arXiv subjects

Stéphane Marchand-Maillet

Publications and source records attributed to Stéphane Marchand-Maillet.

21 records · Page 2Linked to original sources

arXiv2017

Forecasting and Granger Modelling with Non-linear Dynamical Dependencies

Traditional linear methods for forecasting multivariate time series are not able to satisfactorily model the non-linear dependencies that may exist in non-Gaussian series. We build on the theory of learning vector-valued functions in the reproducing kernel Hilbert space and develop a method for learning prediction functions that accommodate such non-linearities. The method not only learns the predictive function but also the matrix-valued kernel underlying the function search space directly from the data. Our approach is based on learning multiple matrix-valued kernels, each of those composed of a set of input kernels and a set of output kernels learned in the cone of positive semi-definite matrices. In addition to superior predictive performance in the presence of strong non-linearities, our method also recovers the hidden dynamic relationships between the series and thus is a new alternative to existing graphical Granger techniques.

cs.LG↗

arXiv2017

On Hölder projective divergences

We describe a framework to build distances by measuring the tightness of inequalities, and introduce the notion of proper statistical divergences and improper pseudo-divergences. We then consider the Hölder ordinary and reverse inequalities, and present two novel classes of Hölder divergences and pseudo-divergences that both encapsulate the special case of the Cauchy-Schwarz divergence. We report closed-form formulas for those statistical dissimilarities when considering distributions belonging to the same exponential family provided that the natural parameter space is a cone (e.g., multivariate Gaussians), or affine (e.g., categorical distributions). Those new classes of Hölder distances are invariant to rescaling, and thus do not require distributions to be normalized. Finally, we show how to compute statistical Hölder centroids with respect to those divergences, and carry out center-based clustering toy experiments on a set of Gaussian distributions that demonstrate empirically that symmetrized Hölder divergences outperform the symmetric Cauchy-Schwarz divergence.

cs.LG↗

arXiv2016

Learning Leading Indicators for Time Series Predictions

We consider the problem of learning models for forecasting multiple time-series systems together with discovering the leading indicators that serve as good predictors for the system. We model the systems by linear vector autoregressive models (VAR) and link the discovery of leading indicators to inferring sparse graphs of Granger-causality. We propose new problem formulations and develop two new methods to learn such models, gradually increasing the complexity of assumptions and approaches. While the first method assumes common structures across the whole system, our second method uncovers model clusters based on the Granger-causality and leading indicators together with learning the model parameters. We study the performance of our methods on a comprehensive set of experiments and confirm their efficacy and their advantages over state-of-the-art sparse VAR and graphical Granger learning methods.

cs.LG↗