Statistical models on full and partial rankings of n items are often of limited practical use for large n due to computational consideration. We explore the use of nonparametric models for partially ranked data and derive efficient procedures for their use for large n. The derivations are largely possible through combinatorial and algebraic manipulations based on the lattice of partial rankings. In particular, we demonstrate for the first time a nonparametric coherent and consistent model capable of efficiently aggregating partially ranked data of different types.

Learning in real-world domains often requires to deal with continuous state and action spaces. Although many solutions have been proposed to apply Reinforcement Learning algorithms to continuous state problems, the same techniques can be hardly extended to continuous action spaces, where, besides the computation of a good approximation of the value function, a fast method for the identification of the highest-valued action is needed. In this paper, we propose a novel actor-critic approach in which the policy of the actor is estimated through sequential Monte Carlo methods. The importance sampling step is performed on the basis of the values learned by the critic, while the resampling step modifies the actor's policy. The proposed approach has been empirically compared to other learning algorithms into several domains; in this paper, we report results obtained in a control problem consisting of steering a boat across a river.

Clustering is often formulated as the maximum likelihood estimation of a mixture model that explains the data. The EM algorithm widely used to solve the resulting optimization problem is inherently a gradient-descent method and is sensitive to initialization. The resulting solution is a local optimum in the neighborhood of the initial guess. This sensitivity to initialization presents a significant challenge in clustering large data sets into many clusters. In this paper, we present a different approach to approximate mixture fitting for clustering. We introduce an exemplar-based likelihood function that approximates the exact likelihood. This formulation leads to a convex minimization problem and an efficient algorithm with guaranteed convergence to the globally optimal solution. The resulting clustering can be thought of as a probabilistic mapping of the data points to the set of exemplars that minimizes the average distance and the information-theoretic cost of mapping.

We extend position and phase-shift tuning, concepts already well established in the disparity energy neuron literature, to motion energy neurons. We show that Reichardt-like detectors can be considered examples of position tuning, and that motion energy filters whose complex valued spatiotemporal receptive fields are space-time separable can be considered examples of phase tuning. By combining these two types of detectors, we obtain an architecture for constructing motion energy neurons whose center frequencies can be adjusted by both phase and position shifts. Similar to recently described neurons in the primary visual cortex, these new motion energy neurons exhibit tuning that is between purely spacetime separable and purely speed tuned. We propose a functional role for this intermediate level of tuning by demonstrating that comparisons between pairs of these motion energy neurons can reliably discriminate between inputs whose velocities lie above or below a given reference velocity.

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.

In many structured prediction problems, the highest-scoring labeling is hard to compute exactly, leading to the use of approximate inference methods. However, when inference is used in a learning algorithm, a good approximation of the score may not be sufficient. We show in particular that learning can fail even with an approximate inference method with rigorous approximation guarantees. There are two reasons for this. First, approximate methods can effectively reduce the expressivity of an underlying model by making it impossible to choose parameters that reliably give good predictions. Second, approximations can respond to parameter changes in such a way that standard learning algorithms are misled. In contrast, we give two positive results in the form of learning bounds for the use of LPrelaxed inference in structured perceptron and empirical risk minimization settings. We argue that without understanding combinations of inference and learning, such as these, that are appropriately compatible, learning performance under approximate inference cannot be guaranteed.

In many applications, one has to actively select among a set of expensive observations before making an informed decision. Often, we want to select observations which perform well when evaluated with an objective function chosen by an adversary. Examples include minimizing the maximum posterior variance in Gaussian Process regression, robust experimental design, and sensor placement for outbreak detection. In this paper, we present the Submodular Saturation algorithm, a simple and efficient algorithm with strong theoretical approximation guarantees for the case where the possible objective functions exhibit submodularity, an intuitive diminishing returns property. Moreover, we prove that better approximation algorithms do not exist unless NPcomplete problems admit efficient algorithms. We evaluate our algorithm on several real-world problems. For Gaussian Process regression, our algorithm compares favorably with state-of-the-art heuristics described in the geostatistics literature, while being simpler, faster and providing theoretical guarantees. For robust experimental design, our algorithm performs favorably compared to SDP-based algorithms.

We consider apprenticeship learning--learning from expert demonstrations--in the setting of large, complex domains. Past work in apprenticeship learning requires that the expert demonstrate complete trajectories through the domain. However, in many problems even an expert has difficulty controlling the system, which makes this approach infeasible. For example, consider the task of teaching a quadruped robot to navigate over extreme terrain; demonstrating an optimal policy (i.e., an optimal set of foot locations over the entire terrain) is a highly nontrivial task, even for an expert. In this paper we propose a method for hierarchical apprenticeship learning, which allows the algorithm to accept isolated advice at different hierarchical levels of the control task. This type of advice is often feasible for experts to give, even if the expert is unable to demonstrate complete trajectories. This allows us to extend the apprenticeship learning paradigm to much larger, more challenging domains. In particular, in this paper we apply the hierarchical apprenticeship learning algorithm to the task of quadruped locomotion over extreme terrain, and achieve, to the best of our knowledge, results superior to any previously published work.

Much of human knowledge is organized into sophisticated systems that are often called intuitive theories. We propose that intuitive theories are mentally represented in a logical language, and that the subjective complexity of a theory is determined by the length of its representation in this language. This complexity measure helps to explain how theories are learned from relational data, and how they support inductive inferences about unobserved relations. We describe two experiments that test our approach, and show that it provides a better account of human learning and reasoning than an approach developed by Goodman [1]. What is a theory, and what makes one theory better than another?

We provide provably privacy-preserving versions of belief propagation, Gibbs sampling, and other local algorithms -- distributed multiparty protocols in which each party or vertex learns only its final local value, and absolutely nothing else.