Face verification remains a challenging problem in very complex conditions with large variations such as pose, illumination, expression, and occlusions. This problem is exacerbated when we rely unrealistically on a single training data source, which is often insufficient to cover the intrinsically complex face variations. This paper proposes a principled multi-task learning approach based on Discriminative Gaussian Process Latent Variable Model, named GaussianFace, to enrich the diversity of training data. In comparison to existing methods, our model exploits additional data from multiple source-domains to improve the generalization performance of face verification in an unknown target-domain. Importantly, our model can adapt automatically to complex data distributions, and therefore can well capture complex face variations inherent in multiple sources. Extensive experiments demonstrate the effectiveness of the proposed model in learning from diverse data sources and generalize to unseen domain. Specifically, the accuracy of our algorithm achieves an impressive accuracy rate of 98.52% on the well-known and challenging Labeled Faces in the Wild (LFW) benchmark. For the first time, the human-level performance in face verification (97.53%) on LFW is surpassed.

Principal Component Analysis (PCA) has wide applications in machine learning, text mining and computer vision. Classical PCA based on a Gaussian noise model is fragile to noise of large magnitude. Laplace noise assumption based PCA methods cannot deal with dense noise effectively. In this paper, we propose Cauchy Principal Component Analysis (Cauchy PCA), a very simple yet effective PCA method which is robust to various types of noise. We utilize Cauchy distribution to model noise and derive Cauchy PCA under the maximum likelihood estimation (MLE) framework with low rank constraint. Our method can robustly estimate the low rank matrix regardless of whether noise is large or small, dense or sparse. We analyze the robustness of Cauchy PCA from a robust statistics view and present an efficient singular value projection optimization method. Experimental results on both simulated data and real applications demonstrate the robustness of Cauchy PCA to various noise patterns.

Kernel methods have great promise for learning rich statistical representations of large modern datasets. However, compared to neural networks, kernel methods have been perceived as lacking in scalability and flexibility. We introduce a family of fast, flexible, lightly parametrized and general purpose kernel learning methods, derived from Fastfood basis function expansions. We provide mechanisms to learn the properties of groups of spectral frequencies in these expansions, which require only O(mlogd) time and O(m) memory, for m basis functions and d input dimensions. We show that the proposed methods can learn a wide class of kernels, outperforming the alternatives in accuracy, speed, and memory consumption.

Machine learning offers novel ways and means to design personalized learning systems wherein each student's educational experience is customized in real time depending on their background, learning goals, and performance to date. SPARse Factor Analysis (SPARFA) is a novel framework for machine learning-based learning analytics, which estimates a learner's knowledge of the concepts underlying a domain, and content analytics, which estimates the relationships among a collection of questions and those concepts. SPARFA jointly learns the associations among the questions and the concepts, learner concept knowledge profiles, and the underlying question difficulties, solely based on the correct/incorrect graded responses of a population of learners to a collection of questions. In this paper, we extend the SPARFA framework significantly to enable: (i) the analysis of graded responses on an ordinal scale (partial credit) rather than a binary scale (correct/incorrect); (ii) the exploitation of tags/labels for questions that partially describe the question{concept associations. The resulting Ordinal SPARFA-Tag framework greatly enhances the interpretability of the estimated concepts. We demonstrate using real educational data that Ordinal SPARFA-Tag outperforms both SPARFA and existing collaborative filtering techniques in predicting missing learner responses.

In this paper we study the consistency of an empirical minimum error entropy (MEE) algorithm in a regression setting. We introduce two types of consistency. The error entropy consistency, which requires the error entropy of the learned function to approximate the minimum error entropy, is shown to be always true if the bandwidth parameter tends to 0 at an appropriate rate. The regression consistency, which requires the learned function to approximate the regression function, however, is a complicated issue. We prove that the error entropy consistency implies the regression consistency for homoskedastic models where the noise is independent of the input variable. But for heteroskedastic models, a counterexample is used to show that the two types of consistency do not coincide. A surprising result is that the regression consistency is always true, provided that the bandwidth parameter tends to infinity at an appropriate rate. Regression consistency of two classes of special models is shown to hold with fixed bandwidth parameter, which further illustrates the complexity of regression consistency of MEE. Fourier transform plays crucial roles in our analysis.

We demonstrate that the primal-dual witness proof method may be used to establish variable selection consistency and $\ell_\infty$-bounds for sparse regression problems, even when the loss function and/or regularizer are nonconvex. Using this method, we derive two theorems concerning support recovery and $\ell_\infty$-guarantees for the regression estimator in a general setting. Our results provide rigorous theoretical justification for the use of nonconvex regularization: For certain nonconvex regularizers with vanishing derivative away from the origin, support recovery consistency may be guaranteed without requiring the typical incoherence conditions present in $\ell_1$-based methods. We then derive several corollaries that illustrate the wide applicability of our method to analyzing composite objective functions involving losses such as least squares, nonconvex modified least squares for errors-in variables linear regression, the negative log likelihood for generalized linear models, and the graphical Lasso. We conclude with empirical studies to corroborate our theoretical predictions.

Detecting faults in electrical power grids is of paramount importance, either from the electricity operator and consumer viewpoints. Modern electric power grids (smart grids) are equipped with smart sensors that allow to gather real-time information regarding the physical status of all the component elements belonging to the whole infrastructure (e.g., cables and related insulation, transformers, breakers and so on). In real-world smart grid systems, usually, additional information that are related to the operational status of the grid itself are collected such as meteorological information. Designing a suitable recognition (discrimination) model of faults in a real-world smart grid system is hence a challenging task. This follows from the heterogeneity of the information that actually determine a typical fault condition. The second point is that, for synthesizing a recognition model, in practice only the conditions of observed faults are usually meaningful. Therefore, a suitable recognition model should be synthesized by making use of the observed fault conditions only. In this paper, we deal with the problem of modeling and recognizing faults in a real-world smart grid system, which supplies the entire city of Rome, Italy. Recognition of faults is addressed by following a combined approach of multiple dissimilarity measures customization and one-class classification techniques. We provide here an in-depth study related to the available data and to the models synthesized by the proposed one-class classifier. We offer also a comprehensive analysis of the fault recognition results by exploiting a fuzzy set based reliability decision rule.

For the problem of binary linear classification and feature selection, we propose algorithmic approaches to classifier design based on the generalized approximate message passing (GAMP) algorithm, recently proposed in the context of compressive sensing. We are particularly motivated by problems where the number of features greatly exceeds the number of training examples, but where only a few features suffice for accurate classification. We show that sum-product GAMP can be used to (approximately) minimize the classification error rate and max-sum GAMP can be used to minimize a wide variety of regularized loss functions. Furthermore, we describe an expectation-maximization (EM)-based scheme to learn the associated model parameters online, as an alternative to cross-validation, and we show that GAMP's state-evolution framework can be used to accurately predict the misclassification rate. Finally, we present a detailed numerical study to confirm the accuracy, speed, and flexibility afforded by our GAMP-based approaches to binary linear classification and feature selection.

We propose the supervised hierarchical Dirichlet process (sHDP), a nonparametric generative model for the joint distribution of a group of observations and a response variable directly associated with that whole group. We compare the sHDP with another leading method for regression on grouped data, the supervised latent Dirichlet allocation (sLDA) model. We evaluate our method on two real-world classification problems and two real-world regression problems. Bayesian nonparametric regression models based on the Dirichlet process, such as the Dirichlet process-generalised linear models (DP-GLM) have previously been explored; these models allow flexibility in modelling nonlinear relationships. However, until now, Hierarchical Dirichlet Process (HDP) mixtures have not seen significant use in supervised problems with grouped data since a straightforward application of the HDP on the grouped data results in learnt clusters that are not predictive of the responses. The sHDP solves this problem by allowing for clusters to be learnt jointly from the group structure and from the label assigned to each group.

This paper proposes a decorrelation-based approach to test hypotheses and construct confidence intervals for the low dimensional component of high dimensional proportional hazards models. Motivated by the geometric projection principle, we propose new decorrelated score, Wald and partial likelihood ratio statistics. Without assuming model selection consistency, we prove the asymptotic normality of these test statistics, establish their semiparametric optimality. We also develop new procedures for constructing pointwise confidence intervals for the baseline hazard function and baseline survival function. Thorough numerical results are provided to back up our theory.