We present a new formulation for binary classification. Instead of relying on convex losses and regularizers such as in SVMs, logistic regression and boosting, or instead non-convex but continuous formulations such as those encountered in neural networks and deep belief networks, our framework entails a non-convex but discrete formulation, where estimation amounts to finding a MAP configuration in a graphical model whose potential functions are low-dimensional discrete surrogates for the misclassification loss. We argue that such a discrete formulation can naturally account for a number of issues that are typically encountered in either the convex or the continuous non-convex approaches, or both. By reducing the learning problem to a MAP inference problem, we can immediately translate the guarantees available for many inference settings to the learning problem itself. We empirically demonstrate in a number of experiments that this approach is promising in dealing with issues such as severe label noise, while still having global optimality guarantees.

Category-level object detection has a crucial need for informative object representations. This demand has led to feature descriptors of ever increasing dimensionality like co-occurrence statistics and self-similarity. In this paper we propose a new object representation based on curvature self-similarity that goes beyond the currently popular approximation of objects using straight lines. However, like all descriptors using second order statistics, ours also exhibits a high dimensionality. Although improving discriminability, the high dimensionality becomes a critical issue due to lack of generalization ability and curse of dimensionality. Given only a limited amount of training data, even sophisticated learning algorithms such as the popular kernel methods are not able to suppress noisy or superfluous dimensions of such high-dimensional data. Consequently, there is a natural need for feature selection when using present-day informative features and, particularly, curvature self-similarity. We therefore suggest an embedded feature selection method for SVMs that reduces complexity and improves generalization capability of object models. By successfully integrating the proposed curvature self-similarity representation together with the embedded feature selection in a widely used state-of-the-art object detection framework we show the general pertinence of the approach.

Linear Support Vector Machines (SVMs) have become very popular in vision as part of state-of-the-art object recognition and other classification tasks but require high dimensional feature spaces for good performance. Deep learning methods can find more compact representations but current methods employ multilayer perceptrons that require solving a difficult, non-convex optimization problem. We propose a deep non-linear classifier whose layers are SVMs and which incorporates random projection as its core stacking element. Our method learns layers of linear SVMs recursively transforming the original data manifold through a random projection of the weak prediction computed from each layer. Our method scales as linear SVMs, does not rely on any kernel computations or nonconvex optimization, and exhibits better generalization ability than kernel-based SVMs. This is especially true when the number of training samples is smaller than the dimensionality of data, a common scenario in many real-world applications. The use of random projections is key to our method, as we show in the experiments section, in which we observe a consistent improvement over previous -often more complicated-methods on several vision and speech benchmarks.

We propose an efficient, generalized, nonparametric, statistical Kolmogorov-Smirnov test for detecting distributional change in high-dimensional data. To implement the test, we introduce a novel, hierarchical, minimum-volume sets estimator to represent the distributions to be tested. Our work is motivated by the need to detect changes in data streams, and the test is especially efficient in this context. We provide the theoretical foundations of our test and show its superiority over existing methods.

A patient's risk for adverse events is affected by temporal processes including the nature and timing of diagnostic and therapeutic activities, and the overall evolution of the patient's pathophysiology over time. Yet many investigators ignore this temporal aspect when modeling patient outcomes, considering only the patient's current or aggregate state. In this paper, we represent patient risk as a time series. In doing so, patient risk stratification becomes a time-series classification task. The task differs from most applications of time-series analysis, like speech processing, since the time series itself must first be extracted. Thus, we begin by defining and extracting approximate risk processes, the evolving approximate daily risk of a patient.

Non-linear dynamical systems (DS) have been used extensively for building generative models of human behavior. Their applications range from modeling brain dynamics to encoding motor commands. Many schemes have been proposed for encoding robot motions using dynamical systems with a single attractor placed at a predefined target in state space. Although these enable the robots to react against sudden perturbations without any re-planning, the motions are always directed towards a single target. In this work, we focus on combining several such DS with distinct attractors, resulting in a multi-stable DS.

Kernel machines such as kernel SVM and kernel ridge regression usually construct high quality models; however, their use in real-world applications remains limited due to the high prediction cost.

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.

Lazy local learning methods train a classifier "on the fly" at test time, using only a subset of the training instances that are most relevant to the novel test example. The goal is to tailor the classifier to the properties of the data surrounding the test example. Existing methods assume that the instances most useful for building the local model are strictly those closest to the test example. However, this fails to account for the fact that the success of the resulting classifier depends on the full distribution of selected training instances. Rather than simply gathering the test example's nearest neighbors, we propose to predict the subset of training data that is jointly relevant to training its local model. We develop an approach to discover patterns between queries and their "good" neighborhoods using large-scale multilabel classification with compressed sensing. Given a novel test point, we estimate both the composition and size of the training subset likely to yield an accurate local model. We demonstrate the approach on image classification tasks on SUN and aPascal and show its advantages over traditional global and local approaches.

In many classification problems, the input is represented as a set of features, e.g., the bag-of-words (BoW) representation of documents. Support vector machines (SVMs) are widely used tools for such classification problems. The performance of the SVMs is generally determined by whether kernel values between data points can be defined properly. However, SVMs for BoW representations have a major weakness in that the co-occurrence of different but semantically similar words cannot be reflected in the kernel calculation. To overcome the weakness, we propose a kernel-based discriminative classifier for BoW data, which we call the latent support measure machine (latent SMM). With the latent SMM, a latent vector is associated with each vocabulary term, and each document is represented as a distribution of the latent vectors for words appearing in the document. To represent the distributions efficiently, we use the kernel embeddings of distributions that hold high order moment information about distributions. Then the latent SMM finds a separating hyperplane that maximizes the margins between distributions of different classes while estimating latent vectors for words to improve the classification performance. In the experiments, we show that the latent SMM achieves state-of-the-art accuracy for BoW text classification, is robust with respect to its own hyper-parameters, and is useful to visualize words.