Ruby C. Weng

A note on Platt's probabilistic outputs for support vector machines

Abstract Platt’s probabilistic outputs for Support Vector Machines (Platt, J. in Smola, A., et al. (eds.) Advances in large margin classifiers. Cambridge, 2000) has been popular for applications that require posterior class probabilities. In this note, we propose an improved algorithm that theoretically converges and avoids numerical difficulties. A simple and ready-to-use pseudo code is included.

Trust Region Newton Method for Logistic Regression

Large-scale logistic regression arises in many applications such as document classification and natural language processing. In this paper, we apply a trust region Newton method to maximize the log-likelihood of the logistic regression model. The proposed method uses only approximate Newton steps in the beginning, but achieves fast convergence in the end. Experiments show that it is faster than the commonly used quasi Newton approach for logistic regression. We also extend the proposed method to large-scale L2-loss linear support vector machines (SVM).

Trust region Newton methods for large-scale logistic regression

Large-scale logistic regression arises in many applications such as document classification and natural language processing. In this paper, we apply a trust region Newton method to maximize the log-likelihood of the logistic regression model. The proposed method uses only approximate Newton steps in the beginning, but achieves fast convergence in the end. Experiments show that it is faster than the commonly used quasi Newton approach for logistic regression. We also compare it with linear SVM implementations.

Analysis of switching dynamics with competing support vector machines

We present a framework for the unsupervised segmentation of switching dynamics using support vector machines. Following the architecture by Pawelzik et al., where annealed competing neural networks were used to segment a nonstationary time series, in this paper, we exploit the use of support vector machines, a well-known learning technique. First, a new formulation of support vector regression is proposed. Second, an expectation-maximization step is suggested to adaptively adjust the annealing parameter. Results indicate that the proposed approach is promising.

Ranking Individuals by Group Comparisons

This paper proposes new approaches to rank individuals from their group competition results. Many real-world problems are of this type. For example, ranking players from team games is important in some sports. We propose an exponential model to solve such problems. To estimate individual rankings through the proposed model we introduce two convex minimization formulas with easy and efficient solution procedures. Experiments on real bridge records and multi-class classification demonstrate the viability of the proposed model.

Analysis of Nonstationary Time Series Using Support Vector Machines

Time series from alternating dynamics have many important applications. In [5], the authors propose an approach to solve the drifting dynamics. Their method directly solves a non-convex optimization problem. In this paper, we propose a strategy which solves a sequence of convex optimization problems by using modified support vector regression. Experimental results showing its practical viability are presented and we also discuss the advantages and disadvantages of the proposed approach.

CORRECTED CONFIDENCE INTERVALS FOR SECONDARY PARAMETERS FOLLOWING SEQUENTIAL TESTS

Corrected confidence intervals are developed for the mean of the second component of a bi- variate normal process when the first component is being monitored sequentially. This is accomplished by constructing a first approximation to a pivotal quantity, and then using very weak expansions to determine the correction terms. The asymptotic sampling distribution of the renormalised pivotal quantity is established in both the case where the covariance matrix is known and when it is unknown. The resulting approximations have a simple form and the results of a simulation study of two well- known sequential tests show that they are very accurate. The practical usefulness of the approach is illustrated by a real example of bivariate data. Detailed proofs of the main results are provided.

A Note on Item Response Theory Modeling for Online Customer Ratings

ABSTRACT Online consumer product ratings data are increasing rapidly. While most of the current graphical displays mainly represent the average ratings, Ho and Quinn proposed an easily interpretable graphical display based on an ordinal item response theory (IRT) model, which successfully accounts for systematic interrater differences. Conventionally, the discrimination parameters in IRT models are constrained to be positive, particularly in the modeling of scored data from educational tests. In this article, we use real-world ratings data to demonstrate that such a constraint can have a great impact on the parameter estimation. This impact on estimation was explained through rater behavior. We also discuss correlation among raters and assess the prediction accuracy for both the constrained and the unconstrained models. The results show that the unconstrained model performs better when a larger fraction of rater pairs exhibit negative correlations in ratings.

Ranking individuals by group comparisons

This paper proposes new approaches to rank individuals from their group competition results. Many real-world problems are of this type. For example, ranking players from team games is important in some sports. We propose an exponential model to solve such problems. To estimate individual rankings through the proposed model we introduce two convex minimization formulas with easy and efficient solution procedures. Experiments on real bridge records and multi-class classification demonstrate the viability of the proposed model.

SEQUENTIAL CONFIDENCE INTERVALS FOR A POPULATION SIZE WITH FIXED PROPORTIONAL ACCURACY

Consider a population of hidden objects of which the total number N is unknown. A search for the objects may be conducted in which the times at which the objects were found is recorded, along with the total number of objects found. From such data, a confidence interval for N is desired with specified proportional accuracy. Two sequential sampling plans are proposed for this problem, for two sets of underlying assumptions, and their properties are studied through asymptotic analysis and simulation.