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Using eigenmode expansion of the Mark-3 and SFI surveys of cosmological radial velocities a goodness-of-fit analysis is applied on a mode-by-mode basis. This differential analysis complements theBayesian maximum likelihood analysis that…
Feature importance scores are ubiquitous tools for understanding the predictions of machine learning models. However, many popular attribution methods suffer from high instability due to random sampling. Leveraging novel ideas from…
We discuss promising recent contributions on quantifying feature relevance using Shapley values, where we observed some confusion on which probability distribution is the right one for dropped features. We argue that the confusion is based…
Many common loss functions such as mean-squared-error, cross-entropy, and reconstruction loss are unnecessarily rigid. Under a probabilistic interpretation, these common losses correspond to distributions with fixed shapes and scales. We…
In this work we propose a framework for constructing goodness of fit tests in both low and high-dimensional linear models. We advocate applying regression methods to the scaled residuals following either an ordinary least squares or Lasso…
Maximum likelihood fits to data can be performed using binned data and unbinned data. The likelihood fits in either case produce only the fitted quantities but not the goodness of fit. With binned data, one can obtain a measure of the…
Quantifying variable importance is essential for answering high-stakes questions in fields like genetics, public policy, and medicine. Current methods generally calculate variable importance for a given model trained on a given dataset.…
Adaptive importance sampling is a widely spread Monte Carlo technique that uses a re-weighting strategy to iteratively estimate the so-called target distribution. A major drawback of adaptive importance sampling is the large variance of the…
The global sensitivity analysis of a numerical model aims to quantify, by means of sensitivity indices estimate, the contributions of each uncertain input variable to the model output uncertainty. The so-called Sobol' indices, which are…
Feature importance aims at measuring how crucial each input feature is for model prediction. It is widely used in feature engineering, model selection and explainable artificial intelligence (XAI). In this paper, we propose a new tree-model…
Shapley effects are attracting increasing attention as sensitivity measures. When the value function is the conditional variance, they account for the individual and higher order effects of a model input. They are also well defined under…
Density-based directed distances -- particularly known as divergences -- between probability distributions are widely used in statistics as well as in the adjacent research fields of information theory, artificial intelligence and machine…
Feature importance techniques have enjoyed widespread attention in the explainable AI literature as a means of determining how trained machine learning models make their predictions. We consider Shapley value based approaches to feature…
We consider Bayesian inference by importance sampling when the likelihood is analytically intractable but can be unbiasedly estimated. We refer to this procedure as importance sampling squared (IS2), as we can often estimate the likelihood…
Thousands of experiments are analyzed and papers are published each year involving the statistical analysis of grouped data. While this area of statistics is often perceived -- somewhat naively -- as saturated, several misconceptions still…
Complex, high-dimensional data is ubiquitous across many scientific disciplines, including machine learning, biology, and the social sciences. One of the primary methods of visualizing these datasets is with two-dimensional scatter plots…
Variational inference with {\alpha}-divergences has been widely used in modern probabilistic machine learning. Compared to Kullback-Leibler (KL) divergence, a major advantage of using {\alpha}-divergences (with positive {\alpha} values) is…
Shapley values are great analytical tools in game theory to measure the importance of a player in a game. Due to their axiomatic and desirable properties such as efficiency, they have become popular for feature importance analysis in data…
Shapley Values (SV) are widely used in explainable AI, but their estimation and interpretation can be challenging, leading to inaccurate inferences and explanations. As a starting point, we remind an invariance principle for SV and derive…
Shapley data valuation provides a principled, axiomatic framework for assigning importance to individual datapoints, and has gained traction in dataset curation, pruning, and pricing. However, it is a combinatorial measure that requires…