Related papers: Approximation of Functions: Optimal Sampling and C…
We propose a function-learning methodology with a control-theoretical foundation. We parametrise the approximating function as the solution to a control system on a reproducing-kernel Hilbert space, and propose several methods to find the…
In this article we consider the problem of choosing an optimal sampling scheme for the regression problem simultaneously with that of model selection. We consider a batch type approach and an on-line approach following algorithms recently…
Optimization algorithms and Monte Carlo sampling algorithms have provided the computational foundations for the rapid growth in applications of statistical machine learning in recent years. There is, however, limited theoretical…
Sequential decision making techniques hold great promise to improve the performance of many real-world systems, but computational complexity hampers their principled application. Influence-based abstraction aims to gain leverage by modeling…
Mathematical Selection is a method in which we select a particular choice from a set of such. It have always been an interesting field of study for mathematicians. Accordingly, Combinatorial Optimization is a sub field of this domain of…
In this paper, we introduce a method for approximating the solution to inference and optimization tasks in uncertain and deterministic reasoning. Such tasks are in general intractable for exact algorithms because of the large number of…
Modern applications require methods that are computationally feasible on large datasets but also preserve statistical efficiency. Frequently, these two concerns are seen as contradictory: approximation methods that enable computation are…
Learning interpretable models has become a major focus of machine learning research, given the increasing prominence of machine learning in socially important decision-making. Among interpretable models, rule lists are among the best-known…
The problem of super-resolution in general terms is to recuperate a finitely supported measure $\mu$ given finitely many of its coefficients $\hat{\mu}(k)$ with respect to some orthonormal system. The interesting case concerns situations,…
We study the expressibility and learnability of convex optimization solution functions and their multi-layer architectural extension. The main results are: \emph{(1)} the class of solution functions of linear programming (LP) and quadratic…
While the theory of operator approximation with any given accuracy is well elaborated, the theory of {best constrained} constructive operator approximation is still not so well developed. Despite increasing demands from applications this…
A rational approximation by a ratio of polynomial functions is a flexible alternative to polynomial approximation. In particular, rational functions exhibit accurate estimations to nonsmooth and non- Lipschitz functions, where polynomial…
We extend the problem of obtaining an estimator for the finite population mean parameter incorporating complete auxiliary information through calibration estimation in survey sampling but considering a functional data framework. The…
Peak Estimation aims to find the maximum value of a state function achieved by a dynamical system. This problem is non-convex when considering standard Barrier and Density methods for invariant sets, and has been treated heuristically by…
Constrained optimization problems appear in a wide variety of challenging real-world problems, where constraints often capture the physics of the underlying system. Classic methods for solving these problems rely on iterative algorithms…
The use of separable approximations is proposed to mitigate the curse of dimensionality related to the approximation of high-dimensional value functions in optimal control. The separable approximation exploits intrinsic decaying sensitivity…
Almost every software system provides configuration options to tailor the system to the target platform and application scenario. Often, this configurability renders the analysis of every individual system configuration infeasible. To…
The task of learning to pick a single preferred example out a finite set of examples, an "optimal choice problem", is a supervised machine learning problem with complex, structured input. Problems of optimal choice emerge often in various…
One of the main problems of importance sampling in Bayesian networks is representation of the importance function, which should ideally be as close as possible to the posterior joint distribution. Typically, we represent an importance…
We investigate Learning from Label Proportions (LLP), a partial information setting where examples in a training set are grouped into bags, and only aggregate label values in each bag are available. Despite the partial observability, the…