Related papers: MAP estimation via agreement on (hyper)trees: Mess…
We study the minimum number of constraints needed to formulate random instances of the maximum stable set problem via linear programs (LPs), in two distinct models. In the uniform model, the constraints of the LP are not allowed to depend…
In high-stakes engineering applications, optimization algorithms must come with provable worst-case guarantees over a mathematically defined class of problems. Designing for the worst case, however, inevitably sacrifices performance on the…
Exploring the power of linear programming for combinatorial optimization problems has been recently receiving renewed attention after a series of breakthrough impossibility results. From an algorithmic perspective, the related questions…
We investigate a remote estimation problem in which a transmitter observes a Markov source and chooses the power level to transmit it over a time-varying packet-drop channel. The channel is modeled as a channel with Markovian state where…
Finding an optimal assignment between two sets of objects is a fundamental problem arising in many applications, including the matching of `bag-of-words' representations in natural language processing and computer vision. Solving the…
The problems of determining the optimal power allocation, within maximum power bounds, to (i) maximize the minimum Shannon capacity, and (ii) minimize the weighted latency are considered. In the first case, the global optima can be achieved…
The hierarchical and recursive expressive capability of rooted trees is applicable to represent statistical models in various areas, such as data compression, image processing, and machine learning. On the other hand, such hierarchical…
Approximate linear programming (ALP) and its variants have been widely applied to Markov Decision Processes (MDPs) with a large number of states. A serious limitation of ALP is that it has an intractable number of constraints, as a result…
This paper explores the benefits of computing arborescent trajectories (trajectory-trees) instead of commonly used sequential trajectories for partially observable robotic planning problems. In such environments, a robot infers knowledge…
Inference problems in graphical models are often approximated by casting them as constrained optimization problems. Message passing algorithms, such as belief propagation, have previously been suggested as methods for solving these…
The article provides a solution algorithm for the linear programming problem (LPP) with the latter being presented as an antagonistic matrix game so the game's further solution is based on the iterative method. The algorithm is presented as…
We introduce a new class of lower bounds on the log partition function of a Markov random field which makes use of a reversed Jensen's inequality. In particular, our method approximates the intractable distribution using a linear…
This paper is aimed to investigate some computational aspects of different isoperimetric problems on weighted trees. In this regard, we consider different connectivity parameters called {\it minimum normalized cuts}/{\it isoperimteric…
This paper shows how to evolve numerically the maximum entropy probability distributions for a given set of constraints, which is a variational calculus problem. An evolutionary algorithm can obtain approximations to some well-known…
We study the problem of computing the tightest upper and lower bounds on the probability that the sum of $n$ dependent Bernoulli random variables exceeds an integer $k$. Under knowledge of all pairs of bivariate distributions denoted by a…
In the classical Maximum Acyclic Subgraph problem (MAS), given a directed-edge weighted graph, we are required to find an ordering of the nodes that maximizes the total weight of forward-directed edges. MAS admits a 2 approximation, and…
A popular class of algorithms to optimize the dual LP relaxation of the discrete energy minimization problem (a.k.a.\ MAP inference in graphical models or valued constraint satisfaction) are convergent message-passing algorithms, such as…
We present a message-passing algorithm to solve the edge disjoint path problem (EDP) on graphs incorporating under a unique framework both traffic optimization and path length minimization. The min-sum equations for this problem present an…
This paper studies predictor functions motivated by maximizing a measure of agreement with the predictand. Specifically, it examines distributional properties and predictive performance of the estimated maximum agreement linear predictor…
We consider the estimation of a signal from the knowledge of its noisy linear random Gaussian projections. A few examples where this problem is relevant are compressed sensing, sparse superposition codes, and code division multiple access.…