Wavelet frames to optimally learn functions on diffusion measure spaces.

Based on the theory of wavelets on data defined manifolds we study the Kolmogorov metric entropy and related measures of complexity of certain function spaces. We also develop constructive algorithms to represent those functions within a prescribed accuracy that is asymptotically optimal up to a logarithmic factor

Vine Copulas as a Way to Describe and Analyze Multi-Variate Dependence in Econometrics: Computational Motivation and Comparison with Bayesian Networks and Fuzzy Approaches

Abstract. In the last decade, vine copulas emerged as a new efficient techniques for describing and analyzing multi-variate dependence in econometrics; see, e.g., [1–3, 7, 9–11, 13, 14, 21]. Our experience has shown, however, that while these techniques have been successfully applied to many practical problems of econometrics, there is still a lot of confusion and misunderstanding related to vine copulas. In this paper, we provide a motivation for this new technique from the computational viewpoint. We show that other techniques used to described dependence – Bayesian networks and fuzzy techniques – can be viewed as a particular case of vine copulas. 1 Copulas – A Useful Tool in Econometrics: Motivations and Descriptions Need for studying dependence in econometrics. Many researchers have observed that economics is more complex than physics. In physics, many parameters, many phenomena are independent. As a result, we can observe (and thoroughl