Related papers: Strong Gaussian approximation for U-statistics in …
The method to derive uniform bounds with Gaussian and Rademacher complexities is extended to the case where the sample average is replaced by a nonlinear statistic. Tight bounds are obtained for U-statistics, smoothened L-statistics and…
Stochastic gradient descent (SGD) and its variants have established themselves as the go-to algorithms for large-scale machine learning problems with independent samples due to their generalization performance and intrinsic computational…
We devise a general result on the consistency of model-based bootstrap methods for U- and V-statistics under easily verifiable conditions. For that purpose, we derive the limit distributions of degree-2 degenerate U- and V-statistics for…
Cumulative sum (CUSUM) statistics are widely used in the change point inference and identification. For the problem of testing for existence of a change point in an independent sample generated from the mean-shift model, we introduce a…
In this paper we provide explicit upper bounds on some distances between the (law of the) output of a random Gaussian NN and (the law of) a random Gaussian vector. Our results concern both shallow random Gaussian neural networks with…
Many statistical applications, such as the Principal Component Analysis, matrix completion, tensor regression and many others, rely on accurate estimation of leading eigenvectors of a matrix. The Davis-Kahan theorem is known to be…
In this work we study a version of the general question of how well a Haar distributed orthogonal matrix can be approximated by a random gaussian matrix. Here, we consider a gaussian random matrix $Y_n$ of order $n$ and apply to it the…
The performance of Gaussian Process (GP) regression is often hampered by the curse of dimensionality, which inflates computational cost and reduces predictive power in high-dimensional problems. Variable selection is thus crucial for…
We continue to study the squared Frobenius norm of a submatrix of a $n \times n$ random unitary matrix. When the choice of the submatrix is deterministic and its size is $[ns] \times [nt]$, we proved in a previous paper that, after…
Exact Gaussian Process (GP) regression has O(N^3) runtime for data size N, making it intractable for large N. Many algorithms for improving GP scaling approximate the covariance with lower rank matrices. Other work has exploited structure…
Gaussian graphical model is one of the powerful tools to analyze conditional independence between two variables for multivariate Gaussian-distributed observations. When the dimension of data is moderate or high, penalized likelihood methods…
Introducing inequality constraints in Gaussian process (GP) models can lead to more realistic uncertainties in learning a great variety of real-world problems. We consider the finite-dimensional Gaussian approach from Maatouk and Bay (2017)…
Motivated by problems on random differences in Szemer\'{e}di's theorem and on large deviations for arithmetic progressions in random sets, we prove upper bounds on the Gaussian width of point sets that are formed by the image of the…
We construct a continuous-time non-commutative random walk on $U(\mathfrak{gl}_N)$ with dilation maps $U(\mathfrak{gl}_N)\rightarrow L^2(U(N))^{\otimes\infty}$. This is an analog of a continuous-time non-commutative random walk on the group…
A classifier for two or more samples is proposed when the data are high-dimensional and the underlying distributions may be non-normal. The classifier is constructed as a linear combination of two easily computable and interpretable…
Bridge sampling is an effective Monte Carlo method for estimating the ratio of normalizing constants of two probability densities, a routine computational problem in statistics, physics, chemistry, and other fields. The Monte Carlo error of…
We reconsider a nonparametric density model based on Gaussian processes. By augmenting the model with latent P\'olya--Gamma random variables and a latent marked Poisson process we obtain a new likelihood which is conjugate to the model's…
We investigate the low-dimensional structure of deterministic transformations between random variables, i.e., transport maps between probability measures. In the context of statistics and machine learning, these transformations can be used…
We investigate the realizations of a random Gaussian field on a finite domain of ${\mathbb R}^d$ in the limit where a given linear functional of the field is large. We prove that if its variance is bounded, the field converges uniformly and…
Simultaneous inference for high-dimensional non-Gaussian time series is always considered to be a challenging problem. Such tasks require not only robust estimation of the coefficients in the random process, but also deriving limiting…