Related papers: Statistical Hypothesis Testing for Information Val…
Instrumental variable (IV) methods offer a valuable approach to account for outcome data missing not-at-random. A valid missing data instrument is a measured factor which (i) predicts the nonresponse process and (ii) is independent of the…
The information bottleneck (IB) problem is a widely studied framework in machine learning for extracting compressed features that are informative for downstream tasks. However, current approaches to solving the IB problem rely on a…
In contrast to its common definition and calculation, interpretation of p-values diverges among statisticians. Since p-value is the basis of various methodologies, this divergence has led to a variety of test methodologies and evaluations…
We derive inferential procedures for large sample sizes that remain valid under data-dependent significance levels (so-called "post-hoc valid inference"). Classical statistical tools require that the significance level -- the "type-I error"…
This paper introduces a comprehensive framework for complex-valued probability measures and explores their novel applications in information theory and statistical analysis. We define a complex probability measure as a phase-modulated…
Much of science is (rightly or wrongly) driven by hypothesis testing. Even in situations where the hypothesis testing paradigm is correct, the common practice of basing inferences solely on p-values has been under intense criticism for over…
Information theory provides ideas for conceptualising information and measuring relationships between objects. It has found wide application in the sciences, but economics and finance have made surprisingly little use of it. We show that…
Many multiple testing procedures make use of the p-values from the individual pairs of hypothesis tests, and are valid if the p-value statistics are independent and uniformly distributed under the null hypotheses. However, it has recently…
Instrumental variable (IV) methods play a central role in causal inference, particularly in settings where treatment assignment is confounded by unobserved variables. IV methods have been extensively developed in recent years and applied…
This paper explores hypothesis testing for the parametric forms of the mean and variance functions in regression models under diverging-dimension settings. To mitigate the curse of dimensionality, we introduce weighted residual empirical…
This paper presents a simple method for carrying out inference in a wide variety of possibly nonlinear IV models under weak assumptions. The method is non-asymptotic in the sense that it provides a finite sample bound on the difference…
We introduce two new classes of measures of information for statistical experiments which generalise and subsume $\phi$-divergences, integral probability metrics, $\mathfrak{N}$-distances (MMD), and $(f,\Gamma)$ divergences between two or…
Score matching is a vital tool for learning the distribution of data with applications across many areas including diffusion processes, energy based modelling, and graphical model estimation. Despite all these applications, little work…
Researchers in explainable artificial intelligence have developed numerous methods for helping users understand the predictions of complex supervised learning models. By contrast, explaining the $\textit{uncertainty}$ of model outputs has…
Term frequency-inverse document frequency, or TF-IDF for short, and its many variants form a class of term weighting functions the members of which are widely used in text analysis applications. While TF-IDF was originally proposed as a…
Understanding the effect of a feature vector $x \in \mathbb{R}^d$ on the response value (label) $y \in \mathbb{R}$ is the cornerstone of many statistical learning problems. Ideally, it is desired to understand how a set of collected…
Instrumental variable (IV) regression is a standard strategy for learning causal relationships between confounded treatment and outcome variables from observational data by utilizing an instrumental variable, which affects the outcome only…
Clustering is part of unsupervised analysis methods that consist in grouping samples into homogeneous and separate subgroups of observations also called clusters. To interpret the clusters, statistical hypothesis testing is often used to…
Accurately estimating the informativeness of individual samples in a dataset is an important objective in deep learning, as it can guide sample selection, which can improve model efficiency and accuracy by removing redundant or potentially…
In the age of big data, data integration is a critical step especially in the understanding of how diverse data types work together and work separately. Among data integration methods, the Angle-Based Joint and Individual Variation…