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We propose and analyze a randomized zeroth-order approach based on approximating the exact gradient byfinite differences computed in a set of orthogonal random directions that changes with each iteration. A number ofpreviously proposed…
In a complete bipartite graph with vertex sets of cardinalities $n$ and $m$, assign random weights from exponential distribution with mean 1, independently to each edge. We show that, as $n\rightarrow\infty$, with $m = \lceil…
The paper gives a wide range, uniform, local approximation of symmetric binomial distribution. The result clearly shows how one has to modify the the classical de Moivre--Laplace normal approximation in order to give an estimate at the tail…
We study the mean estimation problem under communication and local differential privacy constraints. While previous work has proposed \emph{order}-optimal algorithms for the same problem (i.e., asymptotically optimal as we spend more bits),…
Data association, the problem of reasoning over correspondence between targets and measurements, is a fundamental problem in tracking. This paper presents a graphical model formulation of data association and applies an approximate…
We analyze the problem of discrete distribution estimation under $\ell_1$ loss. We provide non-asymptotic upper and lower bounds on the maximum risk of the empirical distribution (the maximum likelihood estimator), and the minimax risk in…
This mini-paper presents a fast and simple algorithm to compute the projection onto the canonical simplex $\triangle^n$. Utilizing the Moreau's identity, we show that the problem is essentially a univariate minimization and the objective…
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…
The Schl\"omilch integral, a generalization of the Dirichlet integral on the simplex, and related probability distributions are reviewed. A distribution that unifies several generalizations of the Dirichlet distribution is presented, with…
This paper considers the distributed smooth optimization problem in which the objective is to minimize a global cost function formed by a sum of local smooth cost functions, by using local information exchange. The standard assumption for…
Distributed algorithms for solving additive or consensus optimization problems commonly rely on first-order or proximal splitting methods. These algorithms generally come with restrictive assumptions and at best enjoy a linear convergence…
We prove existence and uniqueness of the minimizer for the average geodesic distance to the points of a geodesically convex set on the sphere. This implies a corresponding existence and uniqueness result for an optimal algorithm for…
In this paper we give a formula for the probability that $n$ random points chosen under the uniform distribution in a disk are in convex position. While close, the formula is recursive and is totally explicit only for the first values of…
Approximate Bayesian Computation (ABC) can be viewed as an analytic approximation of an intractable likelihood coupled with an elementary simulation step. Such a view, combined with a suitable instrumental prior distribution permits…
We apply a probabilistic approach to study the computational complexity of analog computers which solve linear programming problems. We analyze numerically various ensembles of linear programming problems and obtain, for each of these…
We propose a distributionally robust formulation of the traditional risk parity portfolio optimization problem. Distributional robustness is introduced by targeting the discrete probabilities attached to each observation used during…
There are two common settings in a quantum-state discrimination problem. One is minimum-error discrimination where a wrong guess (error) is allowed and the discrimination success probability is maximized. The other is unambiguous…
Consider $d+2$ i.i.d. random points $X_1,\ldots, X_{d+2}$ in $\mathbb R^d$. In this note, we compute the probability that their convex hull is a simplex focusing on three specific distributional settings: (i) the distribution of $X_1$ is…
Optimal percolation is the problem of finding the minimal set of nodes such that if the members of this set are removed from a network, the network is fragmented into non-extensive disconnected clusters. The solution of the optimal…
The distance of a graph from being triangle-free is a fundamental graph parameter, counting the number of edges that need to be removed from a graph in order for it to become triangle-free. Its corresponding computational problem is the…