Related papers: Setting Parameters by Example
A MapReduce algorithm can be described by a mapping schema, which assigns inputs to a set of reducers, such that for each required output there exists a reducer that receives all the inputs that participate in the computation of this…
Estimating hyperparameters has been a long-standing problem in machine learning. We consider the case where the task at hand is modeled as the solution to an optimization problem. Here the exact gradient with respect to the hyperparameters…
Many core problems in robotics can be framed as constrained optimization problems. Often on these problems, the robotic system has uncertainty, or it would be advantageous to identify multiple high quality feasible solutions. To enable…
We give new results for problems in computational and statistical machine learning using tools from high-dimensional geometry and probability. We break up our treatment into two parts. In Part I, we focus on computational considerations in…
Many AI problems, in robotics and other domains, are goal-directed, essentially seeking a trajectory leading to some goal state. In such problems, the way we choose to represent a trajectory underlies algorithms for trajectory prediction…
The most common approaches for solving stochastic resource allocation problems in the research literature is to either use value functions ("dynamic programming") or scenario trees ("stochastic programming") to approximate the impact of a…
Leveraging machine learning to facilitate the optimization process is an emerging field that holds the promise to bypass the fundamental computational bottleneck caused by classic iterative solvers in critical applications requiring…
We study a general class of convex submodular optimization problems with indicator variables. Many applications such as the problem of inferring Markov random fields (MRFs) with a sparsity or robustness prior can be naturally modeled in…
In this paper, we introduce a graph matching method that can account for constraints of arbitrary order, with arbitrary potential functions. Unlike previous decomposition approaches that rely on the graph structures, we introduce a…
A central problem in business concerns the optimal allocation of limited resources to a set of available tasks, where the payoff of these tasks is inherently uncertain. In credit card fraud detection, for instance, a bank can only assign a…
New versions and extensions of Benson's outer approximation algorithm for solving linear vector optimization problems are presented. Primal and dual variants are provided in which only one scalar linear program has to be solved in each…
Some recent works in machine learning and computer vision involve the solution of a bi-level optimization problem. Here the solution of a parameterized lower-level problem binds variables that appear in the objective of an upper-level…
We discuss the issue of finding a good mathematical programming solver configuration for a particular instance of a given problem, and we propose a two-phase approach to solve it. In the first phase we learn the relationships between the…
The problem of computing minimally sparse solutions of under-determined linear systems is $NP$ hard in general. Subsets with extra properties, may allow efficient algorithms, most notably problems with the restricted isometry property (RIP)…
A wide variety of problems in machine learning, including exemplar clustering, document summarization, and sensor placement, can be cast as constrained submodular maximization problems. A lot of recent effort has been devoted to developing…
This article presents a discussion of optimization problems where the objective function f(x) has parameters that are constrained by some scaling, so that q(x) = constant, where this function q() involves a sum of the parameters, their…
Many optimization problems incorporate uncertainty affecting their parameters and thus their objective functions and constraints. As an example, in chance-constrained optimization the constraints need to be satisfied with a certain…
Most recent machine learning research focuses on developing new classifiers for the sake of improving classification accuracy. With many well-performing state-of-the-art classifiers available, there is a growing need for understanding…
The article discusses the concept of hyperparametric optimization of recommendation algorithms using an integral assessment that combines various performance indicators into a single consolidated criterion. This approach is opposed to…
Vertex direction algorithms have been around for a few decades in the experimental design and mixture models literature. We briefly review this type of algorithm and describe a new member of the family: the support reduction algorithm. The…