In this paper we propose a unified framework for structured prediction with latent variables which includes hidden conditional random fields and latent structured support vector machines as special cases. We describe a local entropy approximation for this general formulation using duality, and derive an efficient message passing algorithm that is guaranteed to converge. We demonstrate its effectiveness in the tasks of image segmentation as well as 3D indoor scene understanding from single images, showing that our approach is superior to latent structured support vector machines and hidden conditional random fields.

We study the problem of unsupervised domain adaptation, which aims to adapt classifiers trained on a labeled source domain to an unlabeled target domain. Many existing approaches first learn domain-invariant features and then construct classifiers with them. We propose a novel approach that jointly learn the both. Specifically, while the method identifies a feature space where data in the source and the target domains are similarly distributed, it also learns the feature space discriminatively, optimizing an information-theoretic metric as an proxy to the expected misclassification error on the target domain. We show how this optimization can be effectively carried out with simple gradient-based methods and how hyperparameters can be cross-validated without demanding any labeled data from the target domain. Empirical studies on benchmark tasks of object recognition and sentiment analysis validated our modeling assumptions and demonstrated significant improvement of our method over competing ones in classification accuracies.

Learning invariant representations is an important problem in machine learning and pattern recognition. In this paper, we present a novel framework of transformation-invariant feature learning by incorporating linear transformations into the feature learning algorithms. For example, we present the transformation-invariant restricted Boltzmann machine that compactly represents data by its weights and their transformations, which achieves invariance of the feature representation via probabilistic max pooling. In addition, we show that our transformation-invariant feature learning framework can also be extended to other unsupervised learning methods, such as autoencoders or sparse coding. We evaluate our method on several image classification benchmark datasets, such as MNIST variations, CIFAR-10, and STL-10, and show competitive or superior classification performance when compared to the state-of-the-art. Furthermore, our method achieves state-of-the-art performance on phone classification tasks with the TIMIT dataset, which demonstrates wide applicability of our proposed algorithms to other domains.

In this paper, we address the problem of embedded feature selection for ranking on top of the list problems. We pose this problem as a regularized empirical risk minimization with $p$-norm push loss function ($p=\infty$) and sparsity inducing regularizers. We leverage the issues related to this challenging optimization problem by considering an alternating direction method of multipliers algorithm which is built upon proximal operators of the loss function and the regularizer. Our main technical contribution is thus to provide a numerical scheme for computing the infinite push loss function proximal operator. Experimental results on toy, DNA microarray and BCI problems show how our novel algorithm compares favorably to competitors for ranking on top while using fewer variables in the scoring function.

Estimating statistical models within sensor networks requires distributed algorithms, in which both data and computation are distributed across the nodes of the network. We propose a general approach for distributed learning based on combining local estimators defined by pseudo-likelihood components, encompassing a number of combination methods, and provide both theoretical and experimental analysis. We show that simple linear combination or max-voting methods, when combined with second-order information, are statistically competitive with more advanced and costly joint optimization. Our algorithms have many attractive properties including low communication and computational cost and "any-time" behavior.

We study the problem of multivariate regression where the data are naturally grouped, and a regression matrix is to be estimated for each group. We propose an approach in which a dictionary of low rank parameter matrices is estimated across groups, and a sparse linear combination of the dictionary elements is estimated to form a model within each group. We refer to the method as conditional sparse coding since it is a coding procedure for the response vectors Y conditioned on the covariate vectors X. This approach captures the shared information across the groups while adapting to the structure within each group. It exploits the same intuition behind sparse coding that has been successfully developed in computer vision and computational neuroscience. We propose an algorithm for conditional sparse coding, analyze its theoretical properties in terms of predictive accuracy, and present the results of simulation and brain imaging experiments that compare the new technique to reduced rank regression.

Conditional modeling x \to y is a central problem in machine learning. A substantial research effort is devoted to such modeling when x is high dimensional. We consider, instead, the case of a high dimensional y, where x is either low dimensional or high dimensional. Our approach is based on selecting a small subset y_L of the dimensions of y, and proceed by modeling (i) x \to y_L and (ii) y_L \to y. Composing these two models, we obtain a conditional model x \to y that possesses convenient statistical properties. Multi-label classification and multivariate regression experiments on several datasets show that this model outperforms the one vs. all approach as well as several sophisticated multiple output prediction methods.

Learning multiple tasks across heterogeneous domains is a challenging problem since the feature space may not be the same for different tasks. We assume the data in multiple tasks are generated from a latent common domain via sparse domain transforms and propose a latent probit model (LPM) to jointly learn the domain transforms, and the shared probit classifier in the common domain. To learn meaningful task relatedness and avoid over-fitting in classification, we introduce sparsity in the domain transforms matrices, as well as in the common classifier. We derive theoretical bounds for the estimation error of the classifier in terms of the sparsity of domain transforms. An expectation-maximization algorithm is derived for learning the LPM. The effectiveness of the approach is demonstrated on several real datasets.

Most prior work on active learning of classifiers has focused on sequentially selecting one unlabeled example at a time to be labeled in order to reduce the overall labeling effort. In many scenarios, however, it is desirable to label an entire batch of examples at once, for example, when labels can be acquired in parallel. This motivates us to study batch active learning, which iteratively selects batches of $k>1$ examples to be labeled. We propose a novel batch active learning method that leverages the availability of high-quality and efficient sequential active-learning policies by attempting to approximate their behavior when applied for $k$ steps. Specifically, our algorithm first uses Monte-Carlo simulation to estimate the distribution of unlabeled examples selected by a sequential policy over $k$ step executions. The algorithm then attempts to select a set of $k$ examples that best matches this distribution, leading to a combinatorial optimization problem that we term "bounded coordinated matching". While we show this problem is NP-hard in general, we give an efficient greedy solution, which inherits approximation bounds from supermodular minimization theory. Our experimental results on eight benchmark datasets show that the proposed approach is highly effective

In the paradigm of multi-task learning, mul- tiple related prediction tasks are learned jointly, sharing information across the tasks. We propose a framework for multi-task learn- ing that enables one to selectively share the information across the tasks. We assume that each task parameter vector is a linear combi- nation of a finite number of underlying basis tasks. The coefficients of the linear combina- tion are sparse in nature and the overlap in the sparsity patterns of two tasks controls the amount of sharing across these. Our model is based on on the assumption that task pa- rameters within a group lie in a low dimen- sional subspace but allows the tasks in differ- ent groups to overlap with each other in one or more bases. Experimental results on four datasets show that our approach outperforms competing methods.