Papers

Large-scale streaming time-series regression requires methods that can detect structural changes while accounting for serially correlated errors and quantifying uncertainty about the current regime. We propose a streaming variational Bayes method for linear regression with autoregressive errors that combines online changepoint detection with sequential posterior inference. The proposed method processes observations in chronological mini-batches and uses a finite-mixture variational approximation to represent separate retention and reset configurations for the regression coefficients and innovation variance, while the autoregressive coefficients are shared across regimes and learned sequentially. This construction yields block-specific changepoint probabilities and posterior uncertainty summaries. Closed-form variational updates and mixture pruning enable scalable sequential inference without repeated full-data refits. In simulations, the proposed method maintains low empirical false-alarm rates under stable regimes, with posterior coverage improving as the sample size increases. Under repeated structural changes, it provides accurate type-specific changepoint detection, small changepoint location errors, and short detection delays relative to frequentist sequential monitoring procedures, while posterior coverage approaches nominal levels after an initial adaptation period. An application to high-frequency Bitcoin volatility data illustrates distinct adaptation of the regression and innovation-variance components while accounting for residual autoregressive dependence.

In off-policy evaluation, merging decision-time histories that matter differently for a specified policy value or comparison can make that evaluation unidentified, even with observed actions and outcomes and known behavior and target policies. We characterize which distinctions must be preserved: identification holds if and only if the action-specific evaluation weights are constant within each released record, and the coarsest exact release groups histories by these weights. For normalized outcomes, the largest sharp width induced by the release equals a behavior-weighted within-record radius of these weights. The same radius becomes a release-design objective when each record may be refined into at most $m$ categories. The optimum has an exact $m$-center characterization. When behavior does not vary within a released record, we give a finite-data repair algorithm whose maximum evaluation-weight radius is at most twice the finite-data optimum. For a fixed action-outcome distribution within a released record, a distinct sharp-identification problem remains. Under the same condition, the action-specific outcome distributions are identified, and optimizing over their couplings gives the sharp interval. We construct an AIPW envelope containing this sharp interval; it matches the interval for all such outcome distributions exactly when the extreme within-record action-coefficient vectors take at most two values in each action coordinate. In 24 KuaiRec tasks, the repair algorithm yields a 93% median reduction in mean pairwise sharp width at $m=64$ relative to the unrepaired release.

Verifier-guided inference-time scaling uses additional computation to score intermediate states and steer generation toward better outputs. However, imperfect intermediate verifiers can distort sampling, and repeated refinement alone does not ensure recovery of the desired reward-tilted distribution. We introduce Continuous-State Verifier-Guided Backtracking (CS-VGB), an inference-time scaling method for sampling from reward-tilted distributions with continuous generative models through repeated denoising and renoising. With correctly paired denoising and renoising transitions, the stationary distribution of CS-VGB at the clean checkpoint equals the desired reward-tilted target, even when intermediate verifiers are inaccurate. Under stated regularity conditions, CS-VGB converges exponentially to the target despite verifier error, and the expected number of updates needed to reach a clean sample grows only linearly with the number of checkpoints. In analytically tractable settings, we empirically demonstrate that CS-VGB recovers the desired reward-tilted distribution despite verifier error, whereas the compared verifier-based sampling methods fail to recover the target under the same verifier errors. We also instantiate the framework with diffusion models and one-step stochastic posterior maps. Across prompt-guided ImageNet generation, facial-attribute generation on CelebA, and multi-robot planning, recurrent CS-VGB search improves reward and task success as inference budgets grow, with image-generation rewards continuing beyond the observed plateaus of denoising-only baselines.

Detection of geometry in random graphs and matrices has been extensively studied in recent years. For testing a dense random geometric graph on $n$ vertices with latent points in dimension $d$ against an Erdős–Rényi graph, the detection threshold $d\asymp n^3$ is well known since Bubeck, Ding, Eldan, and Rácz (2016). We sharpen this result by establishing the optimal asymptotic testing error in the critical regime $d/n^3\to\lambda\in(0,\infty)$. The log-likelihood ratio is shown to be asymptotically normal and dominated by the signed triangle count. Moreover, we consider testing the rank statistics of inner products between latent points against uniformly random ranks. We show that ranks preserve all asymptotic testing information available in the full matrix models, and a cubic statistic based on rank statistics attains the optimal asymptotic error. This then yields an asymptotically optimal test for random kernel matrices with a possibly unknown, strictly monotone kernel. The proofs combine the classical framework of Davies (1985) and Le Cam and Yang (1988) for asymptotic normality under information loss with conditional limit theorems for the models in consideration.

Generalized neural network mixed models (GNMMs) combine neural networks and mixed-effects models to analyze longitudinal and clustered data. Although GNMMs have shown good predictive performance in practice, their statistical properties are not well understood. Therefore, this paper studies several important properties of GNMM and provides theoretical support for its use. First, we show that the neural-network component can approximate an unknown nonlinear fixed-effect function arbitrarily well and establish consistency of the fitted neural- network function for its population target within a given network class. Next, we establish consistency of random-effect estimation under increasing within-subject information and show that the GNMM predictor converges to the true predictor. We then prove consistency of the conditional mean function and show that the excess mean squared prediction error (MSPE) relative to the oracle prediction error converges to zero. We conduct simulation studies to examine nonlinear fixed-effect recovery, random-effect estimation, predictor and conditional mean estimation, and excess prediction error under different numbers of subjects and repeated observations. We also apply GNMM to a longitudinal schizophrenia dataset to predict continuous and binary depression outcomes using smartphone- based behavioral measurements and compare its predictive performance with generalized linear mixed models and conventional artificial neural networks. Both the theoretical and empirical results demonstrate that GNMM provides a flexible framework for modeling nonlinear longitudinal and clustered data. These findings provide a statistical foundation for GNMM prediction and support future methodological developments.

For a fixed conformal score function, standard split conformal prediction calibrates a prediction set using the empirical distribution of the conformal scores, without using available side information about the data. We propose a moment-calibrated approach that uses such information to reduce variability across calibration data sets. Side information involving the covariates, the response, or both is expressed as moment restrictions, which are enforced through empirical likelihood weights on the calibration data points. The resulting weighted empirical distribution of the scores determines the weighted empirical quantile without changing the score function. We establish finite-sample bounds on training-conditional and marginal coverage of the moment-calibrated prediction set. We derive asymptotic distributions for training-conditional coverage and average prediction-set size, show that their asymptotic variances are no larger than the corresponding variances under standard split conformal prediction, and characterize when the reductions are strict. In the semi-supervised setting, we identify an optimal moment function of a given covariate representation, develop implementations using prespecified moment functions or a function learned by cross-fitting, and quantify the effect of the unlabeled sample size. We also extend the method to coverage conditions indexed by a class of functions of the covariates through weighted quantile regression. Numerical studies demonstrate the effectiveness of the proposed methods.

Hoffman constants quantify the distance to the solution set of a polyhedral system in terms of its residual; they control error bounds, geometric conditioning, the convergence rate of first-order iterative algorithms, and the stability of regression estimators to target perturbations. Despite their importance, explicit values of Hoffman constants are rarely available due to their computational complexity. In this paper, we derive explicit bounds on the Hoffman constant for a class of structured polyhedral systems arising in sparse regularization. We show that the constants admit a decomposition into spectral, geometric, and interaction components, which together determine their scaling behavior. This framework explains the gap between worst-case dimension-dependent bounds and the favorable conditioning observed empirically in structured problems. As a primary application, we analyze $\ell_1$-regularized least squares, demonstrating that the effective constants depend on low-dimensional active subspaces rather than the ambient dimension. We then extend to the elastic net and adaptive $\ell_1$-regularized formulations, demonstrating how the underlying optimization geometry is altered by the $\ell_2$ penalty and reweighting scheme. Furthermore, we relate our results to classical statistical assumptions and show that the restricted eigenvalue condition bounds only the primal curvature of the active set, leaving the dual interaction geometry unconstrained and is thus insufficient alone for fast theoretical convergence rates. We further show standard $\ell_\infty$ coherence conditions do not yield dimension-independent Euclidean bounds to close this gap. Our theoretical results show that Hoffman constants admit explicit, interpretable forms in structured regression settings and, in practice, provide actionable tools for post-hoc feature pruning and a priori optimal hyperparameter selection.

In observational studies, the overlap assumption, also called positivity, is frequently strained in practice. Limited overlap destabilizes widely used estimators such as inverse propensity weighting (IPW), whose variance depends on density ratios that explode as propensity scores approach zero or one. To address this challenge, we propose the Stable Transport Estimator (STE), an optimal transport-based approach for estimating average causal effects when overlap holds but strict overlap fails. Unlike IPW, the variance of STE contains no density-ratio factor; it is governed by the transport map itself and stays finite under bounded moments, even when density ratios diverge. By replacing reweighting with a geometry-aware transport map, STE constructs stable counterfactual comparisons without requiring density estimation or propensity score modeling. STE further extends to settings where the overlap condition is violated: when covariate supports overlap only partially, a linear interpolation transport map enables principled extrapolation with explicit bias-variance trade-offs. We establish consistency, asymptotic normality, and a variance characterization that makes explicit the contribution of the estimated transport map to the asymptotic variance. Across synthetic and real datasets, STE demonstrates improved robustness, reduced bias, and markedly more stable variance compared to existing estimators.

Many release rules accept a lot when a statistic built from the sample mean and standard deviation stays within a limit, and the probability that a process passes such a rule can be computed exactly for a broad class of parent distributions. This paper asks how well that probability is itself known once the parent has been estimated. Under a stated reference posterior the answer is an interval, narrow where a lot clearly passes or fails and wide where it is contested. In ninety-eight published content-uniformity lots that position, not the sample size, sets the width: among the forty-eight lots assayed at the same ten units, and so equally informed about the spread, the $95\%$ interval runs from essentially zero width to $0.96$. With the operating point held fixed while test and estimation sample grow together, the interval narrows only slowly, the contraction of the posterior being offset by the steepening of the operating characteristic; a calibrated study at the sample sizes of $1207$ occupational exposure assessments shows the same under a half-plane rule. For a pure-spread rule under a Normal parent the interval has an exact chi-square form in the plug-in value and the two sample sizes, extending to the mean-spread wedge with a measured residual and containing Bergum's lower bound as one endpoint. With the parent's posterior formed from the same published summaries through the evaluator's own likelihood, the qualitative pattern survives but shape moves both endpoints and width: on the same lots a strong right skew lowers the pessimistic endpoint by up to a fifth and widens the interval by up to $0.22$. At the content-uniformity operating point studied, under a Normal parent, the symmetric error bar in standard use puts the lower endpoint $0.21$ too high and returns an upper endpoint above one, even with the full posterior covariance.

Royen's Gaussian Correlation Inequality (GCI) is a fundamental result in statistics and probability, but unfortunately, at least by now, the result is not very well known in the statistical community. In this paper, we demonstrate the potential of GCI in high-dimensional testing problems that involve multivariate Gaussian variables. Leveraging the GCI, we establish sharp Type I error bounds under arbitrary Gaussian covariance structures. We also formulate a conjecture and relate it to the well-known Spherical Cap Covering Conjecture in discrete geometry and Weak Simplex Conjecture in information theory.

The distribution function $F(y)=\Pr(S^2\le y)$ of the sample variance $S^2$ of four independent observations is elementary on its entire support for every polynomial parent density on $[0,1]$ (without loss of generality), and we give it in finite closed form for the uniform, Beta$(2,1)$ and Beta$(2,2)$ parents. The support splits at $y = 1/6$, $2/9$ and $1/4$, with the ceiling at $1/3$, all fixed by geometry: in coordinates aligned with the cube diagonal the event $S^2\le y$ is a ball of radius $\sqrt{3y}$, the cube projects to a rhombic dodecahedron, and these are the levels at which the ball reaches its faces, edges and two kinds of vertices. The divergence theorem reduces every moment of the clipped ball to integrals along circular arcs, so each regime closes in algebraic functions of $\sqrt{y}$ and inverse trigonometric functions. For the uniform parent the only non-obvious constant is $K_g = 12\sqrt2\arctan\sqrt2$, proportional to the mean width of the cuboctahedron; the Beta constants are rational expressions in $\pi$, $\sqrt2$, $\sqrt3$ and $\arctan\sqrt2$, as in the uniform case. At $n = 4$ the normal-theory $\chi^2$ recipe used in acceptance testing misplaces the $99$th percentile of $S^2$ by $50\%$ for the uniform parent. For three observations, polynomial parents also give elementary closed forms (arXiv:2609.25333), but two elementary cases in a row do not guarantee a third, and we make no claim beyond $n = 4$.

The log-rank/Cox hazard-ratio test remains the standard approach for the primary analysis of randomized trials with time-to-event endpoints and is fully efficient under proportional hazards (PH). Two model-free alternatives that have recently gained attention are the difference in restricted mean survival time (D-RMST), a contrast on the time scale, and the more recently proposed ratio of average hazards (RAH), a contrast on the rate scale. Simulation studies suggest that the RAH-based test can outperform both under delayed treatment effects, but its efficiency has not been characterized analytically, and no unified framework explains how censoring and accrual affect the efficiency ordering among these tests. We show that all three statistics share a weighted-log-rank representation and derive their asymptotic relative efficiencies under local alternatives, including the first analytic efficiency results for the RAH-based test. Geometrically, each test defines a direction in a function space and the anticipated treatment effect defines a signal direction. A test's efficiency relative to the oracle test equals the squared cosine of the angle between these directions, so the asymptotic relative efficiency of any two tests is a ratio of squared cosines. Because censoring and accrual enter through an information weight, the framework shows how design choices can alter, and even reverse, the efficiency ordering. We illustrate the framework using the CheckMate 057 immunotherapy trial and corroborate the theoretical results through simulations spanning proportional- and non-proportional-hazards settings.

Decentralized learning must balance collaboration with personalization across heterogeneous agents. This paper studies when cooperation can support statistically coherent groups of personalized models. We show that data-topology compatibility enables robust orbit-wise personalization: when local objectives and communication topology have (approximately) compatible automorphisms, agents within an orbit share (approximately) equal limiting distributions, while different orbits remain distinct without explicit personalization. This creates a new intermediate regime between global consensus and independent local learning. Under exact data-topology compatibility, as a reference system, we decompose the stochastic learning dynamics into orbit-level and transverse components, derive a necessary and sufficient stability criterion for distributional synchronization, and characterize the orbit-structured stationary law. Modelling an approximate data-topology compatible system as an $\varepsilon$-perturbed reference system, we prove the introduced errors have uniform-in-time and stationary $O(\varepsilon)$ bounds in 2-Wasserstein distance. We also prove sufficient conditions for lower stationary average excess risk than both independent local training and the best single shared parameter. Experiments on synthetic data, MNIST, and CIFAR-10 are in full agreement with the theory. The code is available at https://github.com/Veronicaaa1/orbit-personalization.

Data and the governing partial differential equations (PDEs) of continuous-time dynamical systems provide rich structure for statistical learning. A central challenge is how to integrate data with PDE constraints in a principled way to improve generalization. In this paper, we characterize the statistical estimation and generalization properties of learning solutions to the heat equation with a noisy source function from finite, randomly sampled data. We first derive a novel variational formulation, which we characterize as the minimizer of loss function for an energy regularized and ellipticity debiased Sobolev regression. By formulating the learning task as a supervised problem over space-time domains under physically meaningful norms, our approach goes beyond the traditional supervised learning framework by effectively leveraging auxiliary data—samples of the source function of the heat equation—to design a physics-informed energy regularization. Our analysis reveals that learning in linear parabolic PDEs exhibits intrinsic anisotropy between spatial and temporal regularity, in sharp contrast to the static elliptic problems, leading to fundamentally different estimation and generalization behaviors. Specifically, we derive non-asymptotically rate-optimal estimation errors, as well as generalization error, which explicitly capture the interplay among temporal sampling, spatial resolution, and solution smoothness. Our numerical experiments demonstrate substantial orders of magnitude of reduction in testing errors against various physics-informed neural network methods on various parabolic and hyperbolic PDEs.

Historically, phase I oncology trials were designed with the focus to find the highest tolerable dose. However, given the FDA's acknowledgment that the highest tolerable dose might not be the dose which is optimal biologically, there is an increased emphasis the development of designs that explore the dose-toxicity and dose-efficacy relationship. Backfill designs have emerged as a popular response to address this need by allocating participants to doses deemed safe while awaiting participants outcomes. Previous designs have explored how to assign participants to doses in backfill designs in a rigorous manner while providing simplicity and performance (a class of designs known as model-assisted) for single agents. Still, a research gap exists in the lack of model-assisted backfill designs for drug combinations. Frequently, the combinations two of cancer agents are explored in phase I trials, with the goal of identifying the highest tolerable combination. This paper incorporates and extends methodology based on previous model-assisted backfill designs to provide clinicians with a simple-to-use backfill design for phase I drug combination trials.

In many complex systems, such as river networks and financial markets, extreme events propagate from causes to their effects, and the largest observations carry the most information about the underlying causal structure. Existing methods for causal discovery in extremes, however, are tailored to specific mechanisms, such as linear or max-linear models. This work develops causal discovery for heavy-tailed homogeneous structural causal models, a flexible class that contains linear, max-linear and norm-type mechanisms, which may differ from node to node. In these models, the causal structure is encoded by ancestral impulse responses, which measure how a shock at one node is transmitted to its descendants. We propose the extremal minimum ratio estimator of these responses, which uses only observations in which the potential cause is extreme. The estimator is consistent under regular variation alone, and we derive its exact rates of convergence and limiting distributions, which depend on both the causal relation and the type of mechanism. Building on these rates, we construct consistent estimators of the causal order and of the full set of ancestral relations, using a threshold that adapts to the data and requires no knowledge of the tail index. The method is illustrated on simulated data and on river discharges in the upper Danube basin.

Mixture-of-Experts (MoE) models combine specialized experts through an input-dependent routing mechanism, and their sparse variants underpin many modern large-scale systems. Yet the statistical cost of adaptive routing remains only partially understood. We study the estimation error of least-squares MoE estimators when both the experts and the gating network are Lipschitz in their parameters. We represent each MoE as a gate–expert pair in a Gated Hilbert Space, whose norm $\|\cdot\|_\Delta$ separates the contributions of routing and expert discrepancies. Using its empirical representation, we derive an oracle inequality with a fast rate of order $\tilde{\mathcal O}\big((Kd_{\mathrm{pr},e}+d_{\mathrm{pr},g})/n\big)$ for dense MoEs with $K$ experts. For sparse Top-$k$ and Top-$p$ routing, the selection map is discontinuous in the gating parameters. We handle this by partitioning the gating class according to the selection patterns it induces on the sample. The resulting bounds match the dense rate up to an additive routing cost governed by the Natarajan dimension of the selector. We show that such a routing-complexity condition cannot be dropped: Lipschitz continuity in the parameters alone does not suffice. For linear softmax gating, the routing cost is of the same order as the gating term. Finally, for linear experts, we establish a matching minimax lower bound of order $Kd_{\mathrm{pr},e}/n$, showing that the rates are optimal up to logarithmic factors.

This dissertation has two parts. In the first part we theoretically develop a framework that extends the optimal transport barycenter problem from independent data with observed covariates to processes whose relevant covariate is their own history. Given a stationary stochastic process, our framework shows there exists an invertible transport map that extracts from it an iid component whose distribution is the barycenter of the conditional distributions of the input process on its own past. This extracted iid sequence thus captures the innovation or noise component of the process that is not explained by the process's own past. In the second part of this thesis we implement an effective algorithm to solve this problem and test it against synthetic data generated with some well-known models in time series analysis for which the solution is known in closed-form. We then show how this method can be applied to build a predictive sampler for such processes, and assess the accuracy of this predictive sampler both with the aforementioned synthetic data and with real-world time series such as the S&P 500 and Bitcoin 4-hour returns, and the daily records of the North Atlantic Oscillation index from the NOAA Physical Sciences Laboratory. Finally, we demonstrate an application of the sampler to path simulation with a well-known time series model.

We present DisCo algebra—a compositional framework for joint probability built from a symmetric cooperad (disintegration) and a symmetric operad (combination) on the bare family $\mathcal{P}_n=\mathrm{Prob}([0,1]^n)$. No probability integral transform, no external summary functions, no enrichment of objects with conditional kernels. The disintegration side uses block-wise joint CDFs as intrinsic, measure-determined 1D summaries, yielding a lossy compression. The combination side reads the same summaries and reconstructs via regular conditional measures, yielding a lossless embedding. We prove that combination followed by disintegration is the identity on admissible inputs, but disintegration followed by combination is not—the information loss is exactly the conditional KL divergence between the true conditional distribution and the conditionally independent product. This asymmetry reveals a hard limit on how much cross-block dependence can be captured by scalar block summaries.

Nonlinear response models remain ubiquitous across disciplines with recruitment curves describing muscle response to neural stimulation. Conventional acquisition methods typically rely on static uniform sampling, requiring many stimuli, while adaptive threshold-hunting designs such as ML-PEST forfeit accurate characterization of the overall curve. We present a Bayesian adaptive design that uses posterior uncertainty over curve parameters to propose stimuli that maximize information gain across the full recruitment curve. We additionally implement a focused acquisition method that can target arbitrary subset of curve parameters, which we use to evaluate and interpret our design. In simulations, our design outperforms uniform sampling in recovering threshold while matching ML-PEST, and outperforms ML-PEST in predictive curve accuracy while matching uniform. It likewise matches our threshold-focused acquisition, suggesting our design doesn't trade off threshold estimation for recovering the curve. We further show data collected using our design yields greater power when detecting a change in threshold in intervention studies. Our design proposes the next stimulus within 5 seconds, making it feasible for transcranial magnetic stimulation (TMS) experiments. Finally, we validate our design in TMS experiments and provide a library for Python, called onMEP, for online acquisition of neural recruitment curves.

Prior-data fitted networks (PFNs) are transformers pretrained on simulated datasets to approximate Bayesian posterior predictive distributions. Standard PFN theory assumes a separable task prior, under which the feature distribution and the mechanism generating labels from features are independent. We show that common PFN priors are non-separable, even in simple settings. Consequently, standard pretraining targets a predictive distribution based on a task posterior updated using both the labeled context and the query features. We characterize its difference from the predictive based on the context posterior alone and show that this difference vanishes under posterior concentration. Under misspecification (i.e., when the true joint distribution lies outside the prior's support), however, prior non-separability can favor better feature fit at the expense of conditional label fit. We illustrate the consequences for feature attribution, Bayesian optimization, and martingale checks of Bayesian behavior. The same dependence also enables PFNs to learn from additional unlabeled observations. We demonstrate this with SemiTabICL, a PFN explicitly pretrained to use these observations, which improves accuracy over a matched supervised baseline. Our findings highlight the need for explicit rules on unlabeled data use in PFN evaluation and establish the dependence between feature and label distributions as a consequential prior design choice.

The average-reward setting for reinforcement learning is challenging because its Bellman operator is known to contract in span only when the underlying Markov chain is mixing. Whereas existing work typically assumes a contraction property, e.g., through environment mixing, we consider the setting where we are given a reward-agnostic $m$-step mixing policy, and we control the contraction and exploration properties of the learned policy by regularizing toward the mixing policy. We provide finite-time analysis of $Q$-learning algorithms that can be instantiated with multiple choices of regularization, with guarantees measured with respect to the regularized fixed point. Our framework exposes novel regularizer-dependent objects that control contraction, exploration, and operator bias. In the one-step setting, our rates match the best known rates for $Q$-iteration and synchronous $Q$-learning, and for $m$-step mixing we derive new rates. We also study $Q$-planning variants, and show that planning acts as time-localized learning, where the planning horizon $H$ trades off the bias from the boundary value against the sample complexity. Finally, we present numerical studies validating the analysis: (i) knowledge of a strong mixing policy improves convergence and exploration, and its advantage increases with bottleneck severity and, (ii) our theory predicts the convergence and bias rankings of regularizers from the $\alpha$-divergence family.

How do language models generalize from their training data? This is a central challenge for alignment: models reliably learn their training distribution given enough samples, but we want models that behave well when deployed in new contexts. We study out-of-distribution (OOD) generalization of propensities. Our central experiment uses a range of elicitation techniques – system prompting, few-shot learning, SFT on reference answers, and GRPO – to increase a target propensity in a model, then measures how it spills over onto others across the resulting cross-elicitation matrices. We find that spillover is highly correlated between models when the same elicitation technique is used, but our SFT and GRPO runs induce different spillover profiles. Elicitation of benign traits can sometimes generalize towards undesired traits, for example a model trained to claim that it is sentient often becomes more power-seeking. We further find that spillover partially resembles trait correlations found in humans and identify three clusters of traits that account for about half of the variance using exploratory factor analysis (EFA). Across many elicitation runs, we observe that models change in characteristic ways that don't depend on the targeted trait, a phenomenon we refer to as drift. Drift moves Qwen3.5-9B towards its base model. When investigating if LLMs are able to predict spillover, we find that Claude Opus 5.5 predicts spillover slightly better than the models themselves, but worse than data-driven approaches using alternative elicitation methods or models. Overall, no single dominant predictor emerges, and generalization remains hard to predict. Code and data are available at https://github.com/nielsrolf/propensity-spillover.

Clustering is typically performed using only object features, although additional information about relationships between objects may be available and can be incorporated through constraints. Among these, pairwise constraints require two objects to belong to the same cluster or to different clusters. Several extensions of the k-means algorithm accommodate such constraints, but they sometimes fail to find a feasible assignment or incur high computational cost. Motivated by these limitations, we propose an algebraic approach to k-means clustering with pairwise constraints. The algorithm simplifies the constraints using Gröbner bases before optimization, improving the efficiency of cluster assignment. It can also detect whether the constraint set has a feasible assignment before optimization. Comparative experiments with existing algorithms showed that the proposed algorithm achieved comparable or better clustering quality at a lower computational cost, particularly when the numbers of constraints and clusters were small.

Language models are increasingly used to create synthetic survey samples, also called silicon samples. Decision models are a new class of language models that return a probability for each point of a rating scale instead of text. We ask whether these models, or the newest generative LLMs, can stand in for human respondents on a psychometric survey. We test fourteen decision models from eleven providers and 47 generative LLMs on an open Lithuanian organisational-psychology survey (n=263, 68 items), with 100 real respondent profiles, the Psychometric Similarity Score (PSS) and statistical baselines. The best generative model, MiniMax M3, reaches PSS 0.813. This is level with a Gaussian copula fit only on other respondents (0.824) and below a copula fit in sample (0.927). A second sample of 100 real people scores below the best models, so at this size PSS cannot rank them against real respondents. In 5 of 10 product lines the newest generative release scores below an earlier release of the same line beyond resampling noise, and none gains beyond it. With the default rounded readout, 13 of 14 decision models score below the generative reference gpt-5.4-mini. Of the 47 generative models, 33 reproduce the pattern of item correlations better than any decision model. Averaged over respondents, the probability vectors are much closer to the human item marginals than rounded answers. They also rank respondents about as well as a profile regression fit on 163 real people. As forecasts of each person's own answers, however, every decision model is worse than the answer frequencies of other respondents, mainly because its average vector differs from them. The profile regression improves on these frequencies by only 1.0%, so the profile fields say little about how a person answers. Synthetic respondents built on such profiles should therefore aim at sample-level fidelity.

Optimal transport (OT) enables multivariate conformal prediction (CP) to construct flexible prediction sets that reflect the underlying complex distributional geometry while retaining distribution-free coverage guarantees. Existing OT-based methods typically rely on a fixed Euclidean transport cost, which can be suboptimal in terms of the volume of prediction sets. We propose Minimum-Volume OTCP, a framework that learns a Mahalanobis ground cost to directly minimize prediction-region volume over a class of positive-definite metrics. Using a metric Brenier representation, we derive a volume-based objective that depends explicitly on the Mahalanobis cost matrix and optimize it jointly with the transport map. We establish finite-sample marginal coverage of the output prediction sets and optimality of volume metrics. We further develop an individualized extension that learns covariate-dependent transport metrics, adapting the shape and orientation of prediction sets to heterogeneous conditional distributions. For this extension, we also show the asymptotic conditional coverage of our method. Simulations and real-data experiments demonstrate substantial reductions in prediction-set volume.

We study prediction with expert advice over $T$ rounds with $K$ experts under heavy-tailed losses whose $(1+\epsilon)$-moment is bounded by $\theta>0$ for some $\epsilon\in(0,1]$. In this setting, existing algorithms designed for the case $\epsilon=1$ can be suboptimal when $\epsilon<1$, suffering an additional polynomial dependence on $K$. We characterize the minimax pseudo-regret rate as $\Theta((\theta T)^{\frac{1}{1+\epsilon}}(\log K)^{\frac{\epsilon}{1+\epsilon}})$ and establish gap-dependent lower bounds in a self-bounded environment. To attain this minimax rate without prior knowledge of either $\epsilon$ or $\theta$, we propose Adaptive Heavy-Tailed FTRL, which uses robust data-dependent scale adaptation together with truncation. We further develop Adaptive Heavy-Tailed OMD, which likewise requires neither $\epsilon$ nor $\theta$ and achieves near-optimal regret guarantees in both adversarial and self-bounded environments. Finally, when $\epsilon$ and $\theta$ are known, an FTRL algorithm with Shannon-entropy regularization achieves optimal regret guarantees in both environments.

Disagreements between randomized trials that address the same causal question pose challenges for the interpretation and synthesis of evidence. We sketch a causal framework for comparing the results of randomized trials that explicitly accommodates the possibility of trial engagement effects. Using counterfactual outcomes defined under joint interventions on treatment assignment and trial-related actions, we compare trial-native treatment effects with the effects transported from one trial to the population of another in a common target population. We show that standard conditions for transporting treatment effects across trial populations are not sufficient to guarantee agreement between transported and trial-native effects. Agreement additionally requires conditions governing how trial-related actions affect outcome across studies - for example, absence of trial engagement effects, equivalence of such effects across trials, or lack of interaction between trial engagement and treatment assignment. Our framework clarifies potential sources of disagreement across trials and extends existing approaches to study comparison to settings in which trial engagement effects may be present.

We introduce stochastic physics-informed neural networks (SPINNs) for stochastic boundary-value problems (SBVPs) with random operators. The method enforces physics through a structural probabilistic coupling: a common Gaussian stochastic germ drives both the SBVP random operator and a manifold-based stochastic neural architecture. The stochastic neural network is non-feedforward and intrinsically random. A latent Gaussian field and an inhomogeneous Poisson point process on a compact, boundaryless, multiply connected manifold generate random neuron locations, geodesically local sparse connectivity, and a sparse random weight matrix, all governed by a low-dimensional hyperparameter. For deterministic inputs, the network output is random and can represent non-Gaussian random operators. Training is performed in observation space: SBVP simulations produce random observables, while the SNN defines a predictive conditional probability density function. The supervised objective combines data fidelity, through negative log-likelihood, with a cross-entropy alignment term relative to the SBVP-induced conditional distribution. The resulting target is a convex mixture of observation-induced and SBVP-induced distributions, with a dimensionless parameter controlling robustness to model–data mismatch. The shared stochastic germ yields common-random-numbers Monte Carlo estimators and reduced-variance gradients. The method uses only evaluations of the SBVP solution mapping, without differentiating or modifying it, and avoids PDE-residual or boundary-penalty losses. A stochastic elliptic problem on a periodic cylindrical surface illustrates the approach in SBVP-consistent and SBVP-misspecified regimes. A generalized-posterior formulation is also outlined for hyperparameter inference and posterior averaging without per-query reoptimization.

Predictively-oriented (PrO) filtering for state-space models was proposed in Shen et al. [2026] as a promising route to avoiding over-confident inferences in settings where either the dynamical model, the measurement model, or both, could be misspecified. Our focus is on nonlinear state-space models, where the local linearisation used to construct the PrO filter in Shen et al. [2026] deteriorates as nonlinearities enter either the dynamical model or the measurement model. Our proposed solution is based on unscented transforms, an established tool from classical filtering which provides a more accurate mechanism to propagate Gaussian uncertainty through a nonlinear functional, and which includes the cubature rule as a special case. We introduce two variants: replacing the linearisation in the predict step alone, which we call UKF-PrO, has a computational cost comparable to the existing PrO filter; replacing it in the update step as well, UKF-PrO+, requires a substantially more expensive joint optimisation. Performance is empirically assessed on the Lorenz96 model under conditions of increasing difficulty, in which the state-space model is systematically misspecified; we find that UKF-PrO with the parameters of the cubature Kalman filter offers consistent improvements, which become substantial under strong nonlinearity, whereas the default unscented parameters are unreliable, and that the full update-step extension with the same parameters does not justify its additional cost.