Related papers: Discussion: A tale of three cousins: Lasso, L2Boos…

Let $V \subset \mathbb{R}$ be a finite set with $|V| = n $ and suppose we are given each pairwise distance independently with probability $p$. We show that if $p = (1+\epsilon)/n$, for some fixed $\epsilon >0$, then we can reconstruct a…

Let $\mathcal{P}$ denote the set of all primes. $P_{1},P_{2},P_{3}$ are three subsets of $\mathcal{P}$. Let $\underline{\delta}(P_{i})$ $(i=1,2,3)$ denote the lower density of $P_{i}$ in $\mathcal{P}$, respectively. It is proved that if…

In October 2017 the Italian National Institute of Statistics (ISTAT), Italy's body for official statistics, has published the book of fairy tales Le streghe di Bayes (The witches of Bayes) written by ISTAT staff members with the commendable…

This paper deals with the proportional hazards model proposed by D. R. Cox in a high-dimensional and sparse setting for a regression parameter. To estimate the regression parameter, the Dantzig selector is applied. The variable selection…

Paul Erd\H{o}s and L\'{a}szl\'{o} Lov\'{a}sz proved in a landmark article that, for any positive integer $k$, up to isomorphism there are only finitely many maximal intersecting families of $k-$sets (maximal $k-$cliques). So they posed the…

We formulate a Serre-type conjecture for n-dimensional Galois representations that are tamely ramified at p. The weights are predicted using a representation-theoretic recipe. For n = 3 some of these weights were not predicted by the…

This paper studies hypothesis testing and parameter estimation in the context of the divide and conquer algorithm. In a unified likelihood based framework, we propose new test statistics and point estimators obtained by aggregating various…

Extending the methods developed in the author's previous paper and using adapted coordinate systems in two variables, an L^p boundedness theorem is proven for maximal operators over hypersurfaces in R^3 when p > 2. When the best possible p…

Monte Carlo simulations of a Sznajd model show that if a near-consensus is formed out of four initially equally widespread opinions, the one which at intermediate times is second in the number of adherents usually loses out against the…

In exciting new work, Bertsimas et al. (2016) showed that the classical best subset selection problem in regression modeling can be formulated as a mixed integer optimization (MIO) problem. Using recent advances in MIO algorithms, they…

Many real-world prediction tasks have outcome variables that have characteristic heavy-tail distributions. Examples include copies of books sold, auction prices of art pieces, demand for commodities in warehouses, etc. By learning…

In 1961, P. Erd\H{o}s, A. Ginzburg, and A. Ziv proved a remarkable theorem stating that each set of $2n-1$ integers contains a subset of size $n$, the sum of whose elements is divisible by $n$. We will prove a similar result for pairs of…

The determination of the maximal ranks of a set of a given type of tensors is a basic problem both in theory and application. In statistical applications, the maximal rank is related to the number of necessary parameters to be built in a…

Let $\{s_n\}$ and $\{t_n\}$ be two sequences of positive real numbers. Under some mild conditions on $\{s_n\}$ and $\{t_n\}$, we give the precise formula of the Hausdorff dimension of the set \[ \mathbb{E}(\{s_n\},\{t_n\}):=\Big\{x\in(0,1):…

The likelihood function is central to both frequentist and Bayesian formulations of parametric statistical inference, and large-sample approximations to the sampling distributions of estimators and test statistics, and to posterior…

Improvement in machine learning-based NLP performance are often presented with bigger models and more complex code. This presents a trade-off: better scores come at the cost of larger tools; bigger models tend to require more during…

We propose a general family of algorithms for regression estimation with quadratic loss. Our algorithms are able to select relevant functions into a large dictionary. We prove that a lot of algorithms that have already been studied for this…

We consider learning high-dimensional multi-response linear models with structured parameters. By exploiting the noise correlations among responses, we propose an alternating estimation (AltEst) procedure to estimate the model parameters…

Variable selection is one of the most important tasks in statistics and machine learning. To incorporate more prior information about the regression coefficients, the constrained Lasso model has been proposed in the literature. In this…

For $n \geq 3,$ let $ p_n $ denote the $n^{\rm th}$ prime number. Let $[ \; ]$ denote the floor or greatest integer function. For a positive integer $m,$ let $\pi_2(m)$ denote the number of twin primes not exceeding $m.$ The twin prime…