When the distribution of unlabeled data in feature space lies along a manifold, the information it provides may be used by a learner to assist classification in a semi-supervised setting. While manifold learning is well-known in machine learning, the use of manifolds in human learning is largely unstudied. We perform a set of experiments which test a human's ability to use a manifold in a semi-supervised learning task, under varying conditions. We show that humans may be encouraged into using the manifold, overcoming the strong preference for a simple, axis-parallel linear boundary.

We develop an online variational Bayes (VB) algorithm for Latent Dirichlet Allocation (LDA). Online LDA is based on online stochastic optimization with a natural gradient step, which we show converges to a local optimum of the VB objective function. It can handily analyze massive document collections, including those arriving in a stream. We study the performance of online LDA in several ways, including by fitting a 100-topic topic model to 3.3M articles from Wikipedia in a single pass. We demonstrate that online LDA finds topic models as good or better than those found with batch VB, and in a fraction of the time.

This paper is concerned with the generalization analysis on learning to rank for information retrieval (IR). In IR, data are hierarchically organized, i.e., consisting of queries and documents per query. Previous generalization analysis for ranking, however, has not fully considered this structure, and cannot explain how the simultaneous change of query number and document number in the training data will affect the performance of algorithms. In this paper, we propose performing generalization analysis under the assumption of two-layer sampling, i.e., the i.i.d. sampling of queries and the conditional i.i.d sampling of documents per query. Such a sampling can better describe the generation mechanism of real data, and the corresponding generalization analysis can better explain the real behaviors of learning to rank algorithms. However, it is challenging to perform such analysis, because the documents associated with different queries are not identically distributed, and the documents associated with the same query become no longer independent if represented by features extracted from the matching between document and query. To tackle the challenge, we decompose the generalization error according to the two layers, and make use of the new concept of two-layer Rademacher average. The generalization bounds we obtained are quite intuitive and are in accordance with previous empirical studies on the performance of ranking algorithms.

We consider problems for which one has incomplete binary matrices that evolve with time (e.g., the votes of legislators on particular legislation, with each year characterized by a different such matrix). An objective of such analysis is to infer structure and inter-relationships underlying the matrices, here defined by latent features associated with each axis of the matrix. In addition, it is assumed that documents are available for the entities associated with at least one of the matrix axes. By jointly analyzing the matrices and documents, one may be used to inform the other within the analysis, and the model offers the opportunity to predict matrix values (e.g., votes) based only on an associated document (e.g., legislation). The research presented here merges two areas of machine-learning that have previously been investigated separately: incomplete-matrix analysis and topic modeling. The analysis is performed from a Bayesian perspective, with efficient inference constituted via Gibbs sampling. The framework is demonstrated by considering all voting data and available documents (legislation) during the 220-year lifetime of the United States Senate and House of Representatives.

This paper outlines a hierarchical Bayesian model for human category learning that learns both the organization of objects into categories, and the context in which this knowledge should be applied. The model is fit to multiple data sets, and provides a parsimonious method for describing how humans learn context specific conceptual representations.

The sequence memoizer is a model for sequence data with state-of-the-art performance on language modeling and compression. We propose a number of improvements to the model and inference algorithm, including an enlarged range of hyperparameters, a memory-efficient representation, and inference algorithms operating on the new representation. Our derivations are based on precise definitions of the various processes that will also allow us to provide an elementary proof of the mysterious" coagulation and fragmentation properties used in the original paper on the sequence memoizer by Wood et al. (2009). We present some experimental results supporting our improvements."

Lifted inference algorithms for representations that combine first-order logic and probabilistic graphical models have been the focus of much recent research. All lifted algorithms developed to date are based on the same underlying idea: take a standard probabilistic inference algorithm (e.g., variable elimination, belief propagation etc.) and improve its efficiency by exploiting repeated structure in the first-order model. In this paper, we propose an approach from the other side in that we use techniques from logic for probabilistic inference. In particular, we define a set of rules that look only at the logical representation to identify models for which exact efficient inference is possible. We show that our rules yield several new tractable classes that cannot be solved efficiently by any of the existing techniques.

Despite the ubiquity of clustering as a tool in unsupervised learning, there is not yet a consensus on a formal theory, and the vast majority of work in this direction has focused on unsupervised clustering. We study a recently proposed framework for supervised clustering where there is access to a teacher. We give an improved generic algorithm to cluster any concept class in that model. Our algorithm is query-efficient in the sense that it involves only a small amount of interaction with the teacher. We also present and study two natural generalizations of the model. The model assumes that the teacher response to the algorithm is perfect. We eliminate this limitation by proposing a noisy model and give an algorithm for clustering the class of intervals in this noisy model. We also propose a dynamic model where the teacher sees a random subset of the points. Finally, for datasets satisfying a spectrum of weak to strong properties, we give query bounds, and show that a class of clustering functions containing Single-Linkage will find the target clustering under the strongest property.

We consider the problem of reinforcement learning in high-dimensional spaces when the number of features is bigger than the number of samples. In particular, we study the least-squares temporal difference (LSTD) learning algorithm when a space of low dimension is generated with a random projection from a high-dimensional space. We provide a thorough theoretical analysis of the LSTD with random projections and derive performance bounds for the resulting algorithm. We also show how the error of LSTD with random projections is propagated through the iterations of a policy iteration algorithm and provide a performance bound for the resulting least-squares policy iteration (LSPI) algorithm.

The Random Projection Tree (RPTree) structures proposed in [Dasgupta-Freund-STOC-08] are space partitioning data structures that automatically adapt to various notions of intrinsic dimensionality of data. We prove new results for both the RPTree-Max and the RPTree-Mean data structures. Our result for RPTree-Max gives a near-optimal bound on the number of levels required by this data structure to reduce the size of its cells by a factor s >= 2. We also prove a packing lemma for this data structure. Our final result shows that low-dimensional manifolds possess bounded Local Covariance Dimension. As a consequence we show that RPTree-Mean adapts to manifold dimension as well.