A new Bayesian formulation is developed for nonlinear support vector machines (SVMs), based on a Gaussian process and with the SVM hinge loss expressed as a scaled mixture of normals. We then integrate the Bayesian SVM into a factor model, in which feature learning and nonlinear classifier design are performed jointly; almost all previous work on such discriminative feature learning has assumed a linear classifier. Inference is performed with expectation conditional maximization (ECM) and Markov Chain Monte Carlo (MCMC). An extensive set of experiments demonstrate the utility of using a nonlinear Bayesian SVM within discriminative feature learning and factor modeling, from the standpoints of accuracy and interpretability.

A new Bayesian formulation is developed for nonlinear support vector machines (SVMs), based on a Gaussian process and with the SVM hinge loss expressed as a scaled mixture of normals. We then integrate the Bayesian SVM into a factor model, in which feature learning and nonlinear classifier design are performed jointly; almost all previous work on such discriminative feature learning has assumed a linear classifier. Inference is performed with expectation conditional maximization (ECM) and Markov Chain Monte Carlo (MCMC). An extensive set of experiments demonstrate the utility of using a nonlinear Bayesian SVM within discriminative feature learning and factor modeling, from the standpoints of accuracy and interpretability.

We propose a novel semi-parametric classifier based on Mahalanobis distances of an observation from the competing classes. Our tool is a generalized additive model with the logistic link function that uses these distances as features to estimate the posterior probabilities of the different classes. While popular parametric classifiers like linear and quadratic discriminant analyses are mainly motivated by the normality of the underlying distributions, the proposed classifier is more flexible and free from such parametric assumptions. Since the densities of elliptic distributions are functions of Mahalanobis distances, this classifier works well when the competing classes are (nearly) elliptic. In such cases, it often outperforms popular nonparametric classifiers, especially when the sample size is small compared to the dimension of the data. To cope with non-elliptic and possibly multimodal distributions, we propose a local version of the Mahalanobis distance. Subsequently, we propose another classifier based on a generalized additive model that uses the local Mahalanobis distances as features. This nonparametric classifier usually performs like the Mahalanobis distance based semiparametric classifier when the underlying distributions are elliptic, but outperforms it for several non-elliptic and multimodal distributions. We also investigate the behaviour of these two classifiers in high dimension, low sample size situations. A thorough numerical study involving several simulated and real datasets demonstrate the usefulness of the proposed classifiers in comparison to many state-of-the-art methods.

Recent advance on linear support vector machine with the 0-1 soft margin loss ($L_{0/1}$-SVM) shows that the 0-1 loss problem can be solved directly. However, its theoretical and algorithmic requirements restrict us extending the linear solving framework to its nonlinear kernel form directly, the absence of explicit expression of Lagrangian dual function of $L_{0/1}$-SVM is one big deficiency among of them. In this paper, by applying the nonparametric representation theorem, we propose a nonlinear model for support vector machine with 0-1 soft margin loss, called $L_{0/1}$-KSVM, which cunningly involves the kernel technique into it and more importantly, follows the success on systematically solving its linear task. Its optimal condition is explored theoretically and a working set selection alternating direction method of multipliers (ADMM) algorithm is introduced to acquire its numerical solution. Moreover, we firstly present a closed-form definition to the support vector (SV) of $L_{0/1}$-KSVM. Theoretically, we prove that all SVs of $L_{0/1}$-KSVM are only located on the parallel decision surfaces. The experiment part also shows that $L_{0/1}$-KSVM has much fewer SVs, simultaneously with a decent predicting accuracy, when comparing to its linear peer $L_{0/1}$-SVM and the other six nonlinear benchmark SVM classifiers.

Most supervised learning models are trained for full automation. However, their predictions are sometimes worse than those by human experts on some specific instances. Motivated by this empirical observation, our goal is to design classifiers that are optimized to operate under different automation levels. More specifically, we focus on convex margin-based classifiers and first show that the problem is NP-hard. Then, we further show that, for support vector machines, the corresponding objective function can be expressed as the difference of two functions f = g - c, where g is monotone, non-negative and {\gamma}-weakly submodular, and c is non-negative and modular. This representation allows a recently introduced deterministic greedy algorithm, as well as a more efficient randomized variant of the algorithm, to enjoy approximation guarantees at solving the problem. Experiments on synthetic and real-world data from several applications in medical diagnosis illustrate our theoretical findings and demonstrate that, under human assistance, supervised learning models trained to operate under different automation levels can outperform those trained for full automation as well as humans operating alone.

A new Bayesian formulation is developed for nonlinear support vector machines (SVMs), based on a Gaussian process and with the SVM hinge loss expressed as a scaled mixture of normals. We then integrate the Bayesian SVM into a factor model, in which feature learning and nonlinear classifier design are performed jointly; almost all previous work on such discriminative feature learning has assumed a linear classifier. Inference is performed with expectation conditional maximization (ECM) and Markov Chain Monte Carlo (MCMC). An extensive set of experiments demonstrate the utility of using a nonlinear Bayesian SVM within discriminative feature learning and factor modeling, from the standpoints of accuracy and interpretability

Spontaneous facial expressions differ substantially from posed expressions, similar to how continuous, spontaneous speech differs from isolated words produced on command. Previous methods for automatic facial expression recognition assumed images were collected in controlled environments in which the subjects deliberately faced the camera. Since people often nod or turn their heads, automatic recognition of spontaneous facial behavior requires methods for handling out-of-image-plane head rotations. Here we explore an approach based on 3-D warping of images into canonical views. We evaluated the performance of the approach as a front-end for a spontaneous expression recognition system using support vector machines and hidden Markov models. This system employed general purpose learning mechanisms that can be applied to recognition of any facial movement. The system was tested for recognition of a set of facial actions defined by the Facial Action Coding System (FACS). We showed that 3D tracking and warping followed by machine learning techniques directly applied to the warped images, is a viable and promising technology for automatic facial expression recognition. One exciting aspect of the approach presented here is that information about movement dynamics emerged out of filters which were derived from the statistics of images.

Spontaneous facial expressions differ substantially from posed expressions, similar to how continuous, spontaneous speech differs from isolated words produced on command. Previous methods for automatic facial expression recognition assumed images were collected in controlled environments in which the subjects deliberately faced the camera. Since people often nod or turn their heads, automatic recognition of spontaneous facial behavior requires methods for handling out-of-image-plane head rotations. Here we explore an approach based on 3-D warping of images into canonical views. We evaluated the performance of the approach as a front-end for a spontaneous expression recognition system using support vector machines and hidden Markov models. This system employed general purpose learning mechanisms that can be applied to recognition of any facial movement. The system was tested for recognition of a set of facial actions defined by the Facial Action Coding System (FACS). We showed that 3D tracking and warping followed by machine learning techniques directly applied to the warped images, is a viable and promising technology for automatic facial expression recognition. One exciting aspect of the approach presented here is that information about movement dynamics emerged out of filters which were derived from the statistics of images.

Spontaneous facial expressions differ substantially from posed expressions, similar to how continuous, spontaneous speech differs from isolated words produced on command. Previous methods for automatic facial expression recognition assumed images were collected in controlled environments in which the subjects deliberately facedthe camera. Since people often nod or turn their heads, automatic recognition of spontaneous facial behavior requires methods for handling out-of-image-plane head rotations. Here we explore an approach basedon 3-D warping of images into canonical views. We evaluated the performance of the approach as a front-end for a spontaneous expression recognition system using support vector machines and hidden Markov models. This system employed general purpose learning mechanisms thatcan be applied to recognition of any facial movement. The system was tested for recognition of a set of facial actions defined by the Facial Action Coding System (FACS). We showed that 3D tracking and warping followed by machine learning techniques directly applied to the warped images, is a viable and promising technology for automatic facial expression recognition. One exciting aspect of the approach presented hereis that information about movement dynamics emerged out of filters which were derived from the statistics of images.