Mihoko Minami | Searcharxiv

arXiv2019

Estimation of Risk Contributions with MCMC

Determining risk contributions of unit exposures to portfolio-wide economic capital is an important task in financial risk management. Computing risk contributions involves difficulties caused by rare-event simulations. In this study, we address the problem of estimating risk contributions when the total risk is measured by value-at-risk (VaR). Our proposed estimator of VaR contributions is based on the Metropolis-Hasting (MH) algorithm, which is one of the most prevalent Markov chain Monte Carlo (MCMC) methods. Unlike existing estimators, our MH-based estimator consists of samples from conditional loss distribution given a rare event of interest. This feature enhances sample efficiency compared with the crude Monte Carlo method. Moreover, our method has the consistency and asymptotic normality, and is widely applicable to various risk models having joint loss density. Our numerical experiments based on simulation and real-world data demonstrate that in various risk models, even those having high-dimensional (approximately 500) inhomogeneous margins, our MH estimator has smaller bias and mean squared error compared with existing estimators.

q-fin.RM↗

arXiv2018

Revisiting the Vector Space Model: Sparse Weighted Nearest-Neighbor Method for Extreme Multi-Label Classification

Machine learning has played an important role in information retrieval (IR) in recent times. In search engines, for example, query keywords are accepted and documents are returned in order of relevance to the given query; this can be cast as a multi-label ranking problem in machine learning. Generally, the number of candidate documents is extremely large (from several thousand to several million); thus, the classifier must handle many labels. This problem is referred to as extreme multi-label classification (XMLC). In this paper, we propose a novel approach to XMLC termed the Sparse Weighted Nearest-Neighbor Method. This technique can be derived as a fast implementation of state-of-the-art (SOTA) one-versus-rest linear classifiers for very sparse datasets. In addition, we show that the classifier can be written as a sparse generalization of a representer theorem with a linear kernel. Furthermore, our method can be viewed as the vector space model used in IR. Finally, we show that the Sparse Weighted Nearest-Neighbor Method can process data points in real time on XMLC datasets with equivalent performance to SOTA models, with a single thread and smaller storage footprint. In particular, our method exhibits superior performance to the SOTA models on a dataset with 3 million labels.

stat.ML↗