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.

In discriminative machine learning one is interested in training a system to optimize a certain desired measure of performance, or loss. In binary classification one typically tries to minimizes the error rate. But in structured prediction each task often has its own measure of performance such as the BLEU score in machine translation or the intersection-over-union score in PASCAL segmentation. The most common approaches to structured prediction, structural SVMs and CRFs, do not minimize the task loss: the former minimizes a surrogate loss with no guarantees for task loss and the latter minimizes log loss independent of task loss. The main contribution of this paper is a theorem stating that a certain perceptron-like learning rule, involving features vectors derived from loss-adjusted inference, directly corresponds to the gradient of task loss. We give empirical results on phonetic alignment of a standard test set from the TIMIT corpus, which surpasses all previously reported results on this problem.

Multiple-Instance learning has been long known as a hard non-convex problem. In this work, we propose an approach that recasts it as a convex likelihood ratio estimation problem. Firstly, the constraint in multiple-instance learning is reformulated into a convex constraint on the likelihood ratio. Then we show that a joint estimation of a likelihood ratio function and the likelihood on training instances can be learned convexly. Theoretically, we prove a quantitative relationship between the risk estimated under the 0-1 classification loss, and under a loss function for likelihood ratio estimation. It is shown that our likelihood ratio estimation is generally a good surrogate for the 0-1 loss, and separates positive and negative instances well.

It has been established that the second-order stochastic gradient descent (2SGD) method can potentially achieve generalization performance as well as empirical optimum in a single pass (i.e., epoch) through the training examples. However, 2SGD requires computing the inverse of the Hessian matrix of the loss function, which is prohibitively expensive. This paper presents Periodic Step-size Adaptation (PSA), which approximates the Jacobian matrix of the mapping function and explores a linear relation between the Jacobian and Hessian to approximate the Hessian periodically and achieve near-optimal results in experiments on a wide variety of models and tasks. Papers published at the Neural Information Processing Systems Conference.

Integrating semantic and syntactic analysis is essential for document analysis. Using an analogous reasoning, we present an approach that combines bag-of-words and spatial models to perform semantic and syntactic analysis for recognition of an object based on its internal appearance and its context. We argue that while object recognition requires modeling relative spatial locations of image features within the object, a bag-of-word is sufficient for representing context. Learning such a model from weakly labeled data involves labeling of features into two classes: foreground(object) or ''informative'' background(context). labeling. We present a ''shape-aware'' model which utilizes contour information for efficient and accurate labeling of features in the image.

With the advent of the Internet it is now possible to collect hundreds of millions of images. These images come with varying degrees of label information. Clean labels can be manually obtained on a small fraction, noisy labels may be extracted automatically from surrounding text, while for most images there are no labels at all. Semi-supervised learning is a principled framework for combining these different label sources. In this paper we show how to utilize recent results in machine learning to obtain highly efficient approximations for semi-supervised learning that are linear in the number of images.

In this paper we propose an approximated learning framework for large scale graphical models and derive message passing algorithms for learning their parameters efficiently. We first relate CRFs and structured SVMs and show that in the CRF's primal a variant of the log-partition function, known as soft-max, smoothly approximates the hinge loss function of structured SVMs. We then propose an intuitive approximation for structured prediction problems using Fenchel duality based on a local entropy approximation that computes the exact gradients of the approximated problem and is guaranteed to converge. Unlike existing approaches, this allow us to learn graphical models with cycles and very large number of parameters efficiently. We demonstrate the effectiveness of our approach in an image denoising task.

In this paper we present two transductive bounds on the risk of the majority vote estimated over partially labeled training sets. Our first bound is tight when the additional unlabeled training data are used in the cases where the voted classifier makes its errors on low margin observations and where the errors of the associated Gibbs classifier can accurately be estimated. In semi-supervised learning, considering the margin as an indicator of confidence constitutes the working hypothesis of algorithms which search the decision boundary on low density regions. In this case, we propose a second bound on the joint probability that the voted classifier makes an error over an example having its margin over a fixed threshold. As an application we are interested on self-learning algorithms which assign iteratively pseudo-labels to unlabeled training examples having margin above a threshold obtained from this bound.

Most current image categorization methods require large collections of manually annotated training examples to learn accurate visual recognition models. The time-consuming human labeling effort effectively limits these approaches to recognition problems involving a small number of different object classes. In order to address this shortcoming, in recent years several authors have proposed to learn object classifiers from weakly-labeled Internet images, such as photos retrieved by keyword-based image search engines. While this strategy eliminates the need for human supervision, the recognition accuracies of these methods are considerably lower than those obtained with fully-supervised approaches, because of the noisy nature of the labels associated to Web data. In this paper we investigate and compare methods that learn image classifiers by combining very few manually annotated examples (e.g., 1-10 images per class) and a large number of weakly-labeled Web photos retrieved using keyword-based image search.