Fast aggregation of Student mixture models

International audienceThis paper deals with probabilistic models, that take the form of mixtures of Student distributions. Student distributions are known to be more statistically robust than Gaussian distributions, with regard to outliers (i.e. data that cannot be reasonnably explained by any component in the mixture and that do not justifiy an extra component. Our contribution is as follows : we show how several mixtures of Student distributions may be agregated into a single mixture, without resorting to sampling. The trick is that, as is well known, a Student distribution may be expressed as an infinite mixture of Gaussians, where the variances follow a Gamma distribution

Fast aggregation of Student mixture models

International audienceThis paper deals with probabilistic models, that take the form of mixtures of Student distributions. Student distributions are known to be more statistically robust than Gaussian distributions, with regard to outliers (i.e. data that cannot be reasonnably explained by any component in the mixture and that do not justifiy an extra component. Our contribution is as follows : we show how several mixtures of Student distributions may be agregated into a single mixture, without resorting to sampling. The trick is that, as is well known, a Student distribution may be expressed as an infinite mixture of Gaussians, where the variances follow a Gamma distribution

Fast and Robust Rank Aggregation against Model Misspecification

In rank aggregation, preferences from different users are summarized into a total order under the homogeneous data assumption. Thus, model misspecification arises and rank aggregation methods take some noise models into account. However, they all rely on certain noise model assumptions and cannot handle agnostic noises in the real world. In this paper, we propose CoarsenRank, which rectifies the underlying data distribution directly and aligns it to the homogeneous data assumption without involving any noise model. To this end, we define a neighborhood of the data distribution over which Bayesian inference of CoarsenRank is performed, and therefore the resultant posterior enjoys robustness against model misspecification. Further, we derive a tractable closed-form solution for CoarsenRank making it computationally efficient. Experiments on real-world datasets show that CoarsenRank is fast and robust, achieving consistent improvement over baseline methods

Bayesian modeling and forecasting of 24-hour high-frequency volatility: A case study of the financial crisis

This paper estimates models of high frequency index futures returns using `around the clock' 5-minute returns that incorporate the following key features: multiple persistent stochastic volatility factors, jumps in prices and volatilities, seasonal components capturing time of the day patterns, correlations between return and volatility shocks, and announcement effects. We develop an integrated MCMC approach to estimate interday and intraday parameters and states using high-frequency data without resorting to various aggregation measures like realized volatility. We provide a case study using financial crisis data from 2007 to 2009, and use particle filters to construct likelihood functions for model comparison and out-of-sample forecasting from 2009 to 2012. We show that our approach improves realized volatility forecasts by up to 50% over existing benchmarks.Comment: 48 pages, 7 figure

Decorrelation of Neutral Vector Variables: Theory and Applications

In this paper, we propose novel strategies for neutral vector variable decorrelation. Two fundamental invertible transformations, namely serial nonlinear transformation and parallel nonlinear transformation, are proposed to carry out the decorrelation. For a neutral vector variable, which is not multivariate Gaussian distributed, the conventional principal component analysis (PCA) cannot yield mutually independent scalar variables. With the two proposed transformations, a highly negatively correlated neutral vector can be transformed to a set of mutually independent scalar variables with the same degrees of freedom. We also evaluate the decorrelation performances for the vectors generated from a single Dirichlet distribution and a mixture of Dirichlet distributions. The mutual independence is verified with the distance correlation measurement. The advantages of the proposed decorrelation strategies are intensively studied and demonstrated with synthesized data and practical application evaluations