Matrix products for the synthesis of stationary time series with a priori prescribed joint distributions

Inspired from non-equilibrium statistical physics models, a general framework enabling the definition and synthesis of stationary time series with a priori prescribed and controlled joint distributions is constructed. Its central feature consists of preserving for the joint distribution the simple product struc- ture it has under independence while enabling to input con- trolled and prescribed dependencies amongst samples. To that end, it is based on products of d-dimensional matrices, whose entries consist of valid distributions. The statistical properties of the thus defined time series are studied in details. Having been able to recast this framework into that of Hidden Markov Models enabled us to obtain an efficient synthesis procedure. Pedagogical well-chosen examples (time series with the same marginal distribution, same covariance function, but different joint distributions) aim at illustrating the power and potential of the approach and at showing how targeted statistical prop- erties can be actually prescribed.Comment: 4 pages, 2 figures, conference publication published in IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 201

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

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.Comment: 10 pages, 4 figures, submitted to IEEE Transactions on Signal Processin

Synthesis of Attributed Feature Models From Product Descriptions: Foundations

Feature modeling is a widely used formalism to characterize a set of products (also called configurations). As a manual elaboration is a long and arduous task, numerous techniques have been proposed to reverse engineer feature models from various kinds of artefacts. But none of them synthesize feature attributes (or constraints over attributes) despite the practical relevance of attributes for documenting the different values across a range of products. In this report, we develop an algorithm for synthesizing attributed feature models given a set of product descriptions. We present sound, complete, and parametrizable techniques for computing all possible hierarchies, feature groups, placements of feature attributes, domain values, and constraints. We perform a complexity analysis w.r.t. number of features, attributes, configurations, and domain size. We also evaluate the scalability of our synthesis procedure using randomized configuration matrices. This report is a first step that aims to describe the foundations for synthesizing attributed feature models