Semi-supervised inductive learning concerns how to learn a decision rule from a data set containing both labeled and unlabeled data. Several boosting algorithms have been extended to semi-supervised learning with various strategies. To our knowledge, however, none of them takes local smoothness constraints among data into account during ensemble learning. In this paper, we introduce a local smoothness regularizer to semi-supervised boosting algorithms based on the universal optimization framework of margin cost functionals. Our regularizer is applicable to existing semi-supervised boosting algorithms to improve their generalization and speed up their training.

Kernel supervised learning methods can be unified by utilizing the tools from regularization theory. The duality between regularization and prior leads to interpreting regularization methods in terms of maximum a posteriori estimation and has motivated Bayesian interpretations of kernel methods. In this paper we pursue a Bayesian interpretation of sparsity in the kernel setting by making use of a mixture of a point-mass distribution and prior that we refer to as Silverman's g-prior.'' We provide a theoretical analysis of the posterior consistency of a Bayesian model choice procedure based on this prior. We also establish the asymptotic relationship between this procedure and the Bayesian information criterion.

We propose a novel information theoretic approach for semi-supervised learning of conditional random fields. Our approach defines a training objective that combines the conditional likelihood on labeled data and the mutual information on unlabeled data. Different from previous minimum conditional entropy semi-supervised discriminative learning methods, our approach can be naturally cast into the rate distortion theory framework in information theory. We analyze the tractability of the framework for structured prediction and present a convergent variational training algorithm to defy the combinatorial explosion of terms in the sum over label configurations. Our experimental results show that the rate distortion approach outperforms standard $l_2$ regularization and minimum conditional entropy regularization on both multi-class classification and sequence labeling problems.

The problem of learning to predict structured labels is of key importance in many applications. However, for general graph structure both learning and inference in this setting are intractable. Here we show that it is possible to circumvent this difficulty when the input distribution is rich enough via a method similar in spirit to pseudo-likelihood. We show how our new method achieves consistency, and illustrate empirically that it indeed performs as well as exact methods when sufficiently large training sets are used. Papers published at the Neural Information Processing Systems Conference.

We present a new framework for semi-supervised learning with sparse eigenfunction bases of kernel matrices. It turns out that when the \emph{cluster assumption} holds, that is, when the high density regions are sufficiently separated by low density valleys, each high density area corresponds to a unique representative eigenvector. Linear combination of such eigenvectors (or, more precisely, of their Nystrom extensions) provide good candidates for good classification functions. By first choosing an appropriate basis of these eigenvectors from unlabeled data and then using labeled data with Lasso to select a classifier in the span of these eigenvectors, we obtain a classifier, which has a very sparse representation in this basis. Importantly, the sparsity appears naturally from the cluster assumption.

Estimating 3D pose from monocular images is a highly ambiguous problem. Physical constraints can be exploited to restrict the space of feasible configurations. In this paper we propose an approach to constraining the prediction of a discriminative predictor. We first show that the mean prediction of a Gaussian process implicitly satisfies linear constraints if those constraints are satisfied by the training examples. We then show how, by performing a change of variables, a GP can be forced to satisfy quadratic constraints.

For many supervised learning problems, we possess prior knowledge about which features yield similar information about the target variable. In predicting the topic of a document, we might know that two words are synonyms, or when performing image recognition, we know which pixels are adjacent. Such synonymous or neighboring features are near-duplicates and should therefore be expected to have similar weights in a good model. Here we present a framework for regularized learning in settings where one has prior knowledge about which features are expected to have similar and dissimilar weights. This prior knowledge is encoded as a graph whose vertices represent features and whose edges represent similarities and dissimilarities between them.

We consider the problem of zero-shot learning, where the goal is to learn a classifier $f: X \rightarrow Y$ that must predict novel values of $Y$ that were omitted from the training set. To achieve this, we define the notion of a semantic output code classifier (SOC) which utilizes a knowledge base of semantic properties of $Y$ to extrapolate to novel classes. We provide a formalism for this type of classifier and study its theoretical properties in a PAC framework, showing conditions under which the classifier can accurately predict novel classes. As a case study, we build a SOC classifier for a neural decoding task and show that it can often predict words that people are thinking about from functional magnetic resonance images (fMRI) of their neural activity, even without training examples for those words. Papers published at the Neural Information Processing Systems Conference.

We study the behavior of the popular Laplacian Regularization method for Semi-Supervised Learning at the regime of a fixed number of labeled points but a large number of unlabeled points. We show that in $\R d$, $d \geq 2$, the method is actually not well-posed, and as the number of unlabeled points increases the solution degenerates to a noninformative function. We also contrast the method with the Laplacian Eigenvector method, and discuss the smoothness assumptions associated with this alternate method. Papers published at the Neural Information Processing Systems Conference.

Models for near-rigid shape matching are typically based on distance-related features, in order to infer matches that are consistent with the isometric assumption. However, real shapes from image datasets, even when expected to be related by almost isometric" transformations, are actually subject not only to noise but also, to some limited degree, to variations in appearance and scale. In this paper, we introduce a graphical model that parameterises appearance, distance, and angle features and we learn all of the involved parameters via structured prediction. The outcome is a model for near-rigid shape matching which is robust in the sense that it is able to capture the possibly limited but still important scale and appearance variations. Our experimental results reveal substantial improvements upon recent successful models, while maintaining similar running times." Papers published at the Neural Information Processing Systems Conference.