Related papers: Complete Classification of Generalized Santha-Vazi…

For any $d \geq 1$, random $\mathbb{Z}^d$ shifts of finite type (SFTs) were defined in previous work of the authors. For a parameter $\alpha \in [0,1]$, an alphabet $\mathcal{A}$, and a scale $n \in \mathbb{N}$, one obtains a distribution…

We introduce a random coding technique for transmission over discrete memoryless channels, reminiscent of the basic construction attaining the Gilbert-Varshamov bound for codes in Hamming spaces. The code construction is based on drawing…

Let $G$ be a directed graph with $n$ vertices and $m$ edges, and let $s \in V(G)$ be a designated source vertex. We consider the problem of single source reachability (SSR) from $s$ in presence of failures of edges (or vertices). Formally,…

Detection of point sources in images is a fundamental operation in astrophysics, and is crucial for constraining population models of the underlying point sources or characterizing the background emission. Standard techniques fall short in…

In this article, we have proposed a generalized class of estimators, exponential class of estimators based on adaption of Sharma and Singh (2015) and Solanki and Singh (2013) and simple difference estimator for estimating unknown population…

We investigate the fundamental limits of the recently proposed random access coverage depth problem for DNA data storage. Under this paradigm, it is assumed that the user information consists of $k$ information strands, which are encoded…

Diffusion models have emerged as an expressive family of generative models rivaling GANs in sample quality and autoregressive models in likelihood scores. Standard diffusion models typically require hundreds of forward passes through the…

Generative source separation methods such as non-negative matrix factorization (NMF) or auto-encoders, rely on the assumption of an output probability density. Generative Adversarial Networks (GANs) can learn data distributions without…

Domain generalization aims to learn a generalizable model from a known source domain for various unknown target domains. It has been studied widely by domain randomization that transfers source images to different styles in spatial space…

We present efficient counting and sampling algorithms for random $k$-SAT when the clause density satisfies $\alpha \le \frac{2^k}{\mathrm{poly}(k)}.$ In particular, the exponential term $2^k$ matches the satisfiability threshold…

We provide an algorithm for properly learning mixtures of two single-dimensional Gaussians without any separability assumptions. Given $\tilde{O}(1/\varepsilon^2)$ samples from an unknown mixture, our algorithm outputs a mixture that is…

Support Vector Machines (SVMs) are an important tool for performing classification on scattered data, where one usually has to deal with many data points in high-dimensional spaces. We propose solving SVMs in primal form using feature maps…

Randomized methods, such as the randomized SVD (singular value decomposition) and Nystr\"om approximation, are an effective way to compute low-rank approximations of large matrices. Motivated by applications to operator learning, Boull\'e…

The generalized negative binomial distribution (GNB) is a new flexible family of discrete distributions that are mixed Poisson laws with the mixing generalized gamma (GG) distributions. This family of discrete distributions is very wide and…

We present the first sample of 31-GHz selected sources to flux levels of 1 mJy. From late 2005 to mid 2007, the Sunyaev-Zel'dovich Array (SZA) observed 7.7 square degrees of the sky at 31 GHz to a median rms of 0.18 mJy/beam. We identify…

Since the publication of Shannon's theory of one terminal source coding, a number of interesting extensions have been derived by researchers such as Slepian-Wolf, Wyner, Ahlswede-K\"{o}rner, Wyner-Ziv and Berger-Yeung. Specifically, the…

In the problem of variable-length $\delta$-channel resolvability, the channel output is approximated by encoding a variable-length uniform random number under the constraint that the variational distance between the target and approximated…

Probabilistic programming languages and other machine learning applications often require samples to be generated from a categorical distribution where the probability of each one of $n$ categories is specified as a parameter. If the…

Feature extraction and selection in the presence of nonlinear dependencies among the data is a fundamental challenge in unsupervised learning. We propose using a Gram-Schmidt (GS) type orthogonalization process over function spaces to…

We develop two variance-reduced fast operator splitting methods to approximate solutions of a class of generalized equations, covering fundamental problems such as \rvs{minimization}, minimax problems, and variational inequalities as…