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Predictive inference is a fundamental task in statistics, traditionally addressed using parametric assumptions about the data distribution and detailed analyses of how models learn from data. In recent years, conformal prediction has…
Measuring the dependence of data plays a central role in statistics and machine learning. In this work, we summarize and generalize the main idea of existing information-theoretic dependence measures into a higher-level perspective by the…
Interpretability and stability are two important features that are desired in many contemporary big data applications arising in economics and finance. While the former is enjoyed to some extent by many existing forecasting approaches, the…
A salient approach to interpretable machine learning is to restrict modeling to simple models. In the Bayesian framework, this can be pursued by restricting the model structure and prior to favor interpretable models. Fundamentally,…
This paper develops a novel nonparametric significance test based on a tailored nonparametric-type projected weighting function that exhibits appealing theoretical and numerical properties. We derive the asymptotic properties of the…
Most traditional models of uncertainty have focused on the associational relationship among variables as captured by conditional dependence. In order to successfully manage intelligent systems for decision making, however, we must be able…
Forecasting has become a natural benchmark for reasoning under uncertainty. Yet existing evaluations of large language models remain limited to judgmental tasks in simple formats, such as binary or multiple-choice questions. In practice,…
This paper presents a framework for Quantum causal modeling based on the interpretation of causality as a relation between an observer's probability assignments to hypothetical or counterfactual experiments. The framework is based on the…
While hidden class models of various types arise in many statistical applications, it is often difficult to establish the identifiability of their parameters. Focusing on models in which there is some structure of independence of some of…
Much of uncertainty quantification to date has focused on determining the effect of variables modeled probabilistically, and with a known distribution, on some physical or engineering system. We develop methods to obtain information on the…
Identifying relationships among stochastic processes is a core objective in many fields, such as economics. While the standard toolkit for multivariate time series analysis has many advantages, it can be difficult to capture nonlinear…
Recent years have witnessed the emergence of a variety of post-hoc interpretations that aim to uncover how natural language processing (NLP) models make predictions. Despite the surge of new interpretation methods, it remains an open…
Attribute weighting and differential weighting, two major mechanisms for computing context-dependent similarity or dissimilarity measures are studied and compared. A dissimilarity measure based on subset size in the context is proposed and…
Distinguishability and, by extension, observability are key properties of dynamical systems. Establishing these properties is challenging, especially when no analytical model is available and they are to be inferred directly from…
We investigate the significance of change-points within fully nonparametric regression contexts, with a particular focus on panel data where data generation processes vary across units, and error terms may display complex dependency…
The Guide to the Expression of Uncertainty in Measurement advocates the use of an 'effective number of degrees of freedom' for the calculation of an interval of measurement uncertainty. However, it does not describe how this number is to be…
We present a general framework for uncertainty quantification that is a mosaic of interconnected models. We define global first and second order structural and correlative sensitivity analyses for random counting measures acting on risk…
Testing for association or dependence between pairs of random variables is a fundamental problem in statistics. In some applications, data are subject to selection bias that causes dependence between observations even when it is absent from…
Structural independence is the (conditional) independence that arises from the structure rather than the precise numerical values of a distribution. We develop this concept and relate it to $d$-separation and structural causal models.…
We take a different look at the problem of testing the independence of two metric-space-valued random variables using the distance correlation. Instead of testing if the distance correlation vanishes exactly, we are interested in the…