Model comparison and calibrated uncertainty quantification often require integrating over parameters, but scalable inference can be challenging for complex, multimodal targets. Nested Sampling is a robust alternative to standard MCMC, yet its typically sequential structure and hard constraints make efficient accelerator implementations difficult. This paper introduces Nested Slice Sampling (NSS), a GPU-friendly, vectorized formulation of Nested Sampling that uses Hit-and-Run Slice Sampling for constrained updates. A tuning analysis yields a simple near-optimal rule for setting the slice width, improving high-dimensional behavior and making per-step compute more predictable for parallel execution. Experiments on challenging synthetic targets, high dimensional Bayesian inference, and Gaussian process hyperparameter marginalization show that NSS maintains accurate evidence estimates and high-quality posterior samples, and is particularly robust on difficult multimodal problems where current state-of-the-art methods such as tempered SMC baselines can struggle. An open-source implementation is released to facilitate adoption and reproducibility.

Large-scale AI evaluation increasingly relies on aggregating binary judgments from $K$ annotators, including LLMs used as judges. Most classical methods, e.g., Dawid-Skene or (weighted) majority voting, assume annotators are conditionally independent given the true label $Y\in\{0,1\}$, an assumption often violated by LLM judges due to shared data, architectures, prompts, and failure modes. Ignoring such dependencies can yield miscalibrated posteriors and even confidently incorrect predictions. We study label aggregation through a hierarchy of dependence-aware models based on Ising graphical models and latent factors. For class-dependent Ising models, the Bayes log-odds is generally quadratic in votes; for class-independent couplings, it reduces to a linear weighted vote with correlation-adjusted parameters. We present finite-$K$ examples showing that methods based on conditional independence can flip the Bayes label despite matching per-annotator marginals. We prove separation results demonstrating that these methods remain strictly suboptimal as the number of judges grows, incurring nonvanishing excess risk under latent factors. Finally, we evaluate the proposed method on three real-world datasets, demonstrating improved performance over the classical baselines.

Generalized Bayesian Inference (GBI) tempers a loss with a temperature $β>0$ to mitigate overconfidence and improve robustness under model misspecification, but existing GBI methods typically rely on costly MCMC or SDE-based samplers and must be re-run for each new dataset and each $β$ value. We give the first fully amortized variational approximation to the tempered posterior family $p_β(θ\mid x) \propto π(θ)\,p(x \mid θ)^β$ by training a single $(x,β)$-conditioned neural posterior estimator $q_ϕ(θ\mid x,β)$ that enables sampling in a single forward pass, without simulator calls or inference-time MCMC. We introduce two complementary training routes: (i) synthesize off-manifold samples $(θ,x) \sim π(θ)\,p(x \mid θ)^β$ and (ii) reweight a fixed base dataset $π(θ)\,p(x \mid θ)$ using self-normalized importance sampling (SNIS). We show that the SNIS-weighted objective provides a consistent forward-KL fit to the tempered posterior with finite weight variance. Across four standard simulation-based inference (SBI) benchmarks, including the chaotic Lorenz-96 system, our $β$-amortized estimator achieves competitive posterior approximations in standard two-sample metrics, matching non-amortized MCMC-based power-posterior samplers over a wide range of temperatures.

Humans learn efficiently from their environment by engaging multiple interacting neural systems that support distinct yet complementary forms of control, including model-based (goal-directed) planning, model-free (habitual) responding, and episodic memory-based learning. Model-based mechanisms compute prospective action values using an internal model of the environment, supporting flexible but computationally costly planning; model-free mechanisms cache value estimates and build heuristics that enable fast, efficient habitual responding; and memory-based mechanisms allow rapid adaptation from individual experience. In this work, we aim to elucidate the computational principles underlying this biological efficiency and translate them into a sampling algorithm for scalable Bayesian inference through effective exploration of the posterior distribution. More specifically, our proposed algorithm comprises three components: a model-based module that uses the target distribution for guided but computationally slow sampling; a model-free module that uses previous samples to learn patterns in the parameter space, enabling fast, reflexive sampling without directly evaluating the expensive target distribution; and an episodic-control module that supports rapid sampling by recalling specific past events (i.e., samples). We show that this approach advances Bayesian methods and facilitates their application to large-scale statistical machine learning problems. In particular, we apply our proposed framework to Bayesian deep learning, with an emphasis on proper and principled uncertainty quantification.

Advances in generative modeling have recently been adapted to tabular data containing discrete and continuous features. However, generating mixed-type features that combine discrete states with an otherwise continuous distribution in a single feature remains challenging. We advance the state-of-the-art in diffusion models for tabular data with a cascaded approach. We first generate a low-resolution version of a tabular data row, that is, the collection of the purely categorical features and a coarse categorical representation of numerical features. Next, this information is leveraged in the high-resolution flow matching model via a novel guided conditional probability path and data-dependent coupling. The low-resolution representation of numerical features explicitly accounts for discrete outcomes, such as missing or inflated values, and therewith enables a more faithful generation of mixed-type features. We formally prove that this cascade tightens the transport cost bound. The results indicate that our model generates significantly more realistic samples and captures distributional details more accurately, for example, the detection score increases by 40%.

Score-based diffusion models have recently been extended to infinite-dimensional function spaces, with uses such as inverse problems arising from partial differential equations. In the Bayesian formulation of inverse problems, the aim is to sample from a posterior distribution over functions obtained by conditioning a prior on noisy observations. While diffusion models provide expressive priors in function space, the theory of conditioning them to sample from the posterior remains open. We address this, assuming that either the prior lies in the Cameron-Martin space, or is absolutely continuous with respect to a Gaussian measure. We prove that the models can be conditioned using an infinite-dimensional extension of Doob's $h$-transform, and that the conditional score decomposes into an unconditional score and a guidance term. As the guidance term is intractable, we propose a simulation-free score matching objective (called Supervised Guidance Training) enabling efficient and stable posterior sampling. We illustrate the theory with numerical examples on Bayesian inverse problems in function spaces. In summary, our work offers the first function-space method for fine-tuning trained diffusion models to accurately sample from a posterior.

We provide a complete theory of optimal universal rates for binary classification in the agnostic setting. This extends the realizable-case theory of Bousquet, Hanneke, Moran, van Handel, and Yehudayoff (2021) by removing the realizability assumption on the distribution. We identify a fundamental tetrachotomy of optimal rates: for every concept class, the optimal universal rate of convergence of the excess error rate is one of $e^{-n}$, $e^{-o(n)}$, $o(n^{-1/2})$, or arbitrarily slow. We further identify simple combinatorial structures which determine which of these categories any given concept class falls into.

Such failure can be caused by distribution shift (also known as dataset shift) between the training and test datasets. For this reason, distribution shift and domain adaptation (a notion comprising techniques for tackling distribution shift) has been a major research topic in machine learning for some time. This paper takes the perspective of Kouw and Loog (2021) and studies the case where feature observations from the test dataset are available for analysis but observations of labels are missing. Under these circumstances, without any assumptions on the nature of the distribution shift between the training and test datasets meaningful prediction of the labels in the test dataset or of their distribution is not feasible. See Kouw and Loog (2021) for a survey of approaches to domain adaptation and their related assumptions. Arguably, covariate shift (also known as population drift) and label shift (also known as prior probability shift or target shift) are the most popular specific distribution shift assumptions, both for their intuiveness as well as their computational manageability. However, exclusive covariate and label shift assumptions have been criticised for being insufficient for common domain adaptation tasks (e.g.

Distributionally robust optimisation (DRO) minimises the worst-case expected loss over an ambiguity set that can capture distributional shifts in out-of-sample environments. While Huber (linear-vacuous) contamination is a classical minimal-assumption model for an $\varepsilon$-fraction of arbitrary perturbations, including it in an ambiguity set can make the worst-case risk infinite and the DRO objective vacuous unless one imposes strong boundedness or support assumptions. We address these challenges by introducing bulk-calibrated credal ambiguity sets: we learn a high-mass bulk set from data while considering contamination inside the bulk and bounding the remaining tail contribution separately. This leads to a closed-form, finite $\mathrm{mean}+\sup$ robust objective and tractable linear or second-order cone programs for common losses and bulk geometries. Through this framework, we highlight and exploit the equivalence between the imprecise probability (IP) notion of upper expectation and the worst-case risk, demonstrating how IP credal sets translate into DRO objectives with interpretable tolerance levels. Experiments on heavy-tailed inventory control, geographically shifted house-price regression, and demographically shifted text classification show competitive robustness-accuracy trade-offs and efficient optimisation times, using Bayesian, frequentist, or empirical reference distributions.

Evaluating large language models (LLMs) on open-ended tasks without ground-truth labels is increasingly done via the LLM-as-a-judge paradigm. A critical but under-modeled issue is that judge LLMs differ substantially in reliability; treating all judges equally can yield biased leaderboards and misleading uncertainty estimates. More data can make evaluation more confidently wrong under misspecified aggregation. We propose a judge-aware ranking framework that extends the Bradley-Terry-Luce model by introducing judge-specific discrimination parameters, jointly estimating latent model quality and judge reliability from pairwise comparisons without reference labels. We establish identifiability up to natural normalizations and prove consistency and asymptotic normality of the maximum likelihood estimator, enabling confidence intervals for score differences and rank comparisons. Across multiple public benchmarks and a newly collected dataset, our method improves agreement with human preferences, achieves higher data efficiency than unweighted baselines, and produces calibrated uncertainty quantification for LLM rankings.