Disturbance Grassmann Kernels for Subspace-Based Learning

In this paper, we focus on subspace-based learning problems, where data elements are linear subspaces instead of vectors. To handle this kind of data, Grassmann kernels were proposed to measure the space structure and used with classifiers, e.g., Support Vector Machines (SVMs). However, the existing discriminative algorithms mostly ignore the instability of subspaces, which would cause the classifiers misled by disturbed instances. Thus we propose considering all potential disturbance of subspaces in learning processes to obtain more robust classifiers. Firstly, we derive the dual optimization of linear classifiers with disturbance subject to a known distribution, resulting in a new kernel, Disturbance Grassmann (DG) kernel. Secondly, we research into two kinds of disturbance, relevant to the subspace matrix and singular values of bases, with which we extend the Projection kernel on Grassmann manifolds to two new kernels. Experiments on action data indicate that the proposed kernels perform better compared to state-of-the-art subspace-based methods, even in a worse environment.Comment: This paper include 3 figures, 10 pages, and has been accpeted to SIGKDD'1

Risk Measurement for Portfolio Credit Risk Based on a Mixed Poisson Model

Experiences manifest the importance of comovement and communicable characters among the risks of financial assets. Therefore, the portfolio view considering dependence relationship among credit entities is at the heart of risk measurement. This paper introduces a mixed Poisson model assuming default probabilities of obligors depending on a set of common economic factors to construct the dependence structure of obligors. Further, we apply mixed Poisson model into an empirical study with data of four industry portfolios in the financial market of China. In the process of model construction, the classical structural approach and option pricing formula contribute to estimate dynamic default probabilities of single obligor, which helps to obtain the dynamic Poisson intensities under the model assumption. Finally, given the values of coefficients in this model calculated by a nonlinear estimation, Monte Carlo technique simulates the progress of loss occurrence. Relationship between default probability and loss level reflected through the MC simulation has practical features. This study illustrates the practical value and effectiveness of mixed Poisson model in risk measurement for credit portfolio

Estimating heterogeneous agents behavior in a two-market financial system

In this paper, we propose a two-market empirical model with heterogeneous agents based on Chiarella et al. (2012). Using monthly data of French and US stock markets, the regression shows that individual markets have feature of two-regime switching process. By including inter-market traders whose trading decision is based on fundamental value of foreign market, the two-market model has a better capability in explaining both markets with domestic fundamental traders turning to be significant. The existence of inter-market traders implies that the two markets impact each other through their fundamental and hence share some common set of factors, which provides foundation of market interactions, such as market co-movement