Related papers: Parameter selection and numerical approximation pr…
We introduce a generalized Fourier ratio, the \(\ell^1/\ell^2\) norm ratio of coefficients in an \emph{arbitrary} orthonormal system, as a single, basis-invariant measure of \emph{effective dimension} that governs fundamental limits across…
Deploying neural networks on edge devices entails a careful balance between the energy required for inference and the accuracy of the resulting classification. One technique for navigating this tradeoff is approximate computing: the process…
Random graph models are widely used to understand network properties and graph algorithms. Key to such analyses are the different parameters of each model, which affect various network features, such as its size, clustering, or degree…
Stability selection is a widely adopted resampling-based framework for high-dimensional variable selection. This paper seeks to broaden the use of an established stability estimator to evaluate the overall stability of the stability…
The main purpose of Feature Subset Selection is to find a reduced subset of attributes from a data set described by a feature set. The task of a feature selection algorithm (FSA) is to provide with a computational solution motivated by a…
Two canonical problems in geostatistics are estimating the parameters in a specified family of stochastic process models and predicting the process at new locations. A number of asymptotic results addressing these problems over a fixed…
Functions on a bounded domain in scientific computing are often approximated using piecewise polynomial approximations on meshes that adapt to the shape of the geometry. We study the problem of function approximation using splines on a…
In this study, I investigate the dynamic decision problem with a finite parameter space when the functional form of conditional expected rewards is misspecified. Traditional algorithms, such as Thompson Sampling, guarantee neither an…
We derive, using functional methods and the bias expansion, the conditional likelihood for observing a specific tracer field given an underlying matter field. This likelihood is necessary for Bayesian-inference methods. If we neglect all…
The study of Fourier transforms of probability measures on fractal sets plays an important role in recent research. Faster decay rates are known to yield enhanced results in areas such as metric number theory. This paper focuses on…
We propose a stochastic approximation method for approximating the efficient frontier of chance-constrained nonlinear programs. Our approach is based on a bi-objective viewpoint of chance-constrained programs that seeks solutions on the…
Hyperparameter selection is a critical step in the deployment of artificial intelligence (AI) models, particularly in the current era of foundational, pre-trained, models. By framing hyperparameter selection as a multiple hypothesis testing…
This article studies the behavior of regularized Tyler estimators (RTEs) of scatter matrices. The key advantages of these estimators are twofold. First, they guarantee by construction a good conditioning of the estimate and second, being a…
When computing bounds, spatial branch-and-bound algorithms often linearly outer approximate convex relaxations for non-convex expressions in order to capitalize on the efficiency and robustness of linear programming solvers. Considering…
Functions of one or more variables are usually approximated with a basis: a complete, linearly-independent system of functions that spans a suitable function space. The topic of this paper is the numerical approximation of functions using…
Contemporary state-of-the-art neural networks have increasingly large numbers of parameters, which prevents their deployment on devices with limited computational power. Pruning is one technique to remove unnecessary weights and reduce…
This paper presents a new approach in application of the Fourier transform to the complex error function resulting in an efficient rational approximation. Specifically, the computational test shows that with only $17$ summation terms the…
Basis Function (BF) expansions are a cornerstone of any engineer's toolbox for computational function approximation which shares connections with both neural networks and Gaussian processes. Even though BF expansions are an intuitive and…
Multiwinner Elections have emerged as a prominent area of research with numerous practical applications. We contribute to this area by designing parameterized approximation algorithms and also resolving an open question by Yang and Wang…
For numerous graph problems in the realm of parameterized algorithms, using the size of a smallest deletion set (called a modulator) into well-understood graph families as parameterization has led to a long and successful line of research.…