Related papers: On the conditional distributions of low-dimensiona…
Density regression characterizes the conditional density of the response variable given the covariates, and provides much more information than the commonly used conditional mean or quantile regression. However, it is often computationally…
Domain generalization aims to apply knowledge gained from multiple labeled source domains to unseen target domains. The main difficulty comes from the dataset bias: training data and test data have different distributions, and the training…
This paper provides a framework for estimating the mean and variance of a high-dimensional normal density. The main setting considered is a fixed number of vector following a high-dimensional normal distribution with unknown mean and…
We study quasi-species and closely related evolutionary dynamics like the replicator-mutator equation in high dimensions. In particular, we show that under certain conditions the fitness of almost all quasi-species becomes independent of…
The merit of projecting data onto linear subspaces is well known from, e.g., dimension reduction. One key aspect of subspace projections, the maximum preservation of variance (principal component analysis), has been thoroughly researched…
While conditional diffusion models have achieved remarkable success in various applications, they require abundant data to train from scratch, which is often infeasible in practice. To address this issue, transfer learning has emerged as an…
A random variable $Y_1$ is said to be smaller than $Y_2$ in the increasing concave stochastic order if $\mathbb{E}[\phi(Y_1)] \leq \mathbb{E}[\phi(Y_2)]$ for all increasing concave functions $\phi$ for which the expected values exist, and…
This article studies the quasi-stationary behaviour of absorbed one-dimensional diffusions. We obtain necessary and sufficient conditions for the exponential convergence to a unique quasi-stationary distribution in total variation,…
Controlling the dispersion of a subset of decision variables in an optimization problem is crucial for enforcing fairness or load-balancing across a wide range of applications. Building on the well-known equivalence of finite-dimensional…
In the paper we generalize the following characterization of beta distribution to the symmetric cone setting: let $X$ and $Y$ be independent, non-degenerate random variables with values in $(0,1)$, then $U=1-XY$ and $V=\frac{1-X}{U}$ are…
All models may be wrong -- but that is not necessarily a problem for inference. Consider the standard $t$-test for the significance of a variable $X$ for predicting response $Y$ whilst controlling for $p$ other covariates $Z$ in a random…
The statistics and machine learning communities have recently seen a growing interest in classification-based approaches to two-sample testing. The outcome of a classification-based two-sample test remains a rejection decision, which is not…
This paper is devoted to a fractional generalization of the Dirichlet distribution. The form of the multivariate distribution is derived assuming that the $n$ partitions of the interval $[0,W_n]$ are independent and identically distributed…
The stability of random variables can be generalized in any convex cone. In this case the principal results about the LePage representation and the domains of attraction are analogous but different to those well known for general Banach…
The noncontextual hidden variables models in $d=2$, such as the ones constructed by Bell and by Kochen and Specker, have difficulties in accounting for the conditional measurement of two non-orthogonal projectors. An idea of branching in…
We study the distribution of the maximum likelihood estimate (MLE) in high-dimensional logistic models, extending the recent results from Sur (2019) to the case where the Gaussian covariates may have an arbitrary covariance structure. We…
Suppose X is a random vector, that is distributed uniformly in some n-dimensional convex set. It was conjectured that when the dimension n is very large, there exists a non-zero vector u, such that the distribution of the real random…
We study delay-independent stability in nonlinear models with a distributed delay which have a positive equilibrium. Such models frequently occur in population dynamics and other applications. In particular, we construct a relevant…
We consider causal models with two observed variables and one latent variables, each variable being discrete, with the goal of characterizing the possible distributions on outcomes that can result from controlling one of the observed…
We consider the modulation of data given by random vectors $X_n \in \mathbb{R}^{d_n}$, $n \in \mathbb{N}$. For each $X_n$, one chooses an independent modulating random vector $\Xi_n \in \mathbb{R}^{d_n}$ and forms the projection $Y_n =…