In this paper, we propose a novel dictionary learning method in the semi-supervised setting by dynamically coupling graph and group structures. To this end, samples are represented by sparse codes inheriting their graph structure while the labeled samples within the same class are represented with group sparsity, sharing the same atoms of the dictionary. Instead of statically combining graph and group structures, we take advantage of them in a mutually reinforcing way — in the dictionary learning phase, we introduce the unlabeled samples into groups by an entropy-based method and then update the corresponding local graph, resulting in a more structured and discriminative dictionary. We analyze the relationship between the two structures and prove the convergence of our proposed method. Focusing on image classification task, we evaluate our approach on several datasets and obtain superior performance compared with the state-of-the-art methods, especially in the case of only a few labeled samples and limited dictionary size.

There has been an increasing interest in exploring signed networks with positive and negative links in that they contain more information than unsigned networks. As fundamental problems of signed network analysis, community detection and sign (or attitude) prediction are still primary challenges. To address them, we propose a generative Bayesian approach, in which 1) a signed stochastic blockmodel is proposed to characterize the community structure in context of signed networks, by means of explicitly formulating the distributions of both density and frustration of signed links from a stochastic perspective, and 2) a model learning algorithm is proposed by theoretically deriving a variational Bayes EM for parameter estimation and a variation based approximate evidence for model selection. Through the comparisons with state-of-the-art methods on synthetic and real-world networks, the proposed approach shows its superiority in both community detection and sign prediction for exploratory networks.

The aim of domain adaptation algorithms is to establish a learner, trained on labeled data from a source domain, that can classify samples from a target domain, in which few or no labeled data are available for training. Covariate shift, a primary assumption in several works on domain adaptation, assumes that the labeling functions of source and target domains are identical. We present a domain adaptation algorithm that assumes a relaxed version of covariate shift where the assumption that the labeling functions of the source and target domains are identical holds with a certain probability. Assuming a source deterministic large margin binary classifier, the farther a target instance is from the source decision boundary, the higher the probability that covariate shift holds. In this context, given a target unlabeled sample and no target labeled data, we develop a domain adaptation algorithm that bases its labeling decisions both on the source learner and on the similarities between the target unlabeled instances. The source labeling function decisions associated with probabilistic covariate shift, along with the target similarities are concurrently expressed on a similarity graph. We evaluate our proposed algorithm on a benchmark sentiment analysis (and domain adaptation) dataset, where state-of-the-art adaptation results are achieved. We also derive a lower bound on the performance of the algorithm.

Learning for maximizing AUC performance is an important research problem in machine learning. Unlike traditional batch learning methods for maximizing AUC which often suffer from poor scalability, recent years have witnessed some emerging studies that attempt to maximize AUC by single-pass online learning approaches. Despite their encouraging results reported, the existing online AUC maximization algorithms often adopt simple stochastic gradient descent approaches, which fail to exploit the geometry knowledge of the data observed in the online learning process, and thus could suffer from relatively slow convergence. To overcome the limitation of the existing studies, in this paper, we propose a novel algorithm of Adaptive Online AUC Maximization (AdaOAM), by applying an adaptive gradient method for exploiting the knowledge of historical gradients to perform more informative online learning. The new adaptive updating strategy by AdaOAM is less sensitive to parameter settings due to its natural effect of tuning the learning rate. In addition, the time complexity of the new algorithm remains the same as the previous non-adaptive algorithms. To demonstrate the effectiveness of the proposed algorithm, we analyze its theoretical bound, and further evaluate its empirical performance on both public benchmark datasets and anomaly detection datasets. The encouraging empirical results clearly show the effectiveness and efficiency of the proposed algorithm.

Lasso is a popular method for high-dimensional variable selection, but it hinges on a tuning parameter that is difficult to calibrate in practice. In this study, we introduce TREX, an alternative to Lasso with an inherent calibration to all aspects of the model. This adaptation to the entire model renders TREX an estimator that does not require any calibration of tuning parameters. We show that TREX can outperform cross-validated Lasso in terms of variable selection and computational efficiency. We also introduce a bootstrapped version of TREX that can further improve variable selection. We illustrate the promising performance of TREX both on synthetic data and on two biological data sets from the fields of genomics and proteomics.

This paper presents a large-scale sparse coding algorithm to deal with the challenging problem of noise-robust semi-supervised learning over very large data with only few noisy initial labels. By giving an L1-norm formulation of Laplacian regularization directly based upon the manifold structure of the data, we transform noise-robust semi-supervised learning into a generalized sparse coding problem so that noise reduction can be imposed upon the noisy initial labels. Furthermore, to keep the scalability of noise-robust semi-supervised learning over very large data, we make use of both nonlinear approximation and dimension reduction techniques to solve this generalized sparse coding problem in linear time and space complexity. Finally, we evaluate the proposed algorithm in the challenging task of large-scale semi-supervised image classification with only few noisy initial labels. The experimental results on several benchmark image datasets show the promising performance of the proposed algorithm.

Sampling repeated clinical laboratory tests with appropriate timing is challenging because the latent physiologic function being sampled is in general nonstationary. When ordering repeated tests, clinicians adopt various simple strategies that may or may not be well suited to the behavior of the function. Previous research on this topic has been primarily focused on cost-driven assessments of oversampling. But for monitoring physiologic state or for retrospective analysis, undersampling can be much more problematic than oversampling. In this paper we analyze hundreds of observation sequences of four different clinical laboratory tests to provide principled, data-driven estimates of undersampling and oversampling, and to assess whether the sampling adapts to changing volatility of the latent function. To do this, we developed a new method for fitting a Gaussian process to samples of a nonstationary latent function. Our method includes an explicit estimate of the latent function's volatility over time, which is deterministically related to its nonstationarity. We find on average that the degree of undersampling is up to an order of magnitude greater than oversampling, and that only a small minority are sampled with an adaptive strategy.

This paper proposes a new approach for discriminative clustering. The intuition is, for a good clustering, one should be able to learn a classifier from the clustering labels with high generalization accuracy. Thus we define a novel metric to evaluate the quality of a clustering labeling, named Minimum Separation Probability (MSP), which is a lower bound of the generalization accuracy of a classifier learnt from the clustering labeling. We take MSP as the objective to maximize and propose our approach Maximin Separation Probability Clustering (MSPC), which has several attractive properties, such as invariance to anisotropic feature scaling and intuitive probabilistic explanation for clustering quality. We present three efficient optimization strategies for MSPC, and analyze their interesting connections to existing clustering approaches, such as maximum margin clustering (MMC) and discriminative k-means. Empirical results on real world data sets verify that MSP is a robust and effective clustering quality measure. It is also shown that the proposed algorithms compare favorably to state-of-the-art clustering algorithms in both accuracy and efficiency.

The global financial crisis occurred in 2008 and its contagion to other regions, as well as the long-lasting impact on different markets, show that it is increasingly important to understand the complicated coupling relationships across financial markets. This is indeed very difficult as complex hidden coupling relationships exist between different financial markets in various countries, which are very hard to model. The couplings involve interactions between homogeneous markets from various countries (we call intra-market coupling), interactions between heterogeneous markets (inter-market coupling) and interactions between current and past market behaviors (temporal coupling). Very limited work has been done towards modeling such complex couplings, whereas some existing methods predict market movement by simply aggregating indicators from various markets but ignoring the inbuilt couplings. As a result, these methods are highly sensitive to observations, and may often fail when financial indicators change slightly. In this paper, a coupled deep belief network is designed to accommodate the above three types of couplings across financial markets. With a deep-architecture model to capture the high-level coupled features, the proposed approach can infer market trends. Experimental results on data of stock and currency markets from three countries show that our approach outperforms other baselines, from both technical and business perspectives.

Linear Dynamical System (LDS) is an elegant mathematical framework for modeling and learning Multivariate Time Series (MTS). However, in general, it is difficult to set the dimension of an LDS's hidden state space. A small number of hidden states may not be able to model the complexities of a MTS, while a large number of hidden states can lead to overfitting. In this paper, we study learning methods that impose various regularization penalties on the transition matrix of the LDS model and propose a regularized LDS learning framework (rLDS) which aims to (1) automatically shut down LDSs' spurious and unnecessary dimensions, and consequently, address the problem of choosing the optimal number of hidden states; (2) prevent the overfitting problem given a small amount of MTS data; and (3) support accurate MTS forecasting. To learn the regularized LDS from data we incorporate a second order cone program and a generalized gradient descent method into the Maximum a Posteriori framework and use Expectation Maximization to obtain a low-rank transition matrix of the LDS model. We propose two priors for modeling the matrix which lead to two instances of our rLDS. We show that our rLDS is able to recover well the intrinsic dimensionality of the time series dynamics and it improves the predictive performance when compared to baselines on both synthetic and real-world MTS datasets.