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. During learning, each feature's weight is penalized by the amount it differs from the average weight of its neighbors. For text classification, regularization using graphs of word co-occurrences outperforms manifold learning and compares favorably to other recently proposed semi-supervised learning methods. For sentiment analysis, feature graphs constructed from declarative human knowledge, as well as from auxiliary task learning, significantly improve prediction accuracy.

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."

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. Our approach iterates between an MCMC-based labeling and contour based labeling of features to integrate co-occurrence of features and shape similarity.

Is accurate classification possible in the absence of hand-labeled data?

We address the problem of learning classifiers for several related tasks that may differ in their joint distribution of input and output variables. For each task, small - possibly even empty - labeled samples and large unlabeled samples are available. While the unlabeled samples reflect the target distribution, the labeled samples may be biased. We derive a solution that produces resampling weights which match the pool of all examples to the target distribution of any given task. Our work is motivated by the problem of predicting sociodemographic features for users of web portals, based on the content which they have accessed. Here, questionnaires offered to a small portion of each portal's users produce biased samples. Transfer learning enables us to make predictions even for new portals with few or no training data and improves the overall prediction accuracy.

By adding a spatial regularization kernel to a standard loss function formulation of the boosting problem, we develop a framework for spatially informed boosting. From this regularized loss framework we derive an efficient boosting algorithm that uses additional weights/priors on the base classifiers. We prove that the proposed algorithm exhibits a ``grouping effect, which encourages the selection of all spatially local, discriminative base classifiers. The algorithms primary advantage is in applications where the trained classifier is used to identify the spatial pattern of discriminative information, e.g. the voxel selection problem in fMRI. We demonstrate the algorithms performance on various data sets.

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.

We study pool-based active learning in the presence of noise, i.e. the agnostic setting. Previousworks have shown that the effectiveness of agnostic active learning depends on the learning problem and the hypothesis space. Although there are many cases on which active learning is very useful, it is also easy to construct examples that no active learning algorithm can have advantage. In this paper, we propose intuitively reasonable sufficient conditions under which agnostic active learning algorithm is strictly superior to passive supervised learning. We show that under some noise condition, if the Bayesian classification boundary and the underlying distribution are smooth to a finite order, active learning achieves polynomial improvementin the label complexity; if the boundary and the distribution are infinitely smooth, the improvement is exponential.

We investigate how well Gaussian process regression can learn functions defined on graphs, using large regular random graphs as a paradigmatic example. Random-walk based kernels are shown to have some surprising properties: within the standard approximation of a locally tree-like graph structure, the kernel does not become constant, i.e.neighbouring function values do not become fully correlated, when the lengthscale $\sigma$ of the kernel is made large. Instead the kernel attains a non-trivial limiting form, which we calculate. The fully correlated limit is reached only once loops become relevant, and we estimate where the crossover to this regime occurs. Our main subject are learning curves of Bayes error versus training set size. We show that these are qualitatively well predicted by a simple approximation using only the spectrum of a large tree as input, and generically scale with $n/V$, the number of training examples per vertex. We also explore how this behaviour changes once kernel lengthscales are large enough for loops to become important.

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. Experimental results on a number of real-world data-sets show that our method is competitive with the state of the art semi-supervised learning algorithms and outperforms the natural base-line algorithm (Lasso in the Kernel PCA basis).