Age-specific fertility rates (ASFRs) provide the most extensive record of reproductive change, but their aggregate nature obscures the individual-level behavioral mechanisms that drive fertility trends. To bridge this micro-macro divide, we introduce a likelihood-free Bayesian framework that couples a demographically interpretable, individual-level simulation model of the reproductive process with Sequential Neural Posterior Estimation (SNPE). We show that this framework successfully recovers core behavioral parameters governing contemporary fertility, including preferences for family size, reproductive timing, and contraceptive failure, using only ASFRs. The framework's effectiveness is validated on cohorts from four countries with diverse fertility regimes. Most compellingly, the model, estimated solely on aggregate data, successfully predicts out-of-sample distributions of individual-level outcomes, including age at first sex, desired family size, and birth intervals. Because our framework yields complete synthetic life histories, it significantly reduces the data requirements for building microsimulation models and enables behaviorally explicit demographic forecasts.

Reinforcement learning (RL) provides a principled framework for decision-making in partially observable environments, which can be modeled as Markov decision processes and compactly represented through dynamic decision Bayesian networks. Recent advances demonstrate that inference on sparse Bayesian networks can be accelerated using quantum rejection sampling combined with amplitude amplification, leading to a computational speedup in estimating acceptance probabilities.\\ Building on this result, we introduce Quantum Bayesian Reinforcement Learning (QBRL), a hybrid quantum-classical look-ahead algorithm for model-based RL in partially observable environments. We present a rigorous, oracle-free time complexity analysis under fault-tolerant assumptions for the quantum device. Unlike standard treatments that assume a black-box oracle, we explicitly specify the inference process, allowing our bounds to more accurately reflect the true computational cost. We show that, for environments whose dynamics form a sparse Bayesian network, horizon-based near-optimal planning can be achieved sub-quadratically faster through quantum-enhanced belief updates. Furthermore, we present numerical experiments benchmarking QBRL against its classical counterpart on simple yet illustrative decision-making tasks. Our results offer a detailed analysis of how the quantum computational advantage translates into decision-making performance, highlighting that the magnitude of the advantage can vary significantly across different deployment settings.

This research addresses the critical lack of comprehensive studies on feature scaling by systematically evaluating 12 scaling techniques - including several less common transformations - across 14 different Machine Learning algorithms and 16 datasets for classification and regression tasks. We meticulously analyzed impacts on predictive performance (using metrics such as accuracy, MAE, MSE, and $R^2$) and computational costs (training time, inference time, and memory usage). Key findings reveal that while ensemble methods (such as Random Forest and gradient boosting models like XGBoost, CatBoost and LightGBM) demonstrate robust performance largely independent of scaling, other widely used models such as Logistic Regression, SVMs, TabNet, and MLPs show significant performance variations highly dependent on the chosen scaler. This extensive empirical analysis, with all source code, experimental results, and model parameters made publicly available to ensure complete transparency and reproducibility, offers model-specific crucial guidance to practitioners on the need for an optimal selection of feature scaling techniques.

We present a novel approach to help decision-makers efficiently identify preferred solutions from the Pareto set of a multi-objective optimization problem. Our method uses a Bayesian model to estimate the decision-maker's utility function based on pairwise comparisons. Aided by this model, a principled elicitation strategy selects queries interactively to balance exploration and exploitation, guiding the discovery of high-utility solutions. The approach is flexible: it can be used interactively or a posteriori after estimating the Pareto front through standard multi-objective optimization techniques. Additionally, at the end of the elicitation phase, it generates a reduced menu of high-quality solutions, simplifying the decision-making process. Through experiments on test problems with up to nine objectives, our method demonstrates superior performance in finding high-utility solutions with a small number of queries. We also provide an open-source implementation of our method to support its adoption by the broader community.

Inverse problems governed by partial differential equations (PDEs) play a crucial role in various fields, including computational science, image processing, and engineering. Particularly, Darcy flow equation is a fundamental equation in fluid mechanics, which plays a crucial role in understanding fluid flow through porous media. Bayesian methods provide an effective approach for solving PDEs inverse problems, while their numerical implementation requires numerous evaluations of computationally expensive forward solvers. Therefore, the adoption of surrogate models with lower computational costs is essential. However, constructing a globally accurate surrogate model for high-dimensional complex problems demands high model capacity and large amounts of data. To address this challenge, this study proposes an efficient locally accurate surrogate that focuses on the high-probability regions of the true likelihood in inverse problems, with relatively low model complexity and few training data requirements. Additionally, we introduce a sequential Bayesian design strategy to acquire the proposed surrogate since the high-probability region of the likelihood is unknown. The strategy treats the posterior evolution process of sequential Bayesian design as a Gaussian process, enabling algorithmic acceleration through one-step ahead prior. The complete algorithmic framework is referred to as Sequential Bayesian design for locally accurate surrogate (SBD-LAS). Finally, three experiments based the Darcy flow equation demonstrate the advantages of the proposed method in terms of both inversion accuracy and computational speed.

Previous studies have shown that hazard ratios between treatment groups estimated with the Cox model are uninterpretable because the indefinite baseline hazard of the model fails to identify temporal change in the risk set composition due to treatment assignment and unobserved factors among multiple, contradictory scenarios. To alleviate this problem, especially in studies based on observational data with uncontrolled dynamic treatment and real-time measurement of many covariates, we propose abandoning the baseline hazard and using machine learning to explicitly model the change in the risk set with or without latent variables. For this framework, we clarify the context in which hazard ratios can be causally interpreted, and then develop a method based on Neyman orthogonality to compute debiased maximum-likelihood estimators of hazard ratios. Computing the constructed estimators is more efficient than computing those based on weighted regression with marginal structural Cox models. Numerical simulations confirm that the proposed method identifies the ground truth with minimal bias. These results lay the foundation for developing a useful, alternative method for causal inference with uncontrolled, observational data in modern epidemiology.

Most existing methods for adapting models to out-of-distribution (OOD) domains rely on invariant representation learning to eliminate the influence of biased features. However, should bias always be eliminated -- and if not, when should it be retained, and how can it be leveraged? To address these questions, we first present a theoretical analysis that explores the conditions under which biased features can be identified and effectively utilized. Building on this theoretical foundation, we introduce a novel framework that strategically leverages bias to complement invariant representations during inference. The framework comprises two key components that leverage bias in both direct and indirect ways: (1) using invariance as guidance to extract predictive ingredients from bias, and (2) exploiting identified bias to estimate the environmental condition and then use it to explore appropriate bias-aware predictors to alleviate environment gaps. We validate our approach through experiments on both synthetic datasets and standard domain generalization benchmarks. Results consistently demonstrate that our method outperforms existing approaches, underscoring its robustness and adaptability.

--Federated learning is a paradigm of increasing relevance in real world applications, aimed at building a global model across a network of heterogeneous users without requiring the sharing of private data. We focus on model learning over decentralized architectures, where users collaborate directly to update the global model without relying on a central server . In this context, the current paper proposes a novel approach to collaboratively learn probabilistic generative classifiers with a parametric form. The framework is composed by a communication network over a set of local nodes, each of one having its own local data, and a local updating rule. The proposal involves sharing local statistics with neighboring nodes, where each node aggregates the neighbors' information and iteratively learns its own local classifier, which progressively converges to a global model. Extensive experiments demonstrate that the algorithm consistently converges to a globally competitive model across a wide range of network topologies, network sizes, local dataset sizes, and extreme non-i.i.d. In recent years, federated learning (FL) [1], [2] has gained increasing attention from both the research community [3], [4] and private companies [5], [6], as it enables the development of machine learning models across multiple users without requiring data centralization. This design inherently offers a fundamental layer of privacy while reducing the costs associated with massive data storage. FL traditionally achieves this by using a user-server architecture, where users train local models and share updates with a central server that aggregates them to build a global model [7], [8]. In contrast, decentralized FL [4], [9], [10] eliminates the need for a central server by enabling users to communicate directly and collaboratively train machine learning models.

Probabilistic graphical modeling is a branch of machine learning that uses probability distributions to describe the world, make predictions, and support decision-making under uncertainty. Underlying this modeling framework is an elegant body of theory that bridges two mathematical traditions: probability and graph theory. This framework provides compact yet expressive representations of joint probability distributions, yielding powerful generative models for probabilistic reasoning. This tutorial provides a concise introduction to the formalisms, methods, and applications of this modeling framework. After a review of basic probability and graph theory, we explore three dominant themes: (1) the representation of multivariate distributions in the intuitive visual language of graphs, (2) algorithms for learning model parameters and graphical structures from data, and (3) algorithms for inference, both exact and approximate.

This PhD thesis presents a distributional view of optimization in place of a worst-case perspective. We motivate this view with an investigation of the failure point of classical optimization. Subsequently we consider the optimization of a randomly drawn objective function. This is the setting of Bayesian Optimization. After a review of Bayesian optimization we outline how such a distributional view may explain predictable progress of optimization in high dimension. It further turns out that this distributional view provides insights into optimal step size control of gradient descent. To enable these results, we develop mathematical tools to deal with random input to random functions and a characterization of non-stationary isotropic covariance kernels. Finally, we outline how assumptions about the data, specifically exchangability, can lead to random objective functions in machine learning and analyze their landscape.