Related papers: On the separability of multivariate functions
In this article, we consider the problem of testing the independence between two random variables. Our primary objective is to develop tests that are highly effective at detecting associations arising from explicit or implicit functional…
The problem of finding the minimizer of a sum of convex functions is central to the field of optimization. Thus, it is of interest to understand how that minimizer is related to the properties of the individual functions in the sum. In this…
A compression algorithm is introduced for multi-determinant wave functions which can greatly reduce the number of determinants that need to be evaluated in quantum Monte Carlo calculations. We have devised an algorithm with three levels of…
We study approximations of compact linear multivariate operators defined over Hilbert spaces. We provide necessary and sufficient conditions on various notions of tractability. These conditions are mainly given in terms of sums of certain…
We introduce a derivative-free global optimization algorithm that efficiently computes minima for various classes of one-dimensional functions, including non-convex, and non-smooth functions.This algorithm numerically approximates the…
Distributed detection fusion with high-dimension conditionally dependent observations is known to be a challenging problem. When a fusion rule is fixed, this paper attempts to make progress on this problem for the large sensor networks by…
Many scientific fields and applications require compact representations of multivariate functions. For this problem, decoupling methods are powerful techniques for representing the multivariate functions as a combination of linear…
We propose a variant of the Simulated Annealing method for optimization in the multivariate analysis of differentiable functions. The method uses global actualizations via the Hybrid Monte Carlo algorithm in their generalized version for…
Monte Carlo is a simple and flexible tool that is widely used in computational finance. In this context, it is common for the quantity of interest to be the expected value of a random variable defined via a stochastic differential equation.…
This paper considers the problem of maximizing multiple linear functions over the probability simplex. A classification of feasible points is indicated. A necessary and sufficient condition for a member of each class to be an efficient…
Submodular function optimization has numerous applications in machine learning and data analysis, including data summarization which aims to identify a concise and diverse set of data points from a large dataset. It is important to…
We introduce and analyze a parallel sequential Monte Carlo methodology for the numerical solution of optimization problems that involve the minimization of a cost function that consists of the sum of many individual components. The proposed…
Optimization algorithms and Monte Carlo sampling algorithms have provided the computational foundations for the rapid growth in applications of statistical machine learning in recent years. There is, however, limited theoretical…
A function in a class $\mathcal{F}(X)$ is said to be subdifferentially determined in $\mathcal{F}(X)$ if it is equal up to an additive constant to any function in $\mathcal{F}(X)$ with the same subdifferential. A function is said to be…
When a Monte Carlo algorithm is used to evaluate a physical observable A, it is possible to slightly modify the algorithm so that it evaluates simultaneously A and the derivatives $\partial$ $\varsigma$ A of A with respect to each…
Necessary and sufficient conditions under which two real functions defined on the real interval can be separated by a polynomial are given. An immediate consequence of the main result is the existence of the polynomial separation of convex…
We discuss removability problems concerning differentiability and pointwise Lipschitz conditions for functions of a real variable. We prove that, in each of the settings under consideration, a set is removable if and only if it has no…
We presented a separation based optimization algorithm which, rather than optimization the entire variables altogether, This would allow us to employ: 1) a class of nonlinear functions with three variables and 2) a convex quadratic…
The scalability of submodular optimization methods is critical for their usability in practice. In this paper, we study the reducibility of submodular functions, a property that enables us to reduce the solution space of submodular…
Numerical solutions of differential equations are usually not smooth functions. However, they should resemble the smoothness of the corresponding real solutions in one way or another. In two of our recent papers, a kind of spacial…