We investigate quantile regression based on the pinball loss and the ǫ-insensitive loss.

A wide variety of Dirichlet-multinomial'topic' models have found interesting applications in recent years. While Gibbs sampling remains an important method of inference in such models, variational techniques have certain advantages such as easy assessment of convergence, easy optimization without the need to maintain detailed balance, a bound on the marginal likelihood, and sidestepping of issues with topic-identifiability. The most accurate variational technique thus far, namely collapsed variational latent Dirichlet allocation, did not deal with model selection nor did it include inference for hyperparameters. We address both issues by generalizing the technique, obtaining the first variational algorithm to deal with the hierarchical Dirichlet process and to deal with hyperparameters of Dirichlet variables. Experiments show a significant improvement in accuracy.

Semi-supervised methods use unlabeled data in addition to labeled data to construct predictors. While existing semi-supervised methods have shown some promising empirical performance, their development has been based largely based on heuristics. In this paper we study semi-supervised learning from the viewpoint of minimax theory. Our first result shows that some common methods based on regularization using graph Laplacians do not lead to faster minimax rates of convergence. Thus, the estimators that use the unlabeled data do not have smaller risk than the estimators that use only labeled data. We then develop several new approaches that provably lead to improved performance. The statistical tools of minimax analysis are thus used to offer some new perspective on the problem of semi-supervised learning.

Many tasks (e.g., clustering) in machine learning only require the l

We derive an equation for temporal difference learning from statistical principles. Specifically, we start with the variational principle and then bootstrap to produce an updating rule for discounted state value estimates. The resulting equation is similar to the standard equation for temporal difference learning with eligibility traces, so called TD(λ), however it lacks the parameter α that specifies the learning rate. In the place of this free parameter there is now an equation for the learning rate that is specific to each state transition. We experimentally test this new learning rule against TD(λ) and find that it offers superior performance in various settings. Finally, we make some preliminary investigations into how to extend our new temporal difference algorithm to reinforcement learning. To do this we combine our update equation with both Watkins' Q(λ) and Sarsa(λ) and find that it again offers superior performance without a learning rate parameter.

We present a nonparametric Bayesian method of estimating variable order Markov processes up to a theoretically infinite order. By extending a stick-breaking prior, which is usually defined on a unit interval, "vertically" to the trees of infinite depth associated with a hierarchical Chinese restaurant process, our model directly infers the hidden orders of Markov dependencies from which each symbol originated. Experiments on character and word sequences in natural language showed that the model has a comparative performance with an exponentially large full-order model, while computationally much efficient in both time and space. We expect that this basic model will also extend to the variable order hierarchical clustering of general data.

When predicting class labels for objects within a relational database, it is often helpful to consider a model for relationships: this allows for information between class labels to be shared and to improve prediction performance. However, there are different ways by which objects can be related within a relational database. One traditional way corresponds to a Markov network structure: each existing relation is represented by an undirected edge. This encodes that, conditioned on input features, each object label is independent of other object labels given its neighbors in the graph. However, there is no reason why Markov networks should be the only representation of choice for symmetric dependence structures. Here we discuss the case when relationships are postulated to exist due to hidden common causes. We discuss how the resulting graphical model differs from Markov networks, and how it describes different types of real-world relational processes. A Bayesian nonparametric classification model is built upon this graphical representation and evaluated with several empirical studies.

Maximum entropy analysis of binary variables provides an elegant way for studying the role of pairwise correlations in neural populations. Unfortunately, these approaches suffer from their poor scalability to high dimensions. In sensory coding, however, high-dimensional data is ubiquitous. Here, we introduce a new approach using a near-maximum entropy model, that makes this type of analysis feasible for very high-dimensional data--the model parameters can be derived in closed form and sampling is easy. Therefore, our NearMaxEnt approach can serve as a tool for testing predictions from a pairwise maximum entropy model not only for low-dimensional marginals, but also for high dimensional measurements of more than thousand units. We demonstrate its usefulness by studying natural images with dichotomized pixel intensities. Our results indicate that the statistics of such higher-dimensional measurements exhibit additional structure that are not predicted by pairwise correlations, despite the fact that pairwise correlations explain the lower-dimensional marginal statistics surprisingly well up to the limit of dimensionality where estimation of the full joint distribution is feasible.

The problem of obtaining the maximum a posteriori estimate of a general discrete random field (i.e. a random field defined using a finite and discrete set of labels) is known to be

Bayesian model averaging, model selection and their approximations such as BIC are generally statistically consistent, but sometimes achieve slower rates of convergence than other 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. Based on 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.