Related papers: Learning DNF Expressions from Fourier Spectrum

As datasets grow richer, an important challenge is to leverage the full features in the data to maximize the number of useful discoveries while controlling for false positives. We address this problem in the context of multiple hypotheses…

We design a new, fast algorithm for agnostically learning univariate probability distributions whose densities are well approximated by piecewise polynomial functions. Let $f$ be the density function of an arbitrary univariate distribution,…

Classification is a core topic in functional data analysis. A large number of functional classifiers have been proposed in the literature, most of which are based on functional principal component analysis or functional regression. In…

When fine-tuning Deep Neural Networks (DNNs) to new data, DNNs are prone to overwriting network parameters required for task-specific functionality on previously learned tasks, resulting in a loss of performance on those tasks. We propose…

Fourier Neural Operators (FNO) offer a principled approach to solving challenging partial differential equations (PDE) such as turbulent flows. At the core of FNO is a spectral layer that leverages a discretization-convergent representation…

A remarkable recent paper by Rubinfeld and Vasilyan (2022) initiated the study of \emph{testable learning}, where the goal is to replace hard-to-verify distributional assumptions (such as Gaussianity) with efficiently testable ones and to…

In this paper, we consider approximating the parameter-to-solution maps of parametric partial differential equations (PPDEs) using deep neural networks (DNNs). We propose an efficient approach combining reduced collocation methods (RCMs)…

We develop DeepOPF as a Deep Neural Network (DNN) approach for solving security-constrained direct current optimal power flow (SC-DCOPF) problems, which are critical for reliable and cost-effective power system operation.DeepOPF is inspired…

Bayesian network classifiers (BNCs) possess a number of properties desirable for a modern classifier: They are easily interpretable, highly scalable, and offer adaptable complexity. However, traditional methods for learning BNCs have…

Purpose: To develop an algorithm for robust partial Fourier (PF) reconstruction applicable to diffusion-weighted (DW) images with non-smooth phase variations. Methods: Based on an unrolled proximal splitting algorithm, a neural network…

We continue the study of doubly-efficient proof systems for verifying agnostic PAC learning, for which we obtain the following results. - We construct an interactive protocol for learning the $t$ largest Fourier characters of a given…

In this work we consider a model problem of deep neural learning, namely the learning of a given function when it is assumed that we have access to its point values on a finite set of points. The deep neural network interpolant is the the…

Hardness results for maximum agreement problems have close connections to hardness results for proper learning in computational learning theory. In this paper we prove two hardness results for the problem of finding a low degree polynomial…

Trained with a sufficiently large training and testing dataset, Deep Neural Networks (DNNs) are expected to generalize. However, inputs may deviate from the training dataset distribution in real deployments. This is a fundamental issue with…

This paper focuses on understanding how the generalization error scales with the amount of the training data for deep neural networks (DNNs). Existing techniques in statistical learning require computation of capacity measures, such as VC…

Deep neural networks (DNNs) have been introduced for designing wireless policies by approximating the mappings from environmental parameters to solutions of optimization problems. Considering that labeled training samples are hard to…

Unsupervised representation learning has been extensively employed in anomaly detection, achieving impressive performance. Extracting valuable feature vectors that can remarkably improve the performance of anomaly detection are essential in…

The lasso and elastic net linear regression models impose a double-exponential prior distribution on the model parameters to achieve regression shrinkage and variable selection, allowing the inference of robust models from large data sets.…

We address the problem of minimizing a convex smooth function $f(x)$ over a compact polyhedral set $D$ given a stochastic zeroth-order constraint feedback model. This problem arises in safety-critical machine learning applications, such as…

Machine learning for scientific applications faces the challenge of limited data. We propose a framework that leverages a priori known physics to reduce overfitting when training on relatively small datasets. A deep neural network is…