We study a double robust Bayesian inference procedure on the average treatment effect (ATE) under unconfoundedness. Our robust Bayesian approach involves two adjustment steps: first, we make a correction for prior distributions of the conditional mean function; second, we introduce a recentering term on the posterior distribution of the resulting ATE. We prove asymptotic equivalence of our Bayesian estimator and double robust frequentist estimators by establishing a new semiparametric Bernstein-von Mises theorem under double robustness; i.e., the lack of smoothness of conditional mean functions can be compensated by high regularity of the propensity score and vice versa. Consequently, the resulting Bayesian point estimator internalizes the bias correction as the frequentist-type doubly robust estimator, and the Bayesian credible sets form confidence intervals with asymptotically exact coverage probability. In simulations, we find that this robust Bayesian procedure leads to significant bias reduction of point estimation and accurate coverage of confidence intervals, especially when the dimensionality of covariates is large relative to the sample size and the underlying functions become complex. We illustrate our method in an application to the National Supported Work Demonstration.

A central quest in explainable AI relates to understanding the decisions made by (learned) classifiers. There are three dimensions of this understanding that have been receiving significant attention in recent years. The first dimension relates to characterizing conditions on instances that are necessary and sufficient for decisions, therefore providing abstractions of instances that can be viewed as the "reasons behind decisions." The next dimension relates to characterizing minimal conditions that are sufficient for a decision, therefore identifying maximal aspects of the instance that are irrelevant to the decision. The last dimension relates to characterizing minimal conditions that are necessary for a decision, therefore identifying minimal perturbations to the instance that yield alternate decisions. We discuss in this tutorial a comprehensive, semantical and computational theory of explainability along these dimensions which is based on some recent developments in symbolic logic. The tutorial will also discuss how this theory is particularly applicable to non-symbolic classifiers such as those based on Bayesian networks, decision trees, random forests and some types of neural networks.

Probability predictions are essential to inform decision making in medicine, economics, image classification, sports analytics, entertainment, and many other fields. Ideally, probability predictions are (i) well calibrated, (ii) accurate, and (iii) bold, i.e., far from the base rate of the event. Predictions that satisfy these three criteria are informative for decision making. However, there is a fundamental tension between calibration and boldness, since calibration metrics can be high when predictions are overly cautious, i.e., non-bold. The purpose of this work is to develop a hypothesis test and Bayesian model selection approach to assess calibration, and a strategy for boldness-recalibration that enables practitioners to responsibly embolden predictions subject to their required level of calibration. Specifically, we allow the user to pre-specify their desired posterior probability of calibration, then maximally embolden predictions subject to this constraint. We verify the performance of our procedures via simulation, then demonstrate the breadth of applicability by applying these methods to real world case studies in each of the fields mentioned above. We find that very slight relaxation of calibration probability (e.g., from 0.99 to 0.95) can often substantially embolden predictions (e.g., widening Hockey predictions' range from .25-.75 to .10-.90)

Much discussion about large language models and language-and-vision models has focused on whether these models are intelligent agents. We present an alternative perspective. We argue that these artificial intelligence models are cultural technologies that enhance cultural transmission in the modern world, and are efficient imitation engines. We explore what AI models can tell us about imitation and innovation by evaluating their capacity to design new tools and discover novel causal structures, and contrast their responses with those of human children. Our work serves as a first step in determining which particular representations and competences, as well as which kinds of knowledge or skill, can be derived from particular learning techniques and data. Critically, our findings suggest that machines may need more than large scale language and images to achieve what a child can do.

The signature kernel is a positive definite kernel for sequential data. It inherits theoretical guarantees from stochastic analysis, has efficient algorithms for computation, and shows strong empirical performance. In this short survey paper for a forthcoming Springer handbook, we give an elementary introduction to the signature kernel and highlight these theoretical and computational properties.

We propose a novel hierarchical Bayesian approach to Federated Learning (FL), where our model reasonably describes the generative process of clients' local data via hierarchical Bayesian modeling: constituting random variables of local models for clients that are governed by a higher-level global variate. Interestingly, the variational inference in our Bayesian model leads to an optimisation problem whose block-coordinate descent solution becomes a distributed algorithm that is separable over clients and allows them not to reveal their own private data at all, thus fully compatible with FL. We also highlight that our block-coordinate algorithm has particular forms that subsume the well-known FL algorithms including Fed-Avg and Fed-Prox as special cases. Beyond introducing novel modeling and derivations, we also offer convergence analysis showing that our block-coordinate FL algorithm converges to an (local) optimum of the objective at the rate of $O(1/\sqrt{t})$, the same rate as regular (centralised) SGD, as well as the generalisation error analysis where we prove that the test error of our model on unseen data is guaranteed to vanish as we increase the training data size, thus asymptotically optimal.

Model independent techniques for constructing background data templates using generative models have shown great promise for use in searches for new physics processes at the LHC. We introduce a major improvement to the CURTAINs method by training the conditional normalizing flow between two side-band regions using maximum likelihood estimation instead of an optimal transport loss. The new training objective improves the robustness and fidelity of the transformed data and is much faster and easier to train. We compare the performance against the previous approach and the current state of the art using the LHC Olympics anomaly detection dataset, where we see a significant improvement in sensitivity over the original CURTAINs method. Furthermore, CURTAINsF4F requires substantially less computational resources to cover a large number of signal regions than other fully data driven approaches. When using an efficient configuration, an order of magnitude more models can be trained in the same time required for ten signal regions, without a significant drop in performance.

When applying differential privacy to sensitive data, we can often improve performance using external information such as other sensitive data, public data, or human priors. We propose to use the learning-augmented algorithms (or algorithms with predictions) framework -- previously applied largely to improve time complexity or competitive ratios -- as a powerful way of designing and analyzing privacy-preserving methods that can take advantage of such external information to improve utility. This idea is instantiated on the important task of multiple quantile release, for which we derive error guarantees that scale with a natural measure of prediction quality while (almost) recovering state-of-the-art prediction-independent guarantees. Our analysis enjoys several advantages, including minimal assumptions about the data, a natural way of adding robustness, and the provision of useful surrogate losses for two novel ``meta" algorithms that learn predictions from other (potentially sensitive) data. We conclude with experiments on challenging tasks demonstrating that learning predictions across one or more instances can lead to large error reductions while preserving privacy.

ABSTRACT We consider the problem of information aggregation in federated decision making, where a group of agents collaborate to infer the underlying state of nature without sharing their private data with the central processor or each other. We analyze the non-Bayesian social learning strategy in which agents incorporate their individual observations into their opinions (i.e., soft-decisions) with Bayes rule, and the central processor aggregates these opinions by arithmetic or geometric averaging. Building on our previous work, we establish that both pooling strategies result in asymptotic normality characterization of the system, which, for instance, can be utilized to derive approximate expressions for the error probability. We verify the theoretical findings with simulations and compare both strategies. Figure 1: Data types at the edge devices can be highly heterogeneous.

The heavy-tailed behavior of the generalized extreme-value distribution makes it a popular choice for modeling extreme events such as floods, droughts, heatwaves, wildfires, etc. However, estimating the distribution's parameters using conventional maximum likelihood methods can be computationally intensive, even for moderate-sized datasets. To overcome this limitation, we propose a computationally efficient, likelihood-free estimation method utilizing a neural network. Through an extensive simulation study, we demonstrate that the proposed neural network-based method provides Generalized Extreme Value (GEV) distribution parameter estimates with comparable accuracy to the conventional maximum likelihood method but with a significant computational speedup. To account for estimation uncertainty, we utilize parametric bootstrapping, which is inherent in the trained network. Finally, we apply this method to 1000-year annual maximum temperature data from the Community Climate System Model version 3 (CCSM3) across North America for three atmospheric concentrations: 289 ppm $\mathrm{CO}_2$ (pre-industrial), 700 ppm $\mathrm{CO}_2$ (future conditions), and 1400 ppm $\mathrm{CO}_2$, and compare the results with those obtained using the maximum likelihood approach.