Related papers: Bootstraps Regularize Singular Correlation Matrice…
Topic modelling is fundamentally a soft clustering problem (of known objects -- documents, over unknown clusters -- topics). That is, the task is incorrectly posed. In particular, the topic models are unstable and incomplete. All this leads…
Modern technologies are producing a wealth of data with complex structures. For instance, in two-dimensional digital imaging, flow cytometry, and electroencephalography, matrix type covariates frequently arise when measurements are obtained…
The identification of the dependent components in multiple data sets is a fundamental problem in many practical applications. The challenge in these applications is that often the data sets are high-dimensional with few observations or…
The basic random $k$-SAT problem is: Given a set of $n$ Boolean variables, and $m$ clauses of size $k$ picked uniformly at random from the set of all such clauses on our variables, is the conjunction of these clauses satisfiable? Here we…
Spectral analysis plays a crucial role in high-dimensional statistics, where determining the asymptotic distribution of various spectral statistics remains a challenging task. Due to the difficulties of deriving the analytic form, recent…
We use the numerical conformal bootstrap to study six-dimensional $\mathcal{N}=(1,0)$ superconformal field theories with flavor symmetry $\mathfrak{so}_{4k}$. We present evidence that minimal $(D_k, D_k)$ conformal matter saturates the…
We apply the numerical bootstrap program to chiral operators in four-dimensional ${\mathcal N}=2$ SCFTs. In the first part of this work we study four-point functions in which all fields have the same conformal dimension. We give special…
The bootstrap is a popular and convenient method for quantifying the authority of an empirical ordering of attributes, for example of a ranking of the performance of institutions or of the influence of genes on a response variable. In the…
We develop a novel numerical bootstrap for unitary, crossing-symmetric conformal field theories, focusing on moment observables defined as weighted averages over conformal data. Providing a global and coarse-grained probe of the operator…
For N=1,2,..., let S_N be a simple random sample of size n=n_N from a population A_N of size N, where 0<=n<=N. Then with f_N=n/N, the sampling fraction, and 1_A the inclusion indicator that A is in S_N, for any H a subset of A_N of size k>=…
When faced with severely imbalanced binary classification problems, we often train models on bootstrapped data in which the number of instances of each class occur in a more favorable ratio, e.g., one. We view algorithmic inequity through…
Matrix regression plays an important role in modern data analysis due to its ability to handle complex relationships involving both matrix and vector variables. We propose a class of regularized regression models capable of predicting both…
Estimating time-varying correlation matrices is challenging because existing methods may adapt slowly to structural changes, impose insufficient regularization, or produce diffuse posterior uncertainty. In moderate dimensions, an additional…
This work introduces the causal bootstrap, a framework for bounding smeared spectral observables from finite non-perturbative Euclidean data. The method optimizes over the convex set of positive spectral densities compatible with the data…
We show that matrix completion with trace-norm regularization can be significantly hurt when entries of the matrix are sampled non-uniformly. We introduce a weighted version of the trace-norm regularizer that works well also with…
The Correlation Clustering problem is one of the most extensively studied clustering formulations due to its wide applications in machine learning, data mining, computational biology and other areas. We consider the Correlation Clustering…
Consider the following model of strong-majority bootstrap percolation on a graph. Let r be some positive integer, and p in [0,1]. Initially, every vertex is active with probability p, independently from all other vertices. Then, at every…
The paper studies a problem of constructing simultaneous likelihood-based confidence sets. We consider a simultaneous multiplier bootstrap procedure for estimating the quantiles of the joint distribution of the likelihood ratio statistics,…
This paper considers regularizing a covariance matrix of $p$ variables estimated from $n$ observations, by hard thresholding. We show that the thresholded estimate is consistent in the operator norm as long as the true covariance matrix is…
Bootstrap percolation on a graph is a deterministic process that iteratively enlarges a set of occupied sites by adjoining points with at least $\theta$ occupied neighbors. The initially occupied set is random, given by a uniform product…