Related papers: Admissible anytime-valid sequential inference must…
We present a universal framework for constructing confidence sets based on sequential likelihood mixing. Building upon classical results from sequential analysis, we provide a unifying perspective on several recent lines of work, and…
Wasserman et al. (2020, PNAS, vol. 117, pp. 16880-16890) constructed estimator agnostic and finite-sample valid confidence sets and hypothesis tests, using split-data likelihood ratio-based statistics. We demonstrate that the same approach…
This paper develops a theory of distribution- and time-uniform asymptotics, culminating in the first large-sample anytime-valid inference procedures that are shown to be uniformly valid in a rich class of distributions. Historically,…
Positive $T$-martingales were developed as a general framework that extends the positive measure-valued martingales and are meant to model intermittent turbulence. We extend their scope by allowing the martingale to take complex values. We…
Confidence sequences based on test martingales provide time-uniform uncertainty quantification for the mean of bounded IID observations without parametric distributional assumptions. Their practical efficiency, however, depends strongly on…
Linear models are foundational tools in statistics and ubiquitous across the applied sciences. However, conventional statistical inference -- such as $t$-tests and $F$-tests -- are only valid at fixed sample sizes, making them unsuitable…
Probabilistic sentential decision diagrams are logic circuits where the inputs of disjunctive gates are annotated by probability values. They allow for a compact representation of joint probability mass functions defined over sets of…
We propose a sequential, anytime-valid method to test the conditional independence of a response $Y$ and a predictor $X$ given a random vector $Z$. The proposed test is based on e-statistics and test martingales, which generalize likelihood…
In a Monte-Carlo test, the observed dataset is fixed, and several resampled or permuted versions of the dataset are generated in order to test a null hypothesis that the original dataset is exchangeable with the resampled/permuted ones.…
Computing reachability probabilities is a fundamental problem in the analysis of probabilistic programs. This paper aims at a comprehensive and comparative account on various martingale-based methods for over- and under-approximating…
Selective inference is a subfield of statistics that enables valid inference after selection of a data-dependent question. In this paper, we introduce selectively dominant p-values, a class of p-values that allow practitioners to easily…
As inductive inference and machine learning methods in computer science see continued success, researchers are aiming to describe ever more complex probabilistic models and inference algorithms. It is natural to ask whether there is a…
In most prediction and estimation situations, scientists consider various statistical models for the same problem, and naturally want to select amongst the best. Hansen et al. (2011) provide a powerful solution to this problem by the…
Four distinct admissibility geometries govern sequential and distribution-free inference: Blackwell risk dominance over convex risk sets, anytime-valid admissibility within the nonnegative supermartingale cone, marginal coverage validity…
Autoregressive models are a class of time series models that are important in both applied and theoretical statistics. Typically, inferential devices such as confidence sets and hypothesis tests for time series models require nuanced…
We develop scalable methods for producing conformal Bayesian predictive intervals with finite sample calibration guarantees. Bayesian posterior predictive distributions, $p(y \mid x)$, characterize subjective beliefs on outcomes of…
Diffusion models are a remarkably effective way of learning and sampling from a distribution $p(x)$. In posterior sampling, one is also given a measurement model $p(y \mid x)$ and a measurement $y$, and would like to sample from $p(x \mid…
In this paper, we study the nonnegative matrix factorization problem under the separability assumption (that is, there exists a cone spanned by a small subset of the columns of the input nonnegative data matrix containing all columns),…
Hypothesis tests calibrated by (re)sampling methods (such as permutation, rank and bootstrap tests) are useful tools for statistical analysis, at the computational cost of requiring Monte-Carlo sampling for calibration. It is common and…
The aim of this paper is to discuss a recent result which shows that probabilistic inference in the presence of (unknown) causal mechanisms can be tractable for models that have traditionally been viewed as intractable. This result was…