Related papers: Universal Inference Meets Random Projections: A Sc…
We revisit the problem of sampling from a target distribution that has a smooth strongly log-concave density everywhere in $\mathbb R^p$. In this context, if no additional density information is available, the randomized midpoint…
Long event sequences (termed traces) and large data logs that originate from sensors and prediction models are becoming increasingly common in our data-rich world. In such scenarios, conformance checking-validating a data log against an…
We consider the problem of sampling from the posterior distribution of a $d$-dimensional coefficient vector $\boldsymbol{\theta}$, given linear observations $\boldsymbol{y} = \boldsymbol{X}\boldsymbol{\theta}+\boldsymbol{\varepsilon}$. In…
Frank--Wolfe methods avoid projections, but over curved feasible regions the full-space linear minimization oracle (LMO) can itself become the computational bottleneck. We introduce random-subspace Frank--Wolfe (RSFW), the first…
Sampling from log-concave distributions is a well researched problem that has many applications in statistics and machine learning. We study the distributions of the form $p^{*}\propto\exp(-f(x))$, where…
Design-based inference, also known as randomization-based or finite-population inference, provides a principled framework for trustworthy statistical inference by attributing randomness solely to the design mechanism (e.g., treatment…
Suppose that we wish to estimate a finite-dimensional summary of one or more function-valued features of an underlying data-generating mechanism under a nonparametric model. One approach to estimation is by plugging in flexible estimates of…
We consider the branch-length estimation problem on a bifurcating tree: a character evolves along the edges of a binary tree according to a two-state symmetric Markov process, and we seek to recover the edge transition probabilities from…
The computational complexity of some depths that satisfy the projection property, such as the halfspace depth or the projection depth, is known to be high, especially for data of higher dimensionality. In such scenarios, the exact depth is…
We develop a unified $L$-statistic testing framework for high-dimensional regression coefficients that adapts to unknown sparsity. The proposed statistics rank coordinate-wise evidence measures and aggregate the top $k$ signals, bridging…
Multivariate extreme value statistical analysis is concerned with observations on several variables which are thought to possess some degree of tail-dependence. In areas such as the modeling of financial and insurance risks, or as the…
Adaptive experimental designs have gained popularity in clinical trials and online experiments. Unlike traditional, fixed experimental designs, adaptive designs can dynamically adjust treatment randomization probabilities and other design…
Shape-constrained inference has wide applicability in bioassay, medicine, economics, risk assessment, and many other fields. Although there has been a large amount of work on monotone-constrained univariate curve estimation, multivariate…
Profile likelihood provides a general framework to infer on a scalar parameter of a statistical model. A confidence interval is obtained by numerically finding the two abscissas where the profile log-likelihood curve intersects an…
Sampling from various kinds of distributions is an issue of paramount importance in statistics since it is often the key ingredient for constructing estimators, test procedures or confidence intervals. In many situations, the exact sampling…
This paper develops new tools to quantify uncertainty in optimal decision making and to gain insight into which variables one should collect information about given the potential cost of measuring a large number of variables. We investigate…
Constraining the maximum likelihood density estimator to satisfy a sufficiently strong constraint, $\log-$concavity being a common example, has the effect of restoring consistency without requiring additional parameters. Since many results…
Complex phenomena in engineering and the sciences are often modeled with computationally intensive feed-forward simulations for which a tractable analytic likelihood does not exist. In these cases, it is sometimes necessary to estimate an…
Consider a pair of cumulative distribution functions $F$ and $G$, where $F$ is unknown and $G$ is a known reference distribution. Given a sample from $F$, we propose tests to detect the convexity or the concavity of $G^{-1}\circ F$ versus…
Asymptotic methods for hypothesis testing in high-dimensional data usually require the dimension of the observations to increase to infinity, often with an additional condition on its rate of increase compared to the sample size. On the…