Dense neural network (DNN) may face various problems despite its huge successes in AI fields.

This document contains additional details, in-depth discussions, and more results that did not fit into the main paper.

We introduce a framework for inference in general state-space hidden Markov models (HMMs) under likelihood misspecification.

Importantly, our results also show that subpopulation-based recourse is the right approach to adopt when assumptions such as additive noise do not hold.

The following are equivalent: 1. X X as m, and X is a constant a.s., then X A, where A is a constant. The result follows by taking ϵ 0. 4. We adapt the proof of Fatou's lemma that holds for random variables that converge in E[f ( g (X))].

Counterfactual Explanations (CFEs) interpret machine learning models by identifying the smallest change to input features needed to change the model's prediction to a desired output. For classification tasks, CFEs determine how close a given sample is to the decision boundary of a trained classifier. Existing methods are often sample-inefficient, requiring numerous evaluations of a black-box model -- an approach that is both costly and impractical when access to the model is limited. We propose Adaptive sampling for Counterfactual Explanations (ACE), a sample-efficient algorithm combining Bayesian estimation and stochastic optimization to approximate the decision boundary with fewer queries. By prioritizing informative points, ACE minimizes evaluations while generating accurate and feasible CFEs. Extensive empirical results show that ACE achieves superior evaluation efficiency compared to state-of-the-art methods, while maintaining effectiveness in identifying minimal and actionable changes.

Average and conditional treatment effects are fundamental causal quantities used to evaluate the effectiveness of treatments in various critical applications, including clinical settings and policy-making. Beyond the gold-standard estimators from randomized trials, numerous methods have been proposed to estimate treatment effects using observational data. In this paper, we provide a novel characterization of widely used causal inference techniques within the framework of staged event trees, demonstrating their capacity to enhance treatment effect estimation. These models offer a distinct advantage due to their interpretability, making them particularly valuable for practical applications. We implement classical estimators within the framework of staged event trees and illustrate their capabilities through both simulation studies and real-world applications. Furthermore, we showcase how staged event trees explicitly and visually describe when standard causal assumptions, such as positivity, hold, further enhancing their practical utility.