Related papers: Approximately Optimal Subset Selection for Statist…
Selecting a good column (or row) subset of massive data matrices has found many applications in data analysis and machine learning. We propose a new adaptive sampling algorithm that can be used to improve any relative-error column selection…
In this article, we discuss two algorithms tailored to discrete-time deterministic finite-horizon nonlinear optimal control problems or so-called deterministic trajectory optimization problems. Both algorithms can be derived from an…
An algorithm is proposed, analyzed, and tested experimentally for solving stochastic optimization problems in which the decision variables are constrained to satisfy equations defined by deterministic, smooth, and nonlinear functions. It is…
We model the joint distribution of choice probabilities and decision times in binary choice tasks as the solution to a problem of optimal sequential sampling, where the agent is uncertain of the utility of each action and pays a constant…
We consider the problem of constructing optimal designs for model discrimination between competing regression models. Various new properties of optimal designs with respect to the popular $T$-optimality criterion are derived, which in many…
Many combinatorial optimization problems can be formulated as the search for a subgraph that satisfies certain properties and minimizes the total weight. We assume here that the vertices correspond to points in a metric space and can take…
Design of experiments is a fundamental topic in applied statistics with a long history. Yet its application is often limited by the complexity and costliness of constructing experimental designs, which involve searching a high-dimensional…
We study the fundamental problem of selecting optimal features for model construction. This problem is computationally challenging on large datasets, even with the use of greedy algorithm variants. To address this challenge, we extend the…
We propose a method for variable selection in discriminant analysis with mixed categorical and continuous variables. This method is based on a criterion that permits to reduce the variable selection problem to a problem of estimating…
This paper discusses the problem of determining optimal designs for regression models, when the observations are dependent and taken on an interval. A complete solution of this challenging optimal design problem is given for a broad class…
Beam search is a go-to strategy for decoding neural sequence models. The algorithm can naturally be viewed as a subset optimization problem, albeit one where the corresponding set function does not reflect interactions between candidates.…
Given a compact parameter set $Y\subset R^p$, we consider polynomial optimization problems $(P_y$) on $R^n$ whose description depends on the parameter $y\inY$. We assume that one can compute all moments of some probability measure $\phi$ on…
For many tasks of data analysis, we may only have the information of the explanatory variable and the evaluation of the response values are quite expensive. While it is impractical or too costly to obtain the responses of all units, a…
One of the most common problems in statistical experimentation is computing D-optimal designs on large finite candidate sets. While optimal approximate (i.e., infinite-sample) designs can be efficiently computed using convex methods,…
We introduce a new approach aiming at computing approximate optimal designs for multivariate polynomial regressions on compact (semi-algebraic) design spaces. We use the moment-sum-of-squares hierarchy of semidefinite programming problems…
Choosing decision variables deterministically (deterministic decision-making) can be regarded as a particular case of choosing decision variables probabilistically (probabilistic decision-making). It is necessary to investigate whether…
The topic of learning to solve optimization problems has received interest from both the operations research and machine learning communities. In this work, we combine techniques from both fields to address the problem of learning to…
An unconstrained nonlinear binary optimization problem of selecting a maximum expected value subset of items is considered. Each item is associated with a profit and probability. Each of the items succeeds or fails independently with the…
An energy efficient use of large scale sensor networks necessitates activating a subset of possible sensors for estimation at a fusion center. The problem is inherently combinatorial; to this end, a set of iterative, randomized algorithms…
The experimental design problem concerns the selection of k points from a potentially large design pool of p-dimensional vectors, so as to maximize the statistical efficiency regressed on the selected k design points. Statistical efficiency…