Related papers: Matrix liberation process I: Large deviation upper…
We give bounds on the rate of convergence to equilibrium of the symmetric simple exclusion process in $\Z^d$. Our results include the existent results in the literature. We get better bounds and larger class of initial states via a unified…
Free probability theory started in the 1980s has attracted much attention lately in signal processing and communications areas due to its applications in large size random matrices. However, it involves with massive mathematical concepts…
We investigate the problem of approximate Bayesian inference for a general class of observation models by means of the expectation propagation (EP) framework for large systems under some statistical assumptions. Our approach tries to…
The goal of this work is to prove a new sure upper bound in a setting that can be thought of as a simplified function field analogue. This result is comparable to a recent result of the author concerning almost sure upper bound of random…
Motivated by the asymptotic collective behavior of random and deterministic matrices, we propose an approximation (called "free deterministic equivalent") to quite general random matrix models, by replacing the matrices with operators…
In this paper, we propose a novel method for matrix completion under general non-uniform missing structures. By controlling an upper bound of a novel balancing error, we construct weights that can actively adjust for the non-uniformity in…
Many random combinatorial objects have a component structure whose joint distribution is equal to that of a process of mutually independent random variables, conditioned on the value of a weighted sum of the variables. It is interesting to…
Large deviation principles are established for the Fleming-Viot processes with neutral mutation and selection, and the corresponding equilibrium measures as the sampling rate goes to 0. All results are first proved for the finite allele…
Graphical models trained using maximum likelihood are a common tool for probabilistic inference of marginal distributions. However, this approach suffers difficulties when either the inference process or the model is approximate. In this…
This paper is concerned with the problem of exact MAP inference in general higher-order graphical models by means of a traditional linear programming relaxation approach. In fact, the proof that we have developed in this paper is a rather…
In this paper we address the complexity of solving linear programming problems with a set of differential equations that converge to a fixed point that represents the optimal solution. Assuming a probabilistic model, where the inputs are…
In recent years, several algorithms, which approximate matrix decomposition, have been developed. These algorithms are based on metric conservation features for linear spaces of random projection types. We show that an i.i.d sub-Gaussian…
This paper studies probabilistic rates of convergence for consensus+innovations type of algorithms in random, generic networks. For each node, we find a lower and also a family of upper bounds on the large deviations rate function, thus…
In this note, we define a Gaussian probability distribution over matrices. We prove some useful properties of this distribution, namely, the fact that marginalization, conditioning, and affine transformations preserve the matrix Gaussian…
We present a generalization of the maximal inequalities that upper bound the expectation of the maximum of $n$ jointly distributed random variables. We control the expectation of a randomly selected random variable from $n$ jointly…
One of the main applications of free probability is to show that for appropriately chosen independent copies of $d$ random matrix models, any noncommutative polynomial in these $d$ variables has a spectral distribution that converges…
Large random matrices appear in different fields of mathematics and physics such as combinatorics, probability theory, statistics, operator theory, number theory, quantum field theory, string theory etc... In the last ten years, they…
This paper is concerned with the problem of approximating the determinant of A for a large sparse symmetric positive definite matrix A. It is shown that an efficient solution of this problem is obtained by using a sparse approximate inverse…
We introduce a finite version of free probability for rectangular matrices that amounts to operations on singular values of polynomials. We show that we can replicate the transforms from free probability, and that asymptotically there is…
Given an arbitrary long but finite sequence of observations from a finite set, we construct a simple process that approximates the sequence, in the sense that with high probability the empirical frequency, as well as the empirical one-step…