We show how to learn a Mahanalobis distance metric for k-nearest neighbor (kNN) classification by semidefinite programming. The metric is trained with the goal that the k-nearest neighbors always belong to the same class while examples from different classes are separated by a large margin. On seven data sets of varying size and difficulty, we find that metrics trained in this way lead to significant improvements in kNN classification--for example, achieving a test error rate of 1.3% on the MNIST handwritten digits. As in support vector machines (SVMs), the learning problem reduces to a convex optimization based on the hinge loss. Unlike learning in SVMs, however, our framework requires no modification or extension for problems in multiway (as opposed to binary) classification.

We present a probabilistic generative model of entity relationships and their attributes that simultaneously discovers groups among the entities and topics among the corresponding textual attributes. Block-models of relationship data have been studied in social network analysis for some time. Here we simultaneously cluster in several modalities at once, incorporating the attributes (here, words) associated with certain relationships. Significantly, joint inference allows the discovery of topics to be guided by the emerging groups, and vice-versa. We present experimental results on two large data sets: sixteen years of bills put before the U.S. Senate, comprising their corresponding text and voting records, and thirteen years of similar data from the United Nations. We show that in comparison with traditional, separate latent-variable models for words, or Blockstructures for votes, the Group-Topic model's joint inference discovers more cohesive groups and improved topics.

Consider the problem of joint parameter estimation and prediction in a Markov random field: i.e., the model parameters are estimated on the basis of an initial set of data, and then the fitted model is used to perform prediction (e.g., smoothing, denoising, interpolation) on a new noisy observation. Working in the computation-limited setting, we analyze a joint method in which the same convex variational relaxation is used to construct an M-estimator for fitting parameters, and to perform approximate marginalization for the prediction step. The key result of this paper is that in the computation-limited setting, using an inconsistent parameter estimator (i.e., an estimator that returns the "wrong" model even in the infinite data limit) is provably beneficial, since the resulting errors can partially compensate for errors made by using an approximate prediction technique. En route to this result, we analyze the asymptotic properties of M-estimators based on convex variational relaxations, and establish a Lipschitz stability property that holds for a broad class of variational methods. We show that joint estimation/prediction based on the reweighted sum-product algorithm substantially outperforms a commonly used heuristic based on ordinary sum-product.

We determine the asymptotic limit of the function computed by support vector machines (SVM) and related algorithms that minimize a regularized empirical convex loss function in the reproducing kernel Hilbert space of the Gaussian RBF kernel, in the situation where the number of examples tends to infinity, the bandwidth of the Gaussian kernel tends to 0, and the regularization parameter is held fixed.

We consider approximate value iteration with a parameterized approximator in which the state space is partitioned and the optimal cost-to-go function over each partition is approximated by a constant. We establish performance loss bounds for policies derived from approximations associated with fixed points. These bounds identify benefits to having projection weights equal to the invariant distribution of the resulting policy. Such projection weighting leads to the same fixed points as TD(0). Our analysis also leads to the first performance loss bound for approximate value iteration with an average cost objective.

An increasing number of projects in neuroscience requires the statistical analysis of high dimensional data sets, as, for instance, in predicting behavior from neural firing or in operating artificial devices from brain recordings in brain-machine interfaces. Linear analysis techniques remain prevalent in such cases, but classical linear regression approaches are often numerically too fragile in high dimensions. In this paper, we address the question of whether EMG data collected from arm movements of monkeys can be faithfully reconstructed with linear approaches from neural activity in primary motor cortex (M1). To achieve robust data analysis, we develop a full Bayesian approach to linear regression that automatically detects and excludes irrelevant features in the data, regularizing against overfitting. In comparison with ordinary least squares, stepwise regression, partial least squares, LASSO regression and a brute force combinatorial search for the most predictive input features in the data, we demonstrate that the new Bayesian method offers a superior mixture of characteristics in terms of regularization against overfitting, computational efficiency and ease of use, demonstrating its potential as a drop-in replacement for other linear regression techniques. As neuroscientific results, our analyses demonstrate that EMG data can be well predicted from M1 neurons, further opening the path for possible real-time interfaces between brains and machines.

We present a simple and scalable algorithm for large-margin estimation of structured models, including an important class of Markov networks and combinatorial models. We formulate the estimation problem as a convex-concave saddle-point problem and apply the extragradient method, yielding an algorithm with linear convergence using simple gradient and projection calculations. The projection step can be solved using combinatorial algorithms for min-cost quadratic flow. This makes the approach an efficient alternative to formulations based on reductions to a quadratic program (QP). We present experiments on two very different structured prediction tasks: 3D image segmentation and word alignment, illustrating the favorable scaling properties of our algorithm.

This paper proposes a new approach to feature selection based on a statistical feature mining technique for sequence and tree kernels. Since natural language data take discrete structures, convolution kernels, such as sequence and tree kernels, are advantageous for both the concept and accuracy of many natural language processing tasks. However, experiments have shown that the best results can only be achieved when limited small substructures are dealt with by these kernels. This paper discusses this issue of convolution kernels and then proposes a statistical feature selection that enable us to use larger substructures effectively. The proposed method, in order to execute efficiently, can be embedded into an original kernel calculation process by using substructure mining algorithms. Experiments on real NLP tasks confirm the problem in the conventional method and compare the performance of a conventional method to that of the proposed method.

Motivated by the problem of learning to detect and recognize objects with minimal supervision, we develop a hierarchical probabilistic model for the spatial structure of visual scenes. In contrast with most existing models, our approach explicitly captures uncertainty in the number of object instances depicted in a given image. Our scene model is based on the transformed Dirichlet process (TDP), a novel extension of the hierarchical DP in which a set of stochastically transformed mixture components are shared between multiple groups of data. For visual scenes, mixture components describe the spatial structure of visual features in an object-centered coordinate frame, while transformations model the object positions in a particular image. Learning and inference in the TDP, which has many potential applications beyond computer vision, is based on an empirically effective Gibbs sampler. Applied to a dataset of partially labeled street scenes, we show that the TDP's inclusion of spatial structure improves detection performance, flexibly exploiting partially labeled training images.

While classical kernel-based learning algorithms are based on a single kernel, in practice it is often desirable to use multiple kernels. Lankriet et al. (2004) considered conic combinations of kernel matrices for classification, leading to a convex quadratically constraint quadratic program. We show that it can be rewritten as a semi-infinite linear program that can be efficiently solved by recycling the standard SVM implementations. Moreover, we generalize the formulation and our method to a larger class of problems, including regression and one-class classification. Experimental results show that the proposed algorithm helps for automatic model selection, improving the interpretability of the learning result and works for hundred thousands of examples or hundreds of kernels to be combined.