In the superset label learning problem (SLL), each training instance provides a set of candidate labels of which one is the true label of the instance. As in ordinary regression, the candidate label set is a noisy version of the true label. In this work, we solve the problem by maximizing the likelihood of the candidate label sets of training instances. We propose a probabilistic model, the Logistic Stick-Breaking Conditional Multinomial Model (LSB-CMM), to do the job. The LSB-CMM is derived from the logistic stick-breaking process. It first maps data points to mixture components and then assigns to each mixture component a label drawn from a component-specific multinomial distribution.

The empirical success of the belief propagation approximate inference algorithm has inspired numerous theoretical and algorithmic advances. Yet, for continuous non-Gaussian domains performing belief propagation remains a challenging task: recent innovations such as nonparametric or kernel belief propagation, while useful, come with a substantial computational cost and offer little theoretical guarantees, even for tree structured models. In this work we present Nonparanormal BP for performing efficient inference on distributions parameterized by a Gaussian copulas network and any univariate marginals. For tree structured networks, our approach is guaranteed to be exact for this powerful class of non-Gaussian models. Importantly, the method is as efficient as standard Gaussian BP, and its convergence properties do not depend on the complexity of the univariate marginals, even when a nonparametric representation is used.

The representer theorem is a property that lies at the foundation of regularization theory and kernel methods. A class of regularization functionals is said to admit a linear representer theorem if every member of the class admits minimizers that lie in the finite dimensional subspace spanned by the representers of the data. A recent characterization states that certain classes of regularization functionals with differentiable regularization term admit a linear representer theorem for any choice of the data if and only if the regularization term is a radial nondecreasing function. In this paper, we extend such result by weakening the assumptions on the regularization term. In particular, the main result of this paper implies that, for a sufficiently large family of regularization functionals, radial nondecreasing functions are the only lower semicontinuous regularization terms that guarantee existence of a representer theorem for any choice of the data.

The accurate prediction of molecular energetics in chemical compound space is a crucial ingredient for rational compound design. The inherently graph-like, non-vectorial nature of molecular data gives rise to a unique and difficult machine learning problem. In this paper, we adopt a learning-from-scratch approach where quantum-mechanical molecular energies are predicted directly from the raw molecular geometry. The study suggests a benefit from setting flexible priors and enforcing invariance stochastically rather than structurally. Our results improve the state-of-the-art by a factor of almost three, bringing statistical methods one step closer to the holy grail of ''chemical accuracy''.

Approaches to audio classification and retrieval tasks largely rely on detection-based discriminative models. We submit that such models make a simplistic assumption in mapping acoustics directly to semantics, whereas the actual process is likely more complex. We present a generative model that maps acoustics in a hierarchical manner to increasingly higher-level semantics. Our model has 2 layers with the first being generic sound units with no clear semantic associations, while the second layer attempts to find patterns over the generic sound units. We evaluate our model on a large-scale retrieval task from TRECVID 2011, and report significant improvements over standard baselines.

We derive sublinear regret bounds for undiscounted reinforcement learning in continuous state space. The proposed algorithm combines state aggregation with the use of upper confidence bounds for implementing optimism in the face of uncertainty. Beside the existence of an optimal policy which satisfies the Poisson equation, the only assumptions made are Hoelder continuity of rewards and transition probabilities.

A common challenge for Bayesian models of perception is the fact that the two fundamental Bayesian components, the prior distribution and the likelihood function, areformally unconstrained. Here we argue that a neural system that emulates Bayesian inference is naturally constrained by the way it represents sensory information inpopulations of neurons. More specifically, we show that an efficient coding principle creates a direct link between prior and likelihood based on the underlying stimulus distribution. The resulting Bayesian estimates can show biases awayfrom the peaks of the prior distribution, a behavior seemingly at odds with the traditional view of Bayesian estimation, yet one that has been reported in human perception. We demonstrate that our framework correctly accounts for the repulsive biases previously reported for the perception of visual orientation, and show that the predicted tuning characteristics of the model neurons match the reported orientation tuning properties of neurons in primary visual cortex. Our results suggest that efficient coding is a promising hypothesis in constraining Bayesianmodels of perceptual inference.

Topic modeling is a widely used approach to analyzing large text collections. A small number of multilingual topic models have recently been explored to discover latent topics among parallel or comparable documents, such as in Wikipedia. Other topic models that were originally proposed for structured data are also applicable to multilingual documents. Correspondence Latent Dirichlet Allocation (CorrLDA) is one such model; however, it requires a pivot language to be specified in advance. We propose a new topic model, Symmetric Correspondence LDA (SymCorrLDA), that incorporates a hidden variable to control a pivot language, in an extension of CorrLDA. We experimented with two multilingual comparable datasets extracted from Wikipedia and demonstrate that SymCorrLDA is more effective than some other existing multilingual topic models.

Links between probabilistic and non-probabilistic learning algorithms can arise by performing small-variance asymptotics, i.e., letting the variance of particular distributions in a graphical model go to zero. For instance, in the context of clustering, such an approach yields precise connections between the k-means and EM algorithms. In this paper, we explore small-variance asymptotics for exponential family Dirichlet process (DP) and hierarchical Dirichlet process (HDP) mixture models. Utilizing connections between exponential family distributions and Bregman divergences, we derive novel clustering algorithms from the asymptotic limit of the DP and HDP mixtures that feature the scalability of existing hard clustering methods as well as the flexibility of Bayesian nonparametric models. We focus on special cases of our analysis for discrete-data problems, including topic modeling, and we demonstrate the utility of our results by applying variants of our algorithms to problems arising in vision and document analysis.

In categorical data there is often structure in the number of variables that take on each label. For example, the total number of objects in an image and the number of highly relevant documents per query in web search both tend to follow a structured distribution. In this paper, we study a probabilistic model that explicitly includes a prior distribution over such counts, along with a count-conditional likelihood that defines probabilities over all subsets of a given size. When labels are binary and the prior over counts is a Poisson-Binomial distribution, a standard logistic regression model is recovered, but for other count distributions, such priors induce global dependencies and combinatorics that appear to complicate learning and inference. However, we demonstrate that simple, efficient learning procedures can be derived for more general forms of this model. We illustrate the utility of the formulation by exploring applications to multi-object classification, learning to rank, and top-K classification.