Matrix product representation and synthesis for random vectors: Insight from statistical physics

Details Matrix product representation and synthesis for random vectors: Insight from statistical physics Matrix product representation and synthesis for random vectors: Insight from statistical physics

2012-03-20

arxiv.org/abs/1203.4500v1

Physics

Condensed Matter

Statistical Mechanics

10 pages, 4 figures, submitted to IEEE Transactions on Signal Processing

Scientific paper

Inspired from modern out-of-equilibrium statistical physics models, a matrix product based framework permits the formal definition of random vectors (and random time series) whose desired joint distributions are a priori prescribed. Its key feature consists of preserving the writing of the joint distribution as the simple product structure it has under independence, while inputing controlled dependencies amongst components: This is obtained by replacing the product of distributions by a product of matrices of distributions. The statistical properties stemming from this construction are studied theoretically: The landscape of the attainable dependence structure is thoroughly depicted and a stationarity condition for time series is notably obtained. The remapping of this framework onto that of Hidden Markov Models enables us to devise an efficient and accurate practical synthesis procedure. A design procedure is also described permitting the tuning of model parameters to attain targeted properties. Pedagogical well-chosen examples of times series and multivariate vectors aim at illustrating the power and versatility of the proposed approach and at showing how targeted statistical properties can be actually prescribed.

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