Related papers: Optimal E-Values for Exponential Families: the Sim…
Exponential families encompass the distributions central to modern machine learning -- softmax, Gaussians, and Boltzmann distributions -- and underlie the theory of variational inference, entropy-regularized reinforcement learning, and…
Forecasting and forecast evaluation are inherently sequential tasks. Predictions are often issued on a regular basis, such as every hour, day, or month, and their quality is monitored continuously. However, the classical statistical tools…
In this short note we provide an analytical formula for the conditional covariance matrices of the elliptically distributed random vectors, when the conditioning is based on the values of any linear combination of the marginal random…
Exponential family extensions of principal component analysis (EPCA) have received a considerable amount of attention in recent years, demonstrating the growing need for basic modeling tools that do not assume the squared loss or Gaussian…
The classical multivariate extreme-value theory concerns the modeling of extremes in a multivariate random sample, suggesting the use of max-stable distributions. In this work, the classical theory is extended to the case where aggregated…
For a random variable $N = 0, 1, 2, \ldots$ we study the following question: When does the sum of $N$ many independent and identically distributed copies of a random variable $X$ have the same law a a nontrivial rescaling of $X$? We show…
Hypothesis testing of structure in covariance matrices is of significant importance, but faces great challenges in high-dimensional settings. Although consistent frequentist one-sample covariance tests have been proposed, there is a lack of…
We consider growth-optimal e-variables with maximal e-power, both in an absolute and relative sense, for simple null hypotheses for a $d$-dimensional random vector, and multivariate composite alternatives represented as a set of…
A random phenomenon may have two sources of random variation: an unstable identity and a set of external variation-generating factors. When only a single source is active, two mutually exclusive extreme scenarios may ensue that result in…
In the analysis of data sets consisting of (X, Y)-pairs, a tacit assumption is that each pair corresponds to the same observation unit. If, however, such pairs are obtained via record linkage of two files, this assumption can be violated as…
Analysis of low-degree polynomial algorithms is a powerful, newly-popular method for predicting computational thresholds in hypothesis testing problems. One limitation of current techniques for this analysis is their restriction to…
We introduce a family of maps generating continued fractions where the digit $1$ in the numerator is replaced cyclically by some given non-negative integers $(N_1,\ldots,N_m)$. We prove the convergence of the given algorithm, and study the…
We give a complete classification of 1-dimensional exponential families $\mathcal{E}$ defined over a finite space $\Omega=\{x_{0}, ...,x_{n}\}$ whose Hessian scalar curvature is constant. We observe an interesting phenomenon: if…
Estimation of covariance matrices or their inverses plays a central role in many statistical methods. For these methods to work reliably, estimated matrices must not only be invertible but also well-conditioned. In this paper we present an…
The e-value is swiftly rising in prominence in many applications of hypothesis testing and multiple testing, yet its relationship to classical testing theory remains elusive. We unify e-values and classical testing into a single 'continuous…
This report presents an elementary theory of unification for positive conjunctive queries. A positive conjunctive query is a formula constructed from propositional constants, equations and atoms using the conjunction $\wedge$ and the…
This paper investigates a statistical procedure for testing the equality of two independent estimated covariance matrices when the number of potentially dependent data vectors is large and proportional to the size of the vectors, that is,…
In this article, I introduce a group-theoretical method to prove positivity of certain linear combinations (with coefficients generally lying in $\mathbb{C}$) of exponential functions under a set of semidefinite linear constraints. The…
The unconstrained exponential family of random graphs assumes no prior knowledge of the graph before sampling, but it is natural to consider situations where partial information about the graph is known, for example the total number of…
We analyze families of non-autonomous systems of first-order ordinary differential equations admitting a common time-dependent superposition rule, i.e., a time-dependent map expressing any solution of each of these systems in terms of a…