This conditional expected claim amount is called the pure premium and it is the basis of the gross premium charged to the insured. This expected value is conditionned on information available about the insured and about the contract, which we call input profile here. This regression problem is difficult for several reasons: large number of examples, -large number variables (most of which are discrete and multi-valued), non-stationarity of the distribution, and a conditional distribution of the dependent variable which is very different from those usually encountered in typical applications.of

A nonlinear supervised learning model, the Specialized Mappings Architecture (SMA), is described and applied to the estimation of human body pose from monocular images. The SMA consists of several specialized forward mapping functions and an inverse mapping function. Each specialized function maps certain domains of the input space (image features) onto the output space (body pose parameters). The key algorithmic problems faced are those of learning the specialized domains and mapping functions in an optimal way, as well as performing inference given inputs and knowledge of the inverse function. Solutions to these problems employ the EM algorithm and alternating choices of conditional independence assumptions. Performance of the approach is evaluated with synthetic and real video sequences of human motion.

Locally Linear Embedding (LLE) is an elegant nonlinear dimensionality-reduction technique recently introduced by Roweis and Saul [2]. It fails when the data is divided into separate groups. We study a variant of LLE that can simultaneously group the data and calculate local embedding of each group. An estimate for the upper bound on the intrinsic dimension of the data set is obtained automatically. 1 Introduction Consider a collection of N data points Xi E ]RD.

An important issue in applying SVMs to speech recognition is the ability to classify variable length sequences. This paper presents extensions to a standard scheme for handling this variable length data, the Fisher score. A more useful mapping is introduced based on the likelihood-ratio. The score-space defined by this mapping avoids some limitations of the Fisher score. Class-conditional generative models are directly incorporated into the definition of the score-space.

A novel approach for comparing sequences of observations using an explicit-expansion kernel is demonstrated. The kernel is derived using the assumption of the independence of the sequence of observations and a mean-squared error training criterion. The use of an explicit expansion kernel reduces classifier model size and computation dramatically, resulting in model sizes and computation one-hundred times smaller in our application. The explicit expansion also preserves the computational advantages of an earlier architecture based on mean-squared error training. Training using standard support vector machine methodology gives accuracy that significantly exceeds the performance of state-of-the-art mean-squared error training for a speaker recognition task.

This paper describes a clustering algorithm for vector quantizers using a "stochastic association model". It offers a new simple and powerful softmax adaptation rule. The adaptation process is the same as the online K-means clustering method except for adding random fluctuation in the distortion error evaluation process. Simulation results demonstrate that the new algorithm can achieve efficient adaptation as high as the "neural gas" algorithm, which is reported as one of the most efficient clustering methods. It is a key to add uncorrelated random fluctuation in the similarity evaluation process for each reference vector. For hardware implementation of this process, we propose a nanostructure, whose operation is described by a single-electron circuit. It positively uses fluctuation in quantum mechanical tunneling processes.

The support vector machine (SVM) is known for its good performance in binary classification, but its extension to multi-class classification is still an ongoing research issue. In this paper, we propose a new approach for classification, called the import vector machine (IVM), which is built on kernel logistic regression (KLR). We show that the IVM not only performs as well as the SVM in binary classification, but also can naturally be generalized to the multi-class case. Furthermore, the IVM provides an estimate of the underlying probability. Similar to the "support points" of the SVM, the IVM model uses only a fraction of the training data to index kernel basis functions, typically a much smaller fraction than the SVM. This gives the IVM a computational advantage over the SVM, especially when the size of the training data set is large.

In this model, each training example is a set (or bag) of instances along with a single label equal to the maximum label among all instances in the bag. The individual instances within the bag are not given labels. The goal is to learn to accurately predict the label of previously unseen bags. Standard supervised learning can be viewed as a special case of MI learning where each bag holds a single instance. The MI learning model was originally motivated by the drug activity prediction problem where each instance is a possible conformation (or shape) of a molecule and each bag contains all likely low-energy conformations for the molecule.

Greedy approximation algorithms have been frequently used to obtain sparse solutions to learning problems. In this paper, we present a general greedy algorithm for solving a class of convex optimization problems. We derive a bound on the rate of approximation for this algorithm, and show that our algorithm includes a number of earlier studies as special cases.

In K-means clusters are represented by centers of mass of their members, and it can be shown that the K-means algorithm of alternating between assigning cluster membership for each data vector to the nearest cluster center and computing the center of each cluster as the centroid of its member data vectors is equivalent to finding the minimum of a sum-of-squares cost function using coordinate descend. Despite the popularity of K means clustering, one of its major drawbacks is that the coordinate descend search method is prone to local minima. Much research has been done on computing refined initial points and adding explicit constraints to the sum-of-squares cost function for K-means clustering so that the search can converge to better local minimum [1,2]. In this paper we tackle the problem from a different angle: we find an equivalent formulation of the sum-of-squares minimization as a trace maximization problem with special constraints; relaxing the constraints leads to a maximization problem that possesses optimal global solutions. As a byproduct we also have an easily computable lower bound for the minimum of the sum-of-squares cost function. Our work is inspired by [9, 3] where connection to Gram matrix and extension of K means method to general Mercer kernels were investigated. The rest of the paper is organized as follows: in section 2, we derive the equivalent trace maximization formulation and discuss its spectral relaxation. In section 3, we discuss how to assign cluster membership using pivoted QR decomposition, taking into account the special structure of the partial eigenvector matrix. Finally, in section 4, we illustrate the performance of the clustering algorithms using document clustering as an example.