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

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

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.

Predicting individualized potential outcomes in sequential decision-making is central for optimizing therapeutic decisions in personalized medicine (e.g., which dosing sequence to give to a cancer patient). However, predicting potential outcomes over long horizons is notoriously difficult. Existing methods that break the curse of the horizon typically lack strong theoretical guarantees such as orthogonality and quasi-oracle efficiency. In this paper, we revisit the problem of predicting individualized potential outcomes in sequential decision-making (i.e., estimating Q-functions in Markov decision processes with observational data) through a causal inference lens. In particular, we develop a comprehensive theoretical foundation for meta-learners in this setting with a focus on beneficial theoretical properties. As a result, we yield a novel meta-learner called DRQ-learner and establish that it is: (1) doubly robust (i.e., valid inference under the misspecification of one of the nuisances), (2) Neyman-orthogonal (i.e., insensitive to first-order estimation errors in the nuisance functions), and (3) achieves quasi-oracle efficiency (i.e., behaves asymptotically as if the ground-truth nuisance functions were known). Our DRQ-learner is applicable to settings with both discrete and continuous state spaces. Further, our DRQ-learner is flexible and can be used together with arbitrary machine learning models (e.g., neural networks). We validate our theoretical results through numerical experiments, thereby showing that our meta-learner outperforms state-of-the-art baselines.

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.

The Metropolis-within-Gibbs (MwG) algorithm is a widely used Markov Chain Monte Carlo method for sampling from high-dimensional distributions when exact conditional sampling is intractable. We study MwG with Random Walk Metropolis (RWM) updates, using proposal variances tuned to match the target's conditional variances. Assuming the target $π$ is a $d$-dimensional log-concave distribution with condition number $κ$, we establish a spectral gap lower bound of order $\mathcal{O}(1/κd)$ for the random-scan version of MwG, improving on the previously available $\mathcal{O}(1/κ^2 d)$ bound. This is obtained by developing sharp estimates of the conductance of one-dimensional RWM kernels, which can be of independent interest. The result shows that MwG can mix substantially faster with variance-adaptive proposals and that its mixing performance is just a constant factor worse than that of the exact Gibbs sampler, thus providing theoretical support to previously observed empirical behavior.

We survey the field of nonparametric inference under shape constraints, providing a historical overview and a perspective on its current state. An outlook and some open problems offer thoughts on future directions. 1 Introduction. Traditionally, we think of statistical methods as being divided into parametric approaches, which can be restrictive, but where estimation is typically straightforward (e.g. using maximum likelihood), and nonparametric methods, which are more flexible but often require careful choices of tuning parameters. Nonparametric inference under shape constraints sits somewhere in the middle, seeking in some ways the best of both worlds. The origins of the field are often traced to Grenander (1956), who proved that there exists a unique maximum likelihood estimator (MLE) of a decreasing density on the non-negative half-line (and was able to characterise it explicitly).