Related papers: A global optimum-informed greedy algorithm for A-o…
We present a mathematical framework and computational methods to optimally design a finite number of sequential experiments. We formulate this sequential optimal experimental design (sOED) problem as a finite-horizon partially observable…
We propose a class of greedy algorithms for weighted sparse recovery by considering new loss function-based generalizations of Orthogonal Matching Pursuit (OMP). Given a (regularized) loss function, the proposed algorithms alternate the…
Pairwise comparison labels are more informative and less variable than class labels, but generating them poses a challenge: their number grows quadratically in the dataset size. We study a natural experimental design objective, namely,…
The greedy algorithm for monotone submodular function maximization subject to cardinality constraint is guaranteed to approximate the optimal solution to within a $1-1/e$ factor. Although it is well known that this guarantee is essentially…
In the classical selection problem, the input consists of a collection of elements and the goal is to pick a subset of elements from the collection such that some objective function $f$ is maximized. This problem has been studied…
For many popular graph metric sparsifiers, such as spanners, emulators, and preservers, simple and elegant greedy algorithms are known that achieve state-of-the-art or existentially optimal tradeoffs between size and quality. The goal of…
We study online bipartite edge coloring, with nodes on one side of the graph revealed sequentially. The trivial greedy algorithm is $(2-o(1))$-competitive, which is optimal for graphs of low maximum degree, $\Delta=O(\log n)$ [BNMN IPL'92].…
The identification of the interface of an inclusion in a diffusion process is considered. This task is viewed as a parameter identification problem in which the parameter space bears the structure of a shape manifold. A corresponding…
The performance of acquisition functions for Bayesian optimisation to locate the global optimum of continuous functions is investigated in terms of the Pareto front between exploration and exploitation. We show that Expected Improvement…
The Greedy algorithm is the simplest heuristic in sequential decision problem that carelessly takes the locally optimal choice at each round, disregarding any advantages of exploring and/or information gathering. Theoretically, it is known…
Finding a maximum-weight matching is a classical and well-studied problem in computer science, solvable in cubic time in general graphs. We consider the specialization called assignment problem where the input is a bipartite graph, and…
We propose and analyze batch greedy heuristics for cardinality constrained maximization of non-submodular non-decreasing set functions. We consider the standard greedy paradigm, along with its distributed greedy and stochastic greedy…
Decision Tree is a classic formulation of active learning: given $n$ hypotheses with nonnegative weights summing to 1 and a set of tests that each partition the hypotheses, output a decision tree using the provided tests that uniquely…
We investigate the performance of the standard Greedy algorithm for cardinality constrained maximization of non-submodular nondecreasing set functions. While there are strong theoretical guarantees on the performance of Greedy for…
The route planning problem based on the greedy algorithm represents a method of identifying the optimal or near-optimal route between a given start point and end point. In this paper, the PCA method is employed initially to downscale the…
In a number of situations, collecting a function value for every data point may be prohibitively expensive, and random sampling ignores any structure in the underlying data. We introduce a scalable optimization algorithm with no correction…
This paper tackles optimal sensor placement for Bayesian linear inverse problems, a popular version of the more general Optimal Experimental Design (OED) problem, using the D-optimality criterion. This is done by establishing connections…
The ability to design effective experiments is crucial for obtaining data that can substantially reduce the uncertainty in the predictions made using computational models. An optimal experimental design (OED) refers to the choice of a…
In the context of Gaussian conditioning, greedy algorithms iteratively select the most informative measurements, given an observed Gaussian random variable. However, the convergence analysis for conditioning Gaussian random variables…
In this paper we develop a procedure to deal with a family of parameter-dependent ill-posed problems, for which the exact solution in general does not exist. The original problems are relaxed by considering corresponding approximate ones,…