We introduce a characterisation of probabilistic transition systems (PTS) in terms of linear operators on some suitably defined vector space representing the set of states. Various notions of process equivalences can then be re-formulated as abstract linear operators related to the concrete PTS semantics via a probabilistic abstract interpretation. These process equivalences can be turned into ...

Let X be a d×d symmetric random matrix with independent but non-identically distributed Gaussian entries. It has been conjectured by Lata la that the spectral norm of X is always of the same order as the largest Euclidean norm of its rows. A positive resolution of this conjecture would provide a sharp understanding of the probabilistic mechanisms that control the spectral norm of inhomogeneous ...

It is known that each symmetric stable distribution in Rd is related to a norm on Rd that makes Rd embeddable in Lp([0, 1]). In case of a multivariate Cauchy distribution the unit ball in this norm corresponds is the polar set to a convex set in Rd called a zonoid. This work exploits most recent advances in convex geometry in order to come up with new probabilistic results for multivariate stab...

We consider the Poisson equations for denumerable Markov chains with unbounded cost functions. Solutions to the Poisson equations exist in the Banach space of bounded real-valued functions with respect to a weighted supremum norm such that the Markov chain is geometrically ergodic. Under minor additional assumptions the solution is also unique. We give a novel probabilistic proof of this fact u...

It is known that each symmetric stable distribution in Rd is related to a norm on Rd that makes Rd embeddable in Lp([0, 1]). In case of a multivariate Cauchy distribution the unit ball in this norm is the polar set to a convex set in Rd called a zonoid. This work interprets general stable laws using convex or star-shaped sets and exploits recent advances in convex geometry in order to come up w...

Multi-label classification is a critical problem in many areas of data analysis such as image labeling and text categorization. In this paper we propose a probabilistic multi-label classification model based on novel sparse feature learning. By employing an individual sparsity inducing l1-norm and a group sparsity inducing l2,1-norm, the proposed model has the capacity of capturing both label i...

In this paper, we propose a Lasso based framework to generate the sparse total variability supervectors (s-vectors). Rather than the factor analysis framework, which uses a low dimensional Eigenvoice subspace to represent the mean supervector, the proposed Lasso approach utilizes the l norm regularized least square estimation to project the mean supervector on a pre-defined dictionary. The numb...

The approximate Carathéodory theorem states that given a compact convex set $${\mathcal {C}}\subset {\mathbb {R}}^n$$ and $$p\in [2,+\infty [$$ , each point $$x^*\in {\mathcal {C}}$$ can be approximated to $$\epsilon $$ -accuracy in the $$\ell _p$$ -norm as combination of {O}}(pD_p^2/\epsilon ^2)$$ vertices where $$D_p$$ is diameter -norm. A solution satisfying these properties built using prob...

We make a probabilistic analysis related to some inference rules which play an important role in nonmonotonic reasoning. In a coherence-based setting, we study the extensions of a probability assessment defined on n conditional events to their quasi conjunction, and by exploiting duality, to their quasi disjunction. The lower and upper bounds coincide with some well known t-norms and t-conorms:...