Prior knowledge in the form of multiple polyhedral sets, each be(cid:173) longing to one of two categories, is introduced into a reformulation of a linear support vector machine classifier. The resulting formu(cid:173) lation leads to a linear program that can be solved efficiently. Real world examples, from DNA sequencing and breast cancer prognosis, demonstrate the effectiveness of the proposed method. Numerical results show improvement in test set accuracy after the incorpo(cid:173) ration of prior knowledge into ordinary, data-based linear support vector machine classifiers. One experiment also shows that a lin(cid:173) ear classifier, based solely on prior knowledge, far outperforms the direct application of prior knowledge rules to classify data.

Classification trees are one of the most popular types of classifiers, with ease of implementation and interpretation being among their attractive features. Despite the widespread use of classification trees, theoretical analysis of their performance is scarce. In this paper, we show that a new family of classification trees, called dyadic classification trees (DCTs), are near optimal (in a minimax sense) for a very broad range of clas- sification problems. This demonstrates that other schemes (e.g., neural networks, support vector machines) cannot perform significantly better than DCTs in many cases. We also show that this near optimal perfor- mance is attained with linear (in the number of training data) complexity growing and pruning algorithms.

We investigate data based procedures for selecting the kernel when learn- ing with Support Vector Machines. We provide generalization error bounds by estimating the Rademacher complexities of the corresponding function classes. In particular we obtain a complexity bound for function classes induced by kernels with given eigenvectors, i.e., we allow to vary the spectrum and keep the eigenvectors fix. This bound is only a loga- rithmic factor bigger than the complexity of the function class induced by a single kernel. However, optimizing the margin over such classes leads to overfitting.

This paper presents two new formulations of multiple-instance learning as a maximum margin problem. The proposed extensions of the Support Vector Machine (SVM) learning approach lead to mixed integer quadratic programs that can be solved heuristically. Our generalization of SVMs makes a state-of-the-art classification technique, including non-linear classification via kernels, available to an area that up to now has been largely dominated by special purpose methods. We present experimental results on a pharma(cid:173) ceutical data set and on applications in automated image indexing and document categorization.

Forward decoding kernel machines (FDKM) combine large-margin clas(cid:173) sifiers with hidden Markov models (HMM) for maximum a posteriori (MAP) adaptive sequence estimation. State transitions in the sequence are conditioned on observed data using a kernel-based probability model trained with a recursive scheme that deals effectively with noisy and par(cid:173) tially labeled data. Training over very large data sets is accomplished us(cid:173) ing a sparse probabilistic support vector machine (SVM) model based on quadratic entropy, and an on-line stochastic steepest descent algorithm. For speaker-independent continuous phone recognition, FDKM trained over 177,080 samples of the TlMIT database achieves 80.6% recognition accuracy over the full test set, without use of a prior phonetic language model.

We introduce a class of string kernels, called mismatch kernels, for use with support vector machines (SVMs) in a discriminative approach to the protein classification problem. These kernels measure sequence sim- ilarity based on shared occurrences of -length subsequences, counted with up to mismatches, and do not rely on any generative model for the positive training sequences. We compute the kernels efficiently using a mismatch tree data structure and report experiments on a benchmark SCOP dataset, where we show that the mismatch kernel used with an SVM classifier performs as well as the Fisher kernel, the most success- ful method for remote homology detection, while achieving considerable computational savings.

This paper presents a method for learning a distance metric from rel- ative comparison such as "A is closer to B than A is to C". Taking a Support Vector Machine (SVM) approach, we develop an algorithm that provides a flexible way of describing qualitative training data as a set of constraints. We show that such constraints lead to a convex quadratic programming problem that can be solved by adapting standard meth- ods for SVM training. We empirically evaluate the performance and the modelling flexibility of the algorithm on a collection of text documents.

A recent area of significant progress in speaker recognition is the use of high level features--idiolect, phonetic relations, prosody, discourse structure, etc. A speaker not only has a distinctive acoustic sound but uses language in a characteristic manner. Large corpora of speech data available in recent years allow experimentation with long term statistics of phone patterns, word patterns, etc. of an individual. We propose the use of support vector machines and term frequency analysis of phone se- quences to model a given speaker. To this end, we explore techniques for text categorization applied to the problem.

We consider the question of predicting nonlinear time series. Kernel Dy- namical Modeling (KDM), a new method based on kernels, is proposed as an extension to linear dynamical models. The kernel trick is used twice: first, to learn the parameters of the model, and second, to compute preimages of the time series predicted in the feature space by means of Support Vector Regression. Our model shows strong connection with the classic Kalman Filter model, with the kernel feature space as hidden state space. Kernel Dynamical Modeling is tested against two benchmark time series and achieves high quality predictions.

The Minimax Probability Machine Classification (MPMC) framework [Lanckriet et al., 2002] builds classifiers by minimizing the maximum probability of misclassification, and gives direct estimates of the proba- bilistic accuracy bound Ω. The only assumptions that MPMC makes is that good estimates of means and covariance matrices of the classes exist. However, as with Support Vector Machines, MPMC is computationally expensive and requires extensive cross validation experiments to choose kernels and kernel parameters that give good performance. In this paper we address the computational cost of MPMC by proposing an algorithm that constructs nonlinear sparse MPMC (SMPMC) models by incremen- tally adding basis functions (i.e. Therefore the SMPMC algorithm simultaneously addresses the problem of kernel selection and feature selection (i.e.