In most papers establishing consistency for learning algorithms it is assumed that the observations used for training are realizations of an i.i.d. process. In this paper we go far beyond this classical framework by showing that support vector machines (SVMs) essentially only require that the data-generating process satisfies a certain law of large numbers. We then consider the learnability of SVMs for $\a$-mixing (not necessarily stationary) processes for both classification and regression, where for the latter we explicitly allow unbounded noise.

The distance metric plays an important role in nearest neighbor (NN) classification. Usually the Euclidean distance metric is assumed or a Mahalanobis distance metric is optimized to improve the NN performance. In this paper, we study the problem of embedding arbitrary metric spaces into a Euclidean space with the goal to improve the accuracy of the NN classifier. We propose a solution by appealing to the framework of regularization in a reproducing kernel Hilbert space and prove a representer-like theorem for NN classification. The embedding function is then determined by solving a semidefinite program which has an interesting connection to the soft-margin linear binary support vector machine classifier. Although the main focus of this paper is to present a general, theoretical framework for metric embedding in a NN setting, we demonstrate the performance of the proposed method on some benchmark datasets and show that it performs better than the Mahalanobis metric learning algorithm in terms of leave-one-out and generalization errors.

Conformal prediction uses past experience to determine precise levels of confidence in new predictions. Given an error probability $\epsilon$, together with a method that makes a prediction $\hat{y}$ of a label $y$, it produces a set of labels, typically containing $\hat{y}$, that also contains $y$ with probability $1-\epsilon$. Conformal prediction can be applied to any method for producing $\hat{y}$: a nearest-neighbor method, a support-vector machine, ridge regression, etc. Conformal prediction is designed for an on-line setting in which labels are predicted successively, each one being revealed before the next is predicted. The most novel and valuable feature of conformal prediction is that if the successive examples are sampled independently from the same distribution, then the successive predictions will be right $1-\epsilon$ of the time, even though they are based on an accumulating dataset rather than on independent datasets. In addition to the model under which successive examples are sampled independently, other on-line compression models can also use conformal prediction. The widely used Gaussian linear model is one of these. This tutorial presents a self-contained account of the theory of conformal prediction and works through several numerical examples. A more comprehensive treatment of the topic is provided in "Algorithmic Learning in a Random World", by Vladimir Vovk, Alex Gammerman, and Glenn Shafer (Springer, 2005).

This paper introduces and analyzes a battery of inference models for the problem of semantic role labeling: one based on constraint satisfaction, and several strategies that model the inference as a meta-learning problem using discriminative classifiers. These classifiers are developed with a rich set of novel features that encode proposition and sentence-level information. To our knowledge, this is the first work that: (a) performs a thorough analysis of learning-based inference models for semantic role labeling, and (b) compares several inference strategies in this context. We evaluate the proposed inference strategies in the framework of the CoNLL-2005 shared task using only automatically-generated syntactic information. The extensive experimental evaluation and analysis indicates that all the proposed inference strategies are successful -they all outperform the current best results reported in the CoNLL-2005 evaluation exercise- but each of the proposed approaches has its advantages and disadvantages. Several important traits of a state-of-the-art SRL combination strategy emerge from this analysis: (i) individual models should be combined at the granularity of candidate arguments rather than at the granularity of complete solutions; (ii) the best combination strategy uses an inference model based in learning; and (iii) the learning-based inference benefits from max-margin classifiers and global feedback.

In the process of training Support Vector Machines (SVMs) by decomposition methods, working set selection is an important technique, and some exciting schemes were employed into this field. To improve working set selection, we propose a new model for working set selection in sequential minimal optimization (SMO) decomposition methods. In this model, it selects B as working set without reselection. Some properties are given by simple proof, and experiments demonstrate that the proposed method is in general faster than existing methods.

Observations consisting of measurements on relationships for pairs of objects arise in many settings, such as protein interaction and gene regulatory networks, collections of author-recipient email, and social networks. Analyzing such data with probabilisic models can be delicate because the simple exchangeability assumptions underlying many boilerplate models no longer hold. In this paper, we describe a latent variable model of such data called the mixed membership stochastic blockmodel. This model extends blockmodels for relational data to ones which capture mixed membership latent relational structure, thus providing an object-specific low-dimensional representation. We develop a general variational inference algorithm for fast approximate posterior inference. We explore applications to social and protein interaction networks.

Words and phrases acquire meaning from the way they are used in society, from their relative semantics to other words and phrases. For computers the equivalent of `society' is `database,' and the equivalent of `use' is `way to search the database.' We present a new theory of similarity between words and phrases based on information distance and Kolmogorov complexity. To fix thoughts we use the world-wide-web as database, and Google as search engine. The method is also applicable to other search engines and databases. This theory is then applied to construct a method to automatically extract similarity, the Google similarity distance, of words and phrases from the world-wide-web using Google page counts. The world-wide-web is the largest database on earth, and the context information entered by millions of independent users averages out to provide automatic semantics of useful quality. We give applications in hierarchical clustering, classification, and language translation. We give examples to distinguish between colors and numbers, cluster names of paintings by 17th century Dutch masters and names of books by English novelists, the ability to understand emergencies, and primes, and we demonstrate the ability to do a simple automatic English-Spanish translation. Finally, we use the WordNet database as an objective baseline against which to judge the performance of our method. We conduct a massive randomized trial in binary classification using support vector machines to learn categories based on our Google distance, resulting in an a mean agreement of 87% with the expert crafted WordNet categories.

Cluster matching by permuting cluster labels is important in many clustering contexts such as cluster validation and cluster ensemble techniques. The classic approach is to minimize the euclidean distance between two cluster solutions which induces inappropriate stability in certain settings. Therefore, we present the truematch algorithm that introduces two improvements best explained in the crisp case. First, instead of maximizing the trace of the cluster crosstable, we propose to maximize a chi-square transformation of this crosstable. Thus, the trace will not be dominated by the cells with the largest counts but by the cells with the most non-random observations, taking into account the marginals. Second, we suggest a probabilistic component in order to break ties and to make the matching algorithm truly random on random data. The truematch algorithm is designed as a building block of the truecluster framework and scales in polynomial time. First simulation results confirm that the truematch algorithm gives more consistent truecluster results for unequal cluster sizes. Free R software is available.

Data-based classification is fundamental to most branches of science. While recent years have brought enormous progress in various areas of statistical computing and clustering, some general challenges in clustering remain: model selection, robustness, and scalability to large datasets. We consider the important problem of deciding on the optimal number of clusters, given an arbitrary definition of space and clusteriness. We show how to construct a cluster information criterion that allows objective model selection. Differing from other approaches, our truecluster method does not require specific assumptions about underlying distributions, dissimilarity definitions or cluster models. Truecluster puts arbitrary clustering algorithms into a generic unified (sampling-based) statistical framework. It is scalable to big datasets and provides robust cluster assignments and case-wise diagnostics. Truecluster will make clustering more objective, allows for automation, and will save time and costs. Free R software is available.

We introduce the blind subspace deconvolution (BSSD) problem, which is the extension of both the blind source deconvolution (BSD) and the independent subspace analysis (ISA) tasks. We examine the case of the undercomplete BSSD (uBSSD). Applying temporal concatenation we reduce this problem to ISA. The associated `high dimensional' ISA problem can be handled by a recent technique called joint f-decorrelation (JFD). Similar decorrelation methods have been used previously for kernel independent component analysis (kernel-ICA). More precisely, the kernel canonical correlation (KCCA) technique is a member of this family, and, as is shown in this paper, the kernel generalized variance (KGV) method can also be seen as a decorrelation method in the feature space. These kernel based algorithms will be adapted to the ISA task. In the numerical examples, we (i) examine how efficiently the emerging higher dimensional ISA tasks can be tackled, and (ii) explore the working and advantages of the derived kernel-ISA methods.