A Noise-Robust Fast Sparse Bayesian Learning Model

This paper utilizes the hierarchical model structure from the Bayesian Lasso in the Sparse Bayesian Learning process to develop a new type of probabilistic supervised learning approach. The hierarchical model structure in this Bayesian framework is designed such that the priors do not only penalize the unnecessary complexity of the model but will also be conditioned on the variance of the random noise in the data. The hyperparameters in the model are estimated by the Fast Marginal Likelihood Maximization algorithm which can achieve sparsity, low computational cost and faster learning process. We compare our methodology with two other popular learning models; the Relevance Vector Machine and the Bayesian Lasso. We test our model on examples involving both simulated and empirical data, and the results show that this approach has several performance advantages, such as being fast, sparse and also robust to the variance in random noise. In addition, our method can give out a more stable estimation of variance of random error, compared with the other methods in the study.Comment: 15 page

A note on α\alpha-permanent and loop soup

In this paper, it is shown that the $\alpha$-permanent in algebra is closely related to loop soup in probability. We obtain explicit expansions of $\alpha$-permanents of the block matrices associated to tridiagonal-like matrices. It is proved in two ways, one is the direct combinatorial proof, and the other is the probabilistic proof via loop soup.Comment: 8 pages, 1 figur

Investigating the Asymmetric Behavior of Oil Price Volatility Using Support Vector Regression

This paper investigates the asymmetric behavior of oil price volatility using different types of Asymmetric Power ARCH (APARCH) model. We compare the estimation and forecasting performance of the models estimated from the maximum likelihood estimation (MLE) method and support vector machine (SVM) based regressions. Combining nonparametric SVM method with parametric APARCH model not only enables to keep interpretations of the parametric models but also leads to more precise estimation and forecasting results. Daily or weekly oil price volatility is investigated from March 8, 1991 to September 13, 2019. This whole sample period is split into four sub-periods based on the occurrence of certain economic events, and we examine whether the asymmetric behavior of the volatility exists in each sub-period. Our results indicate that SVM regression generally outperforms the other method with lower estimation and forecasting errors, and it is more robust to the choice of different APARCH models than the MLE counterparts are. Besides, the estimation results of the SVM based regressions in each sub-period show that the ARCH models with asymmetric power generally perform better than the models with symmetric power when the data sub-period includes large swings in oil price. The asymmetric behavior of oil price volatility, however, is not detected when the analysis is done using the whole sample period. This result underscores the importance of identifying the dynamics of the dataset in different periods to improve estimation and forecasting performance in modelling oil price volatility. This paper, therefore, examines volatility behavior of oil price with both methodological and economic underpinnings.publishedVersio