Related papers: Exact Real Search: Formalised Optimisation and Reg…

The real-life data have a complex and non-linear structure due to their nature. These non-linearities and the large number of features can usually cause problems such as the empty-space phenomenon and the well-known curse of dimensionality.…

Conformal prediction is an assumption-lean approach to generating distribution-free prediction intervals or sets, for nearly arbitrary predictive models, with guaranteed finite-sample coverage. Conformal methods are an active research topic…

The focus of this article is the approximation of functions which are analytic on a compact interval except at the endpoints. Typical numerical methods for approximating such functions depend upon the use of particular conformal maps from…

We introduce a rotation-invariant representation of planar shapes. In particular, this representation encodes shapes as vectors such that the Euclidean distance between them serves as a valid shape distance. For standardized, star-shaped…

Data driven models of dynamical systems help planners and controllers to provide more precise and accurate motions. Most model learning algorithms will try to minimize a loss function between the observed data and the model's predictions.…

We develop a general framework for estimating function-valued parameters under equality or inequality constraints in infinite-dimensional statistical models. Such constrained learning problems are common across many areas of statistics and…

The efficiency of modern optimization methods, coupled with increasing computational resources, has led to the possibility of real-time optimization algorithms acting in safety critical roles. There is a considerable body of mathematical…

We introduce a numerical framework to verify the finite step convergence of first-order methods for parametric convex quadratic optimization. We formulate the verification problem as a mathematical optimization problem where we maximize a…

This paper develops a unified identification framework for counterfactual analysis in incomplete models characterized by support and moment restrictions. I demonstrate that identifying structural parameters and conducting counterfactual…

To be usable in practice, interactive theorem provers need to provide convenient and efficient means of writing expressions, definitions, and proofs. This involves inferring information that is often left implicit in an ordinary…

Linear regression is a fundamental modeling tool in statistics and related fields. In this paper, we study an important variant of linear regression in which the predictor-response pairs are partially mismatched. We use an optimization…

Inexact computing also referred to as approximate computing is a style of designing algorithms and computing systems wherein the accuracy of correctness of algorithms executing on them is deliberately traded for significant resource…

We study the Regularized A-optimal Design (RAOD) problem, which selects a subset of $k$ experiments to minimize the inverse of the Fisher information matrix, regularized with a scaled identity matrix. RAOD has broad applications in Bayesian…

Dynamical models described by ordinary differential equations (ODEs) are a fundamental tool in the sciences and engineering. Exact reduction aims at producing a lower-dimensional model in which each macro-variable can be directly related to…

In order to work with mathematical content in computer systems, it is necessary to represent it in formal languages. Ideally, these are supported by tools that verify the correctness of the content, allow computing with it, and produce…

We describe an approximate rational arithmetic with round-off errors (both absolute and relative) controlled by the user. The rounding procedure is based on the continued fraction expansion of real numbers. Results of computer experiments…

The main focus in this paper is exact linesearch methods for minimizing a quadratic function whose Hessian is positive definite. We give a class of limited-memory quasi-Newton Hessian approximations which generate search directions parallel…

We investigate finite-dimensional constrained structured optimization problems, featuring composite objective functions and set-membership constraints. Offering an expressive yet simple language, this problem class provides a modeling…

We study truthful mechanisms for matching and related problems in a partial information setting, where the agents' true utilities are hidden, and the algorithm only has access to ordinal preference information. Our model is motivated by the…

We typically construct optimal designs based on a single objective function. To better capture the breadth of an experiment's goals, we could instead construct a multiple objective optimal design based on multiple objective functions. While…