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

A method is proposed for semiparametric estimation where parametric and nonparametric criteria are exploited in density estimation and unsupervised learning.

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.

In problems where input features have varying amounts of noise, using distinct regularization hyperparameters for different features provides an effective means of managing model complexity. While regularizers for neural networks and support vectormachines often rely on multiple hyperparameters, regularizers for structured prediction models (used in tasks such as sequence labeling or parsing) typicallyrely only on a single shared hyperparameter for all features. In this paper, we consider the problem of choosing regularization hyperparameters for log-linear models, a class of structured prediction probabilistic models which includes conditionalrandom fields (CRFs). Using an implicit differentiation trick, we derive an efficient gradient-based method for learning Gaussian regularization priors with multiple hyperparameters. In both simulations and the real-world task of computational RNA secondary structure prediction, we find that multiple hyperparameter learningcan provide a significant boost in accuracy compared to using only a single regularization hyperparameter.

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 investigate the problem of learning a widely-used latent-variable model - the Latent Dirichlet Allocation (LDA) or "topic" model - using distributed computation, whereeach of

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.

In bioinformatics it is often desirable to combine data from various measurement sources and thus structured feature vectors are to be analyzed that possess different intrinsic blocking characteristics (e.g., different patterns of missing values, observation noiselevels, effective intrinsic dimensionalities). We propose a new machine learning tool, heterogeneous component analysis (HCA), for feature extraction in order to better understand the factors that underlie such complex structured heterogeneous data. HCA is a linear block-wise sparse Bayesian PCA based not only on a probabilistic model with block-wise residual variance terms but also on a Bayesian treatment of a block-wise sparse factor-loading matrix. We study various algorithmsthat implement our HCA concept extracting sparse heterogeneous structure by obtaining common components for the blocks and specific components withineach block. Simulations on toy and bioinformatics data underline the usefulness of the proposed structured matrix factorization concept.