While diffusion models excel at image generation, their growing adoption raises critical concerns around copyright issues and model transparency. Existing attribution methods identify training examples influencing an entire image, but fall short in isolating contributions to specific elements, such as styles or objects, that matter most to stakeholders. To bridge this gap, we introduce \emph{concept-level attribution} via a novel method called \emph{Concept-TRAK}. Concept-TRAK extends influence functions with two key innovations: (1) a reformulated diffusion training loss based on diffusion posterior sampling, enabling robust, sample-specific attribution; and (2) a concept-aware reward function that emphasizes semantic relevance. We evaluate Concept-TRAK on the AbC benchmark, showing substantial improvements over prior methods. Through diverse case studies--ranging from identifying IP-protected and unsafe content to analyzing prompt engineering and compositional learning--we demonstrate how concept-level attribution yields actionable insights for responsible generative AI development and governance.

Publicly releasing the specification of a model with its trained parameters means an adversary can attempt to reconstruct information about the training data via training data reconstruction attacks, a major vulnerability of modern machine learning methods. This paper makes three primary contributions: establishing a mathematical framework to express the problem, characterising the features of the training data that are vulnerable via a maximum mean discrepancy equivalance and outlining a score matching framework for reconstructing data in both Bayesian and non-Bayesian models, the former is a first in the literature.

Accurate uncertainty quantification remains a key challenge for standard LLMs, prompting the adoption of Bayesian and ensemble-based methods. However, such methods typically necessitate computationally expensive sampling, involving multiple forward passes to effectively estimate predictive uncertainty. In this paper, we introduce a novel approach enabling efficient and effective uncertainty estimation in LLMs without sacrificing performance. Specifically, we distill uncertainty-aware teacher models - originally requiring multiple forward passes - into compact student models sharing the same architecture but fine-tuned using Low-Rank Adaptation (LoRA). We compare two distinct distillation strategies: one in which the student employs traditional softmax-based outputs, and another in which the student leverages Dirichlet-distributed outputs to explicitly model epistemic uncertainty via evidential learning. Empirical evaluations on classification datasets demonstrate that such students can achieve comparable or superior predictive and uncertainty quantification performance relative to their teacher models, while critically requiring only a single forward pass. To our knowledge, this is the first demonstration that immediate and robust uncertainty quantification can be achieved in LLMs through evidential distillation.

Given a multivariate function taking deterministic and unc ertain inputs, we consider the problem of estimating a quantile set: a set of deterministic inputs f or which the probability that the output belongs to a specific region remains below a given threshold. To solve this problem in the context of expensive-to-evaluate black-box functions, we propose a Bayesian active learning strategy based on Gaussian process modeling. The strategy is driven by a nov el sampling criterion, which belongs to a broader principle that we refer to as Expected Estimator Modification (EEM). More specifically, the strategy relies on a novel sampling criterion combined w ith a sequential Monte Carlo framework that enables the construction of batch-sequential designs for the efficient estimation of small quantile sets. The performance of the strategy is illustrated on seve ral synthetic examples and an industrial application case involving the ROTOR37 compressor model.

We introduce the microclustering Ewens--Pitman model for random partitions, obtained by scaling the strength parameter of the Ewens--Pitman model linearly with the sample size. The resulting random partition is shown to have the microclustering property, namely: the size of the largest cluster grows sub-linearly with the sample size, while the number of clusters grows linearly. By leveraging the interplay between the Ewens--Pitman random partition with the Pitman--Yor process, we develop efficient variational inference schemes for posterior computation in entity resolution. Our approach achieves a speed-up of three orders of magnitude over existing Bayesian methods for entity resolution, while maintaining competitive empirical performance.

Do larger and more capable language models learn to update their "beliefs" about propositions more consistently with Bayes' theorem when presented with evidence in-context? To test this, we formulate a Bayesian Coherence Coefficient (BCC) metric and generate a dataset with which to measure the BCC. We measure BCC for multiple pre-trained-only language models across five model families, comparing against the number of model parameters, the amount of training data, and model scores on common benchmarks. Our results provide evidence for our hypothesis that larger and more capable pre-trained language models assign credences that are more coherent with Bayes' theorem. These results have important implications for our understanding and governance of LLMs.

The most effective differentially private machine learning algorithms in practice rely on an additional source of purportedly public data. This paradigm is most interesting when the two sources combine to be more than the sum of their parts. However, there are settings such as mean estimation where we have strong lower bounds, showing that when the two data sources have the same distribution, there is no complementary value to combining the two data sources. In this work we extend the known lower bounds for public-private learning to setting where the two data sources exhibit significant distribution shift. Our results apply to both Gaussian mean estimation where the two distributions have different means, and to Gaussian linear regression where the two distributions exhibit parameter shift. We find that when the shift is small (relative to the desired accuracy), either public or private data must be sufficiently abundant to estimate the private parameter. Conversely, when the shift is large, public data provides no benefit.

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.