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The paper outlines an exact combinatorial approach to finite coagulating systems. In this approach, cluster sizes and time are discrete, and the binary aggregation alone governs the time evolution of the systems. By considering the growth…
Many realistic decision-making problems in networked scenarios, such as formation control and collaborative task offloading, often involve complicatedly entangled local decisions, which, however, have not been sufficiently investigated yet.…
This paper introduces algorithms for problems where a decision maker has to control a system composed of several components and has access to only partial information on the state of each component. Such problems are difficult because of…
Identifying independence between two random variables or correlated given their samples has been a fundamental problem in Statistics. However, how to do so in a space-efficient way if the number of states is large is not quite well-studied.…
We present a novel selection algorithm for N-2 contingency analysis problem. The algorithm is based on the iterative bounding of line outage distribution factors and successive pruning of the set of contingency pair candidates. The…
We introduce local expectation gradients which is a general purpose stochastic variational inference algorithm for constructing stochastic gradients through sampling from the variational distribution. This algorithm divides the problem of…
We present improved deterministic distributed algorithms for a number of well-studied matching problems, which are simpler, faster, more accurate, and/or more general than their known counterparts. The common denominator of these results is…
Since being analyzed by Rokhlin, Szlam, and Tygert and popularized by Halko, Martinsson, and Tropp, randomized Simultaneous Power Iteration has become the method of choice for approximate singular value decomposition. It is more accurate…
Mixed-effects models are widely used to model data with hierarchical grouping structures and high-cardinality categorical predictor variables. However, for high-dimensional crossed random effects, current standard computations relying on…
Large dimensional least-squares and regularised least-squares problems are expensive to solve. There exist many approximate techniques, some deterministic (like conjugate gradient), some stochastic (like stochastic gradient descent). Among…
We investigate the dual of a Multistage Stochastic Linear Program (MSLP) to study two questions for this class of problems. The first of these questions is the study of the optimal value of the problem as a function of the involved…
We propose an efficient probabilistic method to solve a deterministic problem -- we present a randomized optimization approach that drastically reduces the enormous computational cost of optimizing designs under many load cases for both…
Over the last two decades, a significant line of work in theoretical algorithms has made progress in solving linear systems whose coefficient matrix is the Laplacian matrix of a weighted graph. The solution of the linear system can be…
The Marcus-Lushnikov process is a finite stochastic particle system in which each particle is entirely characterized by its mass. Each pair of particles with masses $x$ and $y$ merges into a single particle at a given rate $K(x,y)$. We…
We consider the least-squares approximation of a matrix C in the set of doubly stochastic matrices with the same sparsity pattern as C. Our approach is based on applying the well-known Alternating Direction Method of Multipliers (ADMM) to a…
The numerical integration of stiff equations is a challenging problem that needs to be approached by specialized numerical methods. Exponential integrators form a popular class of such methods since they are provably robust to stiffness and…
This paper presents a novel optimization for differentiable programming named coarsening optimization. It offers a systematic way to synergize symbolic differentiation and algorithmic differentiation (AD). Through it, the granularity of the…
An idea for evaluating transition probabilities in chemical reaction systems is proposed, which is efficient for repeated calculations with various rate constants. The idea is based on duality relations; instead of direct time-evolutions of…
We review strategies for differentiating matrix-based computations, and derive symbolic and algorithmic update rules for differentiating expressions containing the Cholesky decomposition. We recommend new `blocked' algorithms, based on…
A large class of machine learning techniques requires the solution of optimization problems involving spectral functions of parametric matrices, e.g. log-determinant and nuclear norm. Unfortunately, computing the gradient of a spectral…