We propose two new principal component analysis methods in this paper utilizing a semiparametric model. The according methods are named Copula Component Analysis (COCA) and Copula PCA. The semiparametric model assumes that, after unspecifiedmarginally monotone transformations, the distributions are multivariate Gaussian.The COCA and Copula PCA accordingly estimate the leading eigenvectors of the correlation and covariance matrices of the latent Gaussian distribution. Therobust nonparametric rank-based correlation coefficient estimator, Spearman's rho, is exploited in estimation. We prove that, under suitable conditions, althoughthe marginal distributions can be arbitrarily continuous, the COCA and Copula PCA estimators obtain fast estimation rates and are feature selection consistent in the setting where the dimension is nearly exponentially large relative to the sample size. Careful numerical experiments on the synthetic and real data are conducted to back up the theoretical results. We also discuss the relationship with the transelliptical component analysis proposed by Han and Liu (2012).

Identifying patterns from the neuroimaging recordings of brain activity related to the unobservable psychological or mental state of an individual can be treated as a unsupervised pattern recognition problem. The main challenges, however, for such an analysis of fMRI data are: a) defining a physiologically meaningful feature-space for representing the spatial patterns across time; b) dealing with the high-dimensionality of the data; and c) robustness to the various artifacts and confounds in the fMRI time-series. In this paper, we present a network-aware feature-space to represent the states of a general network, that enables comparing and clustering such states in a manner that is a) meaningful in terms of the network connectivity structure; b)computationally efficient; c) low-dimensional; and d) relatively robust to structured and random noise artifacts. This feature-space is obtained from a spherical relaxation of the transportation distance metric which measures the cost of transporting ``mass'' over the network to transform one function into another. Through theoretical and empirical assessments, we demonstrate the accuracy and efficiency of the approximation, especially for large problems. While the application presented here is for identifying distinct brain activity patterns from fMRI, this feature-space can be applied to the problem of identifying recurring patterns and detecting outliers in measurements on many different types of networks, including sensor, control and social networks.

The ability to predict action content from neural signals in real time before the action occurshas been long sought in the neuroscientific study of decision-making, agency and volition. Online real-time (ORT) prediction is important for understanding therelation between neural correlates of decision-making and conscious, voluntary action as well as for brain-machine interfaces. Here, epilepsy patients, implanted with intracranial depth microelectrodes or subdural grid electrodes for clinical purposes, participated in a "matching-pennies" game against an opponent. In each trial, subjects were given a 5 s countdown, after which they had to raise their left or right hand immediately as the "go" signal appeared on a computer screen. They won a fixed amount of money if they raised a different hand than their opponent and lost that amount otherwise.

We present a simplex algorithm for linear programming in a linear classification formulation. The paramount complexity parameter in linear classification problems is called the margin. We prove that for margin values of practical interest our simplex variant performs a polylogarithmic number of pivot steps in the worst case, and its overall running time is near linear. This is in contrast to general linear programming, for which no sub-polynomial pivot rule is known.

This paper presents a kernel-based discriminative learning framework on probability measures. Rather than relying on large collections of vectorial training examples, our framework learns using a collection of probability distributions that have been constructed to meaningfully represent training data. By representing these probability distributions as mean embeddings in the reproducing kernel Hilbert space (RKHS), we are able to apply many standard kernel-based learning techniques in straightforward fashion. To accomplish this, we construct a generalization of the support vector machine (SVM) called a support measure machine (SMM). Our analyses of SMMs provides several insights into their relationship to traditional SVMs. Based on such insights, we propose a flexible SVM (Flex-SVM) that places different kernel functions on each training example. Experimental results on both synthetic and real-world data demonstrate the effectiveness of our proposed framework.

Latent SVMs (LSVMs) are a class of powerful tools that have been successfully applied to many applications in computer vision. However, a limitation of LSVMs is that they rely on linear models. For many computer vision tasks, linear models are suboptimal and nonlinear models learned with kernels typically perform much better. Therefore it is desirable to develop the kernel version of LSVM. In this paper, we propose kernel latent SVM (KLSVM) -- a new learning framework that combines latent SVMs and kernel methods. We develop an iterative training algorithm to learn the model parameters. We demonstrate the effectiveness of KLSVM using three different applications in visual recognition. Our KLSVM formulation is very general and can be applied to solve a wide range of applications in computer vision and machine learning.

We address the problem of general supervised learning when data can only be accessed through an (indefinite) similarity function between data points. Existing work on learning with indefinite kernels has concentrated solely on binary/multiclass classification problems. We propose a model that is generic enough to handle any supervised learning task and also subsumes the model previously proposed for classification. We give a ''goodness'' criterion for similarity functions w.r.t. a given supervised learning task and then adapt a well-known landmarking technique to provide efficient algorithms for supervised learning using ''good'' similarity functions. We demonstrate the effectiveness of our model on three important supervised learning problems: a) real-valued regression, b) ordinal regression and c) ranking where we show that our method guarantees bounded generalization error. Furthermore, for the case of real-valued regression, we give a natural goodness definition that, when used in conjunction with a recent result in sparse vector recovery, guarantees a sparse predictor with bounded generalization error. Finally, we report results of our learning algorithms on regression and ordinal regression tasks using non-PSD similarity functions and demonstrate the effectiveness of our algorithms, especially that of the sparse landmark selection algorithm that achieves significantly higher accuracies than the baseline methods while offering reduced computational costs.

The partition function plays a key role in probabilistic modeling including conditional random fields, graphical models, and maximum likelihood estimation. To optimize partition functions, this article introduces a quadratic variational upper bound. This inequality facilitates majorization methods: optimization of complicated functions through the iterative solution of simpler sub-problems. Such bounds remain efficient to compute even when the partition function involves a graphical model (with small tree-width) or in latent likelihood settings. For large-scale problems, low-rank versions of the bound are provided and outperform LBFGS as well as first-order methods. Several learning applications are shown and reduce to fast and convergent update rules. Experimental results show advantages over state-of-the-art optimization methods.

This paper addresses the problem of category-level 3D object detection. Given a monocular image, our aim is to localize the objects in 3D by enclosing them with tight oriented 3D bounding boxes. We propose a novel approach that extends the well-acclaimed deformable part-based model[Felz.] to reason in 3D. Our model represents an object class as a deformable 3D cuboid composed of faces and parts, which are both allowed to deform with respect to their anchors on the 3D box. We model the appearance of each face in fronto-parallel coordinates, thus effectively factoring out the appearance variation induced by viewpoint. Our model reasons about face visibility patters called aspects. We train the cuboid model jointly and discriminatively and share weights across all aspects to attain efficiency. Inference then entails sliding and rotating the box in 3D and scoring object hypotheses. While for inference we discretize the search space, the variables are continuous in our model. We demonstrate the effectiveness of our approach in indoor and outdoor scenarios, and show that our approach outperforms the state-of-the-art in both 2D[Felz09] and 3D object detection[Hedau12].

R is a convex but not necessarily differentiable function whose proximal mapping can be evaluated efficiently.We derive a generalization of Newton-type methods to handle such convex but nonsmooth objective functions. We prove such methods are globally convergentand achieve superlinear rates of convergence in the vicinity of an optimal solution. We also demonstrate the performance of these methods using problems of relevance in machine learning and statistics.