We study the problem of identifying change points in high-dimensional generalized linear models, and propose an approach based on sample-weighted empirical risk minimization. Our method, Weighted ERM, encodes priors on the change points via weights assigned to each sample, to obtain weighted versions of standard estimators such as M-estimators and maximum-likelihood estimators. Under mild assumptions on the data, we obtain a precise asymptotic characterization of the performance of our method for general Gaussian designs, in the high-dimensional limit where the number of samples and covariate dimension grow proportionally. We show how this characterization can be used to efficiently construct a posterior distribution over change points. Numerical experiments on both simulated and real data illustrate the efficacy of Weighted ERM compared to existing approaches, demonstrating that sample weights constructed with weakly informative priors can yield accurate change point estimators. Our method is implemented as an open-source package, weightederm, available in Python and R.

Sequential experimental design under expensive, gradient-free objectives is a central challenge in computational statistics: evaluation budgets are tightly constrained and information must be extracted efficiently from each observation. We propose \textbf{ALMAB-DC}, a GP-based sequential design framework combining active learning, multi-armed bandits (MAB), and distributed asynchronous computing for expensive black-box experimentation. A Gaussian process surrogate with uncertainty-aware acquisition identifies informative query points; a UCB or Thompson-sampling bandit controller allocates evaluations across parallel workers; and an asynchronous scheduler handles heterogeneous runtimes. We present cumulative regret bounds for the bandit components and characterize parallel scalability via Amdahl's Law. We validate ALMAB-DC on five benchmarks. On the two statistical experimental-design tasks, ALMAB-DC achieves lower simple regret than Equal Spacing, Random, and D-optimal designs in dose--response optimization, and in adaptive spatial field estimation matches the Greedy Max-Variance benchmark while outperforming Latin Hypercube Sampling; at $K=4$ the distributed setting reaches target performance in one-quarter of sequential wall-clock rounds. On three ML/engineering tasks (CIFAR-10 HPO, CFD drag minimization, MuJoCo RL), ALMAB-DC achieves 93.4\% CIFAR-10 accuracy (outperforming BOHB by 1.7\,pp and Optuna by 1.1\,pp), reduces airfoil drag to $C_D = 0.059$ (36.9\% below Grid Search), and improves RL return by 50\% over Grid Search. All advantages over non-ALMAB baselines are statistically significant under Bonferroni-corrected Mann--Whitney $U$ tests. Distributed execution achieves $7.5\times$ speedup at $K = 16$ agents, consistent with Amdahl's Law.

Gaussian processes (GPs) offer appealing properties but are costly to train at scale. Sparse variational GP (SVGP) approximations reduce cost yet still rely on Cholesky decompositions of kernel matrices, ill-suited to low-precision, massively parallel hardware. While one can construct valid variational bounds that rely only on matrix multiplications (matmuls) via an auxiliary matrix parameter, optimising them with off-the-shelf first-order methods is challenging. We make the inverse-free approach practical by proposing a better-conditioned bound and deriving a matmul-only natural-gradient update for the auxiliary parameter, markedly improving stability and convergence. We further provide simple heuristics, such as step-size schedules and stopping criteria, that make the overall optimisation routine fit seamlessly into existing workflows. Across regression and classification benchmarks, we demonstrate that our method 1) serves as a drop-in replacement in SVGP-based models (e.g., deep GPs), 2) recovers similar performance to traditional methods, and 3) can be faster than baselines when well tuned.

We study the problem of routing queries to large language models (LLMs) under cost, GPU resources, and concurrency constraints. Prior per-query routing methods often fail to control batch-level cost, especially under non-uniform or adversarial batching. To address this, we propose a batch-level, resource-aware routing framework that jointly optimizes model assignment for each batch while respecting cost and model capacity limits. We further introduce a robust variant that accounts for uncertainty in predicted LLM performance, along with an offline instance allocation procedure that balances quality and throughput across multiple models. Experiments on two multi-task LLM benchmarks show that robustness improves accuracy by 1-14% over non-robust counterparts (depending on the performance estimator), batch-level routing outperforms per-query methods by up to 24% under adversarial batching, and optimized instance allocation yields additional gains of up to 3% compared to a non-optimized allocation, all while strictly controlling cost and GPU resource constraints.

Among the different possible strategies for evaluating the reliability of individual predictions of classifiers, robustness quantification stands out as a method that evaluates how much uncertainty a classifier could cope with before changing its prediction. However, its applicability is more limited than some of its alternatives, since it requires the use of generative models and restricts the analyses either to specific model architectures or discrete features. In this work, we propose a new robustness metric applicable to any probabilistic discriminative classifier and any type of features. We demonstrate that this new metric is capable of distinguishing between reliable and unreliable predictions, and use this observation to develop new strategies for dynamic classifier selection.

We study forward and inverse problems for time-dependent probability measures in Bayes--Hilbert spaces. On the forward side, we show that each sufficiently regular Bayes--Hilbert path admits a canonical dynamical realization: a weighted Neumann problem transforms the log-density variation into the unique gradient velocity field of minimum kinetic energy. This construction induces a transport form on Bayes--Hilbert tangent directions, which measures the dynamical cost of realizing prescribed motions, and yields a flow-matching interpretation in which the canonical velocity field is the minimum-energy execution of the prescribed path. On the inverse side, we formulate reconstruction directly on Bayes--Hilbert path space from time-dependent indirect observations. The resulting variational problem combines a data-misfit term with the transport action induced by the forward geometry. In our infinite-dimensional setting, however, this transport geometry alone does not provide sufficient compactness, so we add explicit temporal and spatial regularization to close the theory. The linearized observation operator induces a complementary observability form, which quantifies how strongly tangent directions are seen through the data. Under explicit Sobolev regularity and observability assumptions, we prove existence of minimizers, derive first-variation formulas, establish local stability of the observation map, and deduce recovery of the evolving law, its score, and its canonical velocity field under the strong topologies furnished by the compactness theory.

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Motivated by the principle of satisficing in decision-making, we study satisficing regret guarantees for nonstationary $K$-armed bandits. We show that in the general realizable, piecewise-stationary setting with $L$ stationary segments, the optimal regret is $Θ(L\log T)$ as long as $L\geq 2$. This stands in sharp contrast to the case of $L=1$ (i.e., the stationary setting), where a $T$-independent $Θ(1)$ satisficing regret is achievable under realizability. In other words, the optimal regret has to scale with $T$ even if just a little nonstationarity presents. A key ingredient in our analysis is a novel Fano-based framework tailored to nonstationary bandits via a \emph{post-interaction reference} construction. This framework strictly extends the classical Fano method for passive estimation as well as recent interactive Fano techniques for stationary bandits. As a complement, we also discuss a special regime in which constant satisficing regret is again possible.

Random sample consensus (RANSAC), which is based on a repetitive sampling from a given dataset, is one of the most popular robust estimation methods. In this study, an energy-based model (EBM) for robust estimation that has a similar scheme to RANSAC, energy-based RANSAC (EB-RANSAC), is proposed. EB-RANSAC is applicable to a wide range of estimation problems similar to RANSAC. However, unlike RANSAC, EB-RANSAC does not require a troublesome sampling procedure and has only one hyperparameter. The effectiveness of EB-RANSAC is numerically demonstrated in two applications: a linear regression and maximum likelihood estimation.

Practitioners monitoring deployed probabilistic models face a fundamental trap: any fixed-sample test applied repeatedly over an unbounded stream will eventually raise a false alarm, even when the model remains perfectly stable. Existing methods typically lack formal error guarantees, conflate alarm time with changepoint location, and monitor indirect signals that do not fully characterize calibration. We present PITMonitor, an anytime-valid calibration-specific monitor that detects distributional shifts in probability integral transforms via a mixture e-process, providing Type I error control over an unbounded monitoring horizon as well as Bayesian changepoint estimation. On river's FriedmanDrift benchmark, PITMonitor achieves detection rates competitive with the strongest baselines across all three scenarios, although detection delay is substantially longer under local drift.