Related papers: Deterministic Designs with Deterministic Guarantee…
We consider a family of determinantal random point processes on the two-dimensional lattice and prove that members of our family can be interpreted as a kind of Gibbs ensembles of nonintersecting paths. Examples include probability measures…
In this paper, we investigate when system identification is statistically easy or hard, in the finite sample regime. Statistically easy to learn linear system classes have sample complexity that is polynomial with the system dimension. Most…
A reliable representation of uncertainty is essential for the application of modern machine learning methods in safety-critical settings. In this regard, the use of credal sets (i.e., convex sets of probability distributions) has recently…
In this study we consider domains that are composed of an infinite sequence of self-similar rings and corresponding finite element spaces over those domains. The rings are parameterized using piecewise polynomial or tensor-product B-spline…
The primary goal of this work is to review the importance of data compression and present a fast Fourier-based method for generating the deterministic compression matrix in the area of deterministic compressed sensing. The principle…
We study gradient descent under linearly correlated noise. Our work is motivated by recent practical methods for optimization with differential privacy (DP), such as DP-FTRL, which achieve strong performance in settings where privacy…
Compressed sensing extends from the recovery of sparse vectors from undersampled measurements via efficient algorithms to the recovery of matrices of low rank from incomplete information. Here we consider a further extension to the…
We examine a family of discrete second-order systems which are integrable through reduction to a linear system. These systems were previously identified using the singularity confinement criterion. Here we analyse them using the more…
We present a series of new differentially private (DP) algorithms with dimension-independent margin guarantees. For the family of linear hypotheses, we give a pure DP learning algorithm that benefits from relative deviation margin…
We investigate a rich new class of exactly solvable particle systems generalizing the Totally Asymmetric Simple Exclusion Process (TASEP). Our particle systems can be thought of as new exactly solvable examples of tandem queues, directed…
Label differential privacy (DP) is designed for learning problems involving private labels and public features. While various methods have been proposed for learning under label DP, the theoretical limits remain largely unexplored. In this…
Compressive sensing (CS) has recently emerged as a framework for efficiently capturing signals that are sparse or compressible in an appropriate basis. While often motivated as an alternative to Nyquist-rate sampling, there remains a gap…
This paper is concerned with fundamental limits on the approximation of nonlinear dynamical systems. Specifically, we show that recurrent neural networks (RNNs) can approximate nonlinear systems -- that satisfy a Lipschitz property and…
Percolation theory dictates an intuitive picture depicting correlated regions in complex systems as densely connected clusters. While this picture might be adequate at small scales and apart from criticality, we show that highly correlated…
Implicit neural representations (INRs) such as NeRF and SIREN encode a signal in neural network parameters and show excellent results for signal reconstruction. Using INRs for downstream tasks, such as classification, is however not…
Simplex-valued data appear throughout statistics and machine learning, for example in the context of transfer learning and compression of deep networks. Existing models for this class of data rely on the Dirichlet distribution or other…
The universality class of thermally diluted Ising systems, in which the realization of the disposition of magnetic atoms and vacancies is taken from the local distribution of spins in the pure original Ising model at criticality, is…
Combinatorial features are essential for the success of many commercial models. Manually crafting these features usually comes with high cost due to the variety, volume and velocity of raw data in web-scale systems. Factorization based…
Binary sequences with optimal autocorrelation and large linear complexity have important applications in cryptography and communications. Very recently, a class of binary sequences of period $4p$ with optimal autocorrelation was proposed…
Sequences with excellent ambiguity functions are very useful in radar detection and modern mobile communications. Doppler resilient complementary sequence (DRCS) is a new type of sequence proposed recently, which can achieve lower ambiguity…