Related papers: Numerical Conformal bootstrap with Analytic Functi…
We bootstrap the $4$-point amplitude of $\mathcal{N}=2$ hypermultiplets in $\text{AdS}_2 \times \text{S}^2$ at tree-level and for arbitrary external weights. We hereby explicitly demonstrate the existence of a hidden four-dimensional…
We use analytic bootstrap techniques for a CFT with an interface or a boundary. Exploiting the analytic structure of the bulk and boundary conformal blocks we extract the CFT data. We further constrain the CFT data by applying the equation…
We study the conformal bootstrap for systems of correlators involving non-identical operators. The constraints of crossing symmetry and unitarity for such mixed correlators can be phrased in the language of semidefinite programming. We…
Several new methods have been proposed for performing valid inference after model selection. An older method is sampling splitting: use part of the data for model selection and part for inference. In this paper we revisit sample splitting…
We implement the conformal bootstrap for N=4 superconformal field theories in four dimensions. Consistency of the four-point function of the stress-energy tensor multiplet imposes significant upper bounds for the scaling dimensions of…
We introduce {\tt JuliBootS}, a package for numerical conformal bootstrap computations coded in {\tt Julia}. The centre-piece of {\tt JuliBootS} is an implementation of Dantzig's simplex method capable of handling arbitrary precision linear…
Regression problems with bounded continuous outcomes frequently arise in real-world statistical and machine learning applications, such as the analysis of rates and proportions. A central challenge in this setting is predicting a response…
The task of approximating a function of d variables from its evaluations at a given number of points is ubiquitous in numerical analysis and engineering applications. When d is large, this task is challenged by the so-called curse of…
We review a framework for the conformal bootstrap that does not rely on positivity and treats the infinite tower of high-dimension OPE contributions to conformal correlators through dispersion relations and neural networks. We apply it to…
A bootstrap procedure for constructing prediction bands for a stationary functional time series is proposed. The procedure exploits a general vector autoregressive representation of the time-reversed series of Fourier coefficients appearing…
Functional data analysis has been a growing field of study in recent decades, and one fundamental task in functional data analysis is estimating the sample location. A notion called statistical depth has been extended from multivariate data…
Thanks to the impressive progress of conformal bootstrap methods we have now very precise estimates of both scaling dimensions and OPE coefficients for several 3D universality classes. We show how to use this information to obtain similarly…
Motivated by numerical methods for solving parametric partial differential equations, this paper studies the approximation of multivariate analytic functions by algebraic polynomials. We introduce various anisotropic model classes based on…
In this paper, we examine the validity of non-parametric spatial bootstrap as a procedure to quantify errors in estimates of N-point correlation functions. We do this by means of a small simulation study with simple point process models and…
We consider hypothesis testing for the null hypothesis being represented as an arbitrary-shaped region in the parameter space. We compute an approximate p-value by counting how many times the null hypothesis holds in bootstrap replicates.…
This paper reports on application of bootstrap nonlinear regression method to a design of an experiment dataset with fewer experimental runs. Design with desired properties was augmented and verified using graphical techniques. The…
We consider a conformal field theory in the presence of a boundary, and explain how two-point correlators of mixed bulk-local operators can be bootstrapped by exploiting the analytical structure of the conformal blocks. This yields the…
Although there is an extensive literature on the eigenvalues of high-dimensional sample covariance matrices, much of it is specialized to independent components (IC) models -- in which observations are represented as linear transformations…
We consider the performance of the bootstrap in high-dimensions for the setting of linear regression, where $p<n$ but $p/n$ is not close to zero. We consider ordinary least-squares as well as robust regression methods and adopt a minimalist…
This article studies bootstrap inference for high dimensional weakly dependent time series in a general framework of approximately linear statistics. The following high dimensional applications are covered: (1) uniform confidence band for…