We introduce a novel active-learning scenario in which a user wants to work with a learning algorithm to identify useful anomalies. These are distinguished from the traditional statistical definition of anomalies as outliers or merely ill-modeled points. Our distinction is that the usefulness ofanomalies is categorized subjectively by the user. We make two additional assumptions. First, there exist extremely few useful anomalies tobe hunted down within a massive dataset.

Clustering and prediction of sets of curves is an important problem in many areas of science and engineering. It is often the case that curves tend to be misaligned from each other in a continuous manner, either in space (across the measurements) or in time. We develop a probabilistic framework that allows for joint clustering and continuous alignment of sets of curves in curve space (as opposed to a fixed-dimensional featurevector space).The proposed methodology integrates new probabilistic alignment models with model-based curve clustering algorithms. The probabilistic approach allows for the derivation of consistent EM learning algorithmsfor the joint clustering-alignment problem. Experimental results are shown for alignment of human growth data, and joint clustering andalignment of gene expression time-course data.

Many interesting multiclass problems can be cast in the general framework oflabel ranking defined on a given set of classes. The evaluation for such a ranking is generally given in terms of the number of violated order constraints between classes. In this paper, we propose the Preference LearningModel as a unifying framework to model and solve a large class of multiclass problems in a large margin perspective. In addition, an original kernel-based method is proposed and evaluated on a ranking dataset with state-of-the-art results.

We formulate the problem of graph inference where part of the graph is known as a supervised learning problem, and propose an algorithm to solve it. The method involves the learning of a mapping of the vertices to a Euclidean space where the graph is easy to infer, and can be formulated asan optimization problem in a reproducing kernel Hilbert space. We report encouraging results on the problem of metabolic network reconstruction fromgenomic data.

This paper investigates a new learning model in which the input data is corrupted with noise. We present a general statistical framework to tackle this problem. Based on the statistical reasoning, we propose a novel formulation of support vector classification, which allows uncertainty ininput data. We derive an intuitive geometric interpretation of the proposed formulation, and develop algorithms to efficiently solve it. Empirical results are included to show that the newly formed method is superior to the standard SVM for problems with noisy input.

This paper provides a foundation for multi-task learning using reproducing kernel Hilbertspaces of vector-valued functions. In this setting, the kernel is a matrix-valued function. Some explicit examples will be described which go beyond ourearlier results in [7]. In particular, we characterize classes of matrix-valued kernels which are linear and are of the dot product or the translation invariant type.We discuss how these kernels can be used to model relations between the tasks and present linear multi-task learning algorithms. Finally, we present a novel proof of the representer theorem for a minimizer of a regularization functional whichis based on the notion of minimal norm interpolation.

We propose a convex optimization based strategy to deal with uncertainty in the observations of a classification problem.

We give a fast rejection scheme that is based on image segments and demonstrate it on the canonical example of face detection. However, instead offocusing on the detection step we focus on the rejection step and show that our method is simple and fast to be learned, thus making it an excellent pre-processing step to accelerate standard machine learning classifiers, such as neural-networks, Bayes classifiers or SVM. We decompose acollection of face images into regions of pixels with similar behavior over the image set. The relationships between the mean and variance of image segments are used to form a cascade of rejectors that can reject over 99.8% of image patches, thus only a small fraction of the image patches must be passed to a full-scale classifier. Moreover, the training time for our method is much less than an hour, on a standard PC.

This paper proposes a method for computing fast approximations to support vectordecision functions in the field of object detection. In the present approach we are building on an existing algorithm where the set of support vectors is replaced by a smaller, so-called reduced set of synthesized inputspace points. In contrast to the existing method that finds the reduced set via unconstrained optimization, we impose a structural constraint on the synthetic points such that the resulting approximations can be evaluated via separable filters. For applications that require scanning largeimages, this decreases the computational complexity by a significant amount.Experimental results show that in face detection, rank deficient approximations are 4 to 6 times faster than unconstrained reduced setsystems.

We devise and experiment with a dynamical kernel-based system for tracking hand movements from neural activity. The state of the system corresponds to the hand location, velocity, and acceleration, while the system's input are the instantaneous spike rates. The system's state dynamics isdefined as a combination of a linear mapping from the previous estimated state and a kernel-based mapping tailored for modeling neural activities. In contrast to generative models, the activity-to-state mapping is learned using discriminative methods by minimizing a noise-robust loss function. We use this approach to predict hand trajectories on the basis of neural activity in motor cortex of behaving monkeys and find that the proposed approach is more accurate than both a static approach based on support vector regression and the Kalman filter.