing methods. The analysis also leads to additional insights into the behavior of previous ARD updates as well as the ARD cost function. For example, the standard fixed-point updates of MacKay (1992) are shown to be iteratively solving a particular min-max problem, although they are not guaranteed to lead to a stationary point. The analysis also reveals that ARD is exactly equivalent to performing MAP estimation using a particular feature- and noise-dependent \textit{non-factorial} weight prior with several desirable properties over conventional priors with respect to feature selection. In particular, it provides a tighter approximation to the L0 quasi-norm sparsity measure than the L1 norm. Overall these results suggests alternative cost functions and update procedures for selecting features and promoting sparse solutions.

We introduce supervised latent Dirichlet allocation (sLDA), a statistical model of labelled documents. The model accommodates a variety of response types. We derive a maximum-likelihood procedure for parameter estimation, which relies on variational approximations to handle intractable posterior expectations. Prediction problems motivate this research: we use the fitted model to predict response values for new documents. We test sLDA on two real-world problems: movie ratings predicted from reviews, and web page popularity predicted from text descriptions. We illustrate the benefits of sLDA versus modern regularized regression, as well as versus an unsupervised LDA analysis followed by a separate regression.

We investigate a new, convex relaxation of an expectation-maximization (EM) variant that approximates a standard objective while eliminating local minima. First, a cautionary result is presented, showing that any convex relaxation of EM over hidden variables must give trivial results if any dependence on the missing values is retained. Although this appears to be a strong negative outcome, we then demonstrate how the problem can be bypassed by using equivalence relations instead ofvalue assignments over hidden variables. In particular, we develop new algorithms for estimating exponential conditional models that only require equivalence relationinformation over the variable values. This reformulation leads to an exact expression for EM variants in a wide range of problems. We then develop a semidefinite relaxation that yields global training by eliminating local minima.