Unsupervised feature learning with discriminative encoder

In recent years, deep discriminative models have achieved extraordinary performance on supervised learning tasks, significantly outperforming their generative counterparts. However, their success relies on the presence of a large amount of labeled data. How can one use the same discriminative models for learning useful features in the absence of labels? We address this question in this paper, by jointly modeling the distribution of data and latent features in a manner that explicitly assigns zero probability to unobserved data. Rather than maximizing the marginal probability of observed data, we maximize the joint probability of the data and the latent features using a two step EM-like procedure. To prevent the model from overfitting to our initial selection of latent features, we use adversarial regularization. Depending on the task, we allow the latent features to be one-hot or real-valued vectors and define a suitable prior on the features. For instance, one-hot features correspond to class labels and are directly used for the unsupervised and semi-supervised classification task, whereas real-valued feature vectors are fed as input to simple classifiers for auxiliary supervised discrimination tasks. The proposed model, which we dub discriminative encoder (or DisCoder), is flexible in the type of latent features that it can capture. The proposed model achieves state-of-the-art performance on several challenging tasks.Comment: 10 pages, 4 figures, International Conference on Data Mining, 201

Comprehensive Border Bases for Zero Dimensional Parametric Polynomial Ideals

In this paper, we extend the idea of comprehensive Gr\"{o}bner bases given by Weispfenning (1992) to border bases for zero dimensional parametric polynomial ideals. For this, we introduce a notion of comprehensive border bases and border system, and prove their existence even in the cases where they do not correspond to any term order. We further present algorithms to compute comprehensive border bases and border system. Finally, we study the relation between comprehensive Gr\"{o}bner bases and comprehensive border bases w.r.t. a term order and give an algorithm to compute such comprehensive border bases from comprehensive Gr\"{o}bner bases.Comment: 15 pages, 8 sections and 3 algorithm

Learning to segment with image-level supervision

Deep convolutional networks have achieved the state-of-the-art for semantic image segmentation tasks. However, training these networks requires access to densely labeled images, which are known to be very expensive to obtain. On the other hand, the web provides an almost unlimited source of images annotated at the image level. How can one utilize this much larger weakly annotated set for tasks that require dense labeling? Prior work often relied on localization cues, such as saliency maps, objectness priors, bounding boxes etc., to address this challenging problem. In this paper, we propose a model that generates auxiliary labels for each image, while simultaneously forcing the output of the CNN to satisfy the mean-field constraints imposed by a conditional random field. We show that one can enforce the CRF constraints by forcing the distribution at each pixel to be close to the distribution of its neighbors. This is in stark contrast with methods that compute a recursive expansion of the mean-field distribution using a recurrent architecture and train the resultant distribution. Instead, the proposed model adds an extra loss term to the output of the CNN, and hence, is faster than recursive implementations. We achieve the state-of-the-art for weakly supervised semantic image segmentation on VOC 2012 dataset, assuming no manually labeled pixel level information is available. Furthermore, the incorporation of conditional random fields in CNN incurs little extra time during training.Comment: Published in WACV 201

Consistency of Spectral Hypergraph Partitioning under Planted Partition Model

Hypergraph partitioning lies at the heart of a number of problems in machine learning and network sciences. Many algorithms for hypergraph partitioning have been proposed that extend standard approaches for graph partitioning to the case of hypergraphs. However, theoretical aspects of such methods have seldom received attention in the literature as compared to the extensive studies on the guarantees of graph partitioning. For instance, consistency results of spectral graph partitioning under the stochastic block model are well known. In this paper, we present a planted partition model for sparse random non-uniform hypergraphs that generalizes the stochastic block model. We derive an error bound for a spectral hypergraph partitioning algorithm under this model using matrix concentration inequalities. To the best of our knowledge, this is the first consistency result related to partitioning non-uniform hypergraphs.Comment: 35 pages, 2 figures, 1 tabl