Papers

We study the mixing time of weighted Dikin walks for sampling from exponential distributions on polytopes and truncated positive-semidefinite (PSD) cones. Our first result gives a general total-variation mixing bound under strong self-concordance, $\bar{\nu}$-symmetry, and mixed-trace regularity on the local metric. The key idea is to control the Metropolis–Hastings acceptance probability on a high-probability region rather than at every point. Applying this framework to the Lee–Sidford, Lewis-weight, and John metrics yields an $\widetilde O(d^2)$ mixing bound for sampling from polytopes, while applying it to a hybrid barrier yields an $\widetilde O(d^4)$ mixing bound for sampling from truncated PSD cones. Our second result establishes stronger $\chi^2$-divergence guarantees and pointwise acceptance control using a new fourth-order bootstrap condition. For a suitably scaled Lee–Sidford metric, this yields an $\widetilde O(d^2)$ mixing bound in $\chi^2$-divergence, improving on the previous $\widetilde O(d^{9/4})$ bound.

We study kernel ridge regression under anisotropic Gaussian data, where the input covariance decays as a power law with exponent $\alpha\geq 0$ for polynomial inner-product kernels. We derive asymptotically sharp expressions for the kernel spectrum and the generalization error in the polynomial high-dimensional regime $n=\Theta(d^\kappa)$, revealing how anisotropy reshapes the learning curves. For weak anisotropy ($0<\alpha<1$), the problem remains effectively high-dimensional and retains some features of the isotropic case, while departing from it in others: the variance still peaks at integer sample complexities $\kappa\in\mathbb{N}$, but these peaks are progressively damped as $\alpha$ grows; meanwhile, for targets strongly aligned with the data's principal directions, the bias drops at fractional sample complexities, decoupling the bias transitions from the interpolation peaks. For strong anisotropy ($\alpha > 1$), the effective dimension of the problem is constant, and the variance stops depending on sample size altogether, plateauing under ridgeless interpolation or vanishing at an explicit rate under fixed ridge penalty. The bias undergoes a sharp transition governed by the target's decay rate: below a threshold, learning is abrupt rather than gradual; above it, the bias decays as a power law that recovers the classical source and capacity rates. We finally specialize these results to single-index targets, showing how the alignment of the index with the data's principal directions determines the effect of anisotropy on learning. Together, our results clarify how the input geometry shapes the kernel features and fundamentally impacts its generalization properties.

We prove that every finite multivariate Gaussian mixture density has only finitely many modes. Our approach combines an algebraic formulation of the ridgeline theory of Ray and Lindsay (2005) with a transcendence-degree argument based on Ax's functional-transcendence theorem to bound the cardinality of the set of critical points. Our techniques extend recent work by Wang (2026), who used Ax's theorem together with real-analytic curve selection to prove finiteness of the critical set of homoscedastic Gaussian mixtures. We introduce the ridgeline correspondence and use it to obtain a finiteness result that applies to arbitrary heteroscedastic Gaussian mixtures. Our framework also establishes finiteness of the number of modes for additional classes of polynomial-exponential mixtures and generalized Gaussian mixtures.

Csiszar's formulation of the $f$-divergence introduced a vast family of functionals for quantifying dissimilarity between probability distributions. However, many applications in statistics and information theory rely only on a few $f$-divergences, such as the Kullback-Leibler divergence, the $\chi^2$-divergence, and the squared Hellinger distance. These divergences are especially useful because they admit simple compositional formulas under product measures, a property sometimes referred to as tensorization. In this work, we refine a formalism of tensorization previously introduced in the literature. Then, we show that any possible tensorization formula has a multi-affine form characterized by a single parameter, and identify all tensorizable $f$-divergences under our adopted notion of tensorization.

For finite-dimensional linear inverse problems where the variables are Gaussian, it is well-known that the minimum-mean-square error estimator takes the form of a regularized least-squares data fit. In this chapter, we show that this equivalence extends to a much broader infinite-dimensional setting where generalized splines take the role of linear regressors and generalized Gaussian processes on a nuclear space $S$ are the counterpart of Gaussian random vectors. The scope of this extension is of the same nature as the switch from the classic notion of function to that of a distribution, also known as a "generalized function." Our formalism involves a whitening/regularization operator $L: S\to S'$ whose continuous extension induces a native Hilbert space $H\subset S'$ that plays a central role in our characterization. The presentation is self-contained for the most part and remarkably general and powerful. It allows for the recovery of all known instances of such equivalences; in particular, the methods involving innovations and reproducing-kernel Hilbert spaces developed by Kailath and his students, and the mathematical correspondence between fractional splines and Mandelbrot's fractional Brownian motion (fractals), with the former being the optimal estimators of the latter. It also covers general Bayesian methods for the resolution of infinite-dimensional inverse problems.

Relational Event Models (REMs) provide valuable insights into the dynamics of longitudinal social networks. Yet, the vast availability of potential predictors for a dyad's event rate poses the risk of selecting irrelevant variables and specifying an overfitted model that does not generalize to new data. Despite the recent popularity of Bayesian regularization methods to address this, there has not been a systematic evaluation of the performance of Exact Bayesian Regularization (EBR) and Approximate Bayesian Regularization (ABR) against standard Maximum Likelihood (ML) procedures commonly used for REMs. To address this, we conduct a simulation study in which directed Relational Event History (REH) data is generated with endogenous and exogenous effects of varying strength and compare the performance of (a) unregularized ML estimation, (b) ABR through normal approximations of the likelihood with Ridge and Horseshoe priors, and (c) EBR with Horseshoe priors. We find that threshold-based criteria applied to ABR and EBR with Horseshoe priors outperform univariate selection using p-values from ML estimation in variable selection accuracy. Regarding predictive performance, ABR with Ridge priors and EBR with Horseshoe priors outperform ML REMs, particularly for small sample sizes. Given only small gains with large computational burdens when using EBR, we therefore advise researchers to use ABR with a suitable prior.

Global goodness-of-fit and discrepancy statistics can establish that a sample departs from a reference distribution without identifying which observations drive the departure. We develop a framework for this localization problem by assigning to each observation its conditional or marginal contribution across random statistical contexts. This connects resampling diagnostics and data valuation to projection theory and event-level anomaly detection. For symmetric statistics, fixed-size replacement is exactly equivalent to centered conditional localization. For U-statistics, the addition score equals the first Hoeffding/Hájek contribution; for smooth distributional functionals it is related at leading order to the influence function; and for unbiased known-background MMD it reduces exactly to the MMD witness. This viewpoint also yields more efficient estimators. Matched-context subtraction removes fluctuations unrelated to the observation, while for pairwise MMD the event-containing terms give a simple localizer. On the LHC Olympics anomaly-detection benchmark, the pair estimator converges to the direct empirical MMD witness with the predicted 1/(Rm^2) scaling, where m is batch size and R the number of batches. At m=1000 and R=5x106 it reaches correlation 0.9993 with essentially identical AUC. We also ask when context contains information beyond an event's own features. In a shared-latent toy model, the full single-event signal and background distributions are identical by construction, forcing isolated-event AUC=0.5. Discriminating information survives only in cross-event dependence induced by the shared latent parameter; the ensemble recovers this information, whereas an independent-latent control does not. This separates two roles of context: efficient localization of a global discrepancy and genuinely additional class information when the alternative contains shared structure.

In applications, it is often required to test objects or people to determine their qualities in terms of certain metrics. However, besides being naturally noisy, the test results can be corrupted by adversarial behaviors of objects or people being tested (test takers). For example, dishonest test takers can cheat in the exams to distort the test results. With the development of AI technologies, such distortions driven by cheating using AI technologies are becoming more commonplace and severe. In this paper, we propose optimal testing strategies which can still recover needed test results even if there are cheaters polluting the results. The proposed testing strategies will optimally re-test selected group of test takers using different testing security measures. We determine the optimal testing strategies using a dynamic programming method.

This paper investigates whether five fold cross fitting improves nonresponse adjustment in survey estimation when flexible machine learning methods are used to estimate response propensities. We conduct a finite population Monte Carlo simulation with 90 experimental configurations and 2,000 replications per configuration, varying sample size, response rate, and the structure of the response mechanism. Logistic regression is used as a conventional parametric benchmark, while Random Forest and Gradient Boosting Machine are considered as flexible nonparametric models.

We extend the FLOP (fast learning of order and parents) algorithm recently proposed by Wienöbst et al. (2026) from observational to interventional data. In particular, we use the interventional BIC score of Hauser and Bühlmann (2012), adapting it to be used with the iterative Cholesky-based score updates that are partly responsible for FLOP's speed. We show that, in the sample limit, I-FLOP recovers a DAG in the same interventional Markov equivalence class as the data-generating DAG. We compare I-FLOP to existing causal structure learning algorithms on real and simulated interventional data, where it performs favorably in terms of both performance and run time.

We study the non-uniqueness of exact two-sided $p$-values in continuous one-parameter natural exponential families (NEFs). For directed one-sided problems, the tail $p$-value agrees with the $p$-values using UMP, UMPU, and likelihood-ratio (LR) tests. For a two-sided simple null, we distinguish four constructions: equal-tail, density-ordered, UMPU, and LR $p$-values. At a fixed null parameter, UMPU and equal-tail $p$-values coincide if and only if the null law is symmetric about its mean; under a regular two-branch density-level condition, the same fixed-null symmetry characterization holds for UMPU versus density ordering and equal-tail versus density ordering. Requiring any of these coincidences throughout the NEF characterizes the Gaussian family. We combine these results with the theorem of Bar-Lev, Bshouty and Letac that UMPU and LR $p$-values coincide throughout a continuous NEF precisely for the normal, gamma and inverse-Gaussian families. We also investigate the two LR pairings not covered by those results. If equal-tail and LR $p$-values coincide throughout a NEF satisfying our standing regularity assumptions, then $(V^{2/3})^{\prime \prime \prime }=0$ on the mean domain. The same coincidence also forces an explicit density-at-the-mean identity. For an i.i.d.\ sample with canonical sufficient statistic $T_n=\sum_{i=1}^nX_i$, persistence of equal-tail-LR coincidence throughout the family along an unbounded sequence of sample sizes forces Gaussianity. A corresponding density-LR statement is given conditionally on an explicitly stated differentiated local Edgeworth expansion. Finally, inverse-Gaussian and hyperbolic-secant examples quantify numerical $p$-value differences, disagreement of rejection decisions, and differences in power.

Privacy-preserving learning is often motivated by the idea that protecting users' data can preserve trust and thus participation, improving utility in the long term. However, this claim has not been formalized so far. In parallel, performative learning provides a framework for studying learning systems whose deployment affects the data they later observe. In this work, we bring these two perspectives together and introduce performative privacy, where data leakage reduces future participation. We study a simple model where agents repeatedly contribute data for mean estimation but may leave the system when their data is leaked. Privacy is implemented through differentially private mechanisms, creating a trade-off between estimation noise and future participation. We show, through a theoretical study of the dynamics and numerical experiments, that a finite privacy budget can outperform non-private estimation in the long term when the feedback loop between leakage and participation is sufficiently strong. This provides first evidence that differential privacy can be optimal not only as a protection mechanism, but also from the perspective of long-term utility.

We study risk-averse decision making, in which an agent selects actions while being uncertain about the true system state. The risk is measured via optimized certainty equivalent (OCE) metrics, which generalize popular criteria such as mean-variance risk and conditional value-at-risk (CVaR). We characterize the optimal policy under known distributions, and show that it reduces to a prediction set-based solution for the CVaR. This provides an operational interpretation of conformal prediction-type prediction sets. For unknown distributions, we develop a data-driven calibration strategy, based on a synthetic model for the likelihood and held-out calibration data, yielding high-probability control of the OCE risk. The approach is evaluated on two wireless beamforming settings.

Forecast combination is a reliable way to improve predictive performance when several forecasting models are available. Simple aggregation rules such as the mean, median, trimmed mean, inverse-loss weighting, and exponential weighting are often strong baselines, but their relative performance can vary across datasets, forecast horizons, deployment settings, and levels of disagreement among base forecasters. We develop Generalized Gibbs Ensemble Weighting (GGEW), a probabilistic framework that treats forecasting models as experts and assigns ensemble weights using a Gibbs-style exponential transformation of normalized predictive loss. The framework extends this basic weighting rule through numerical stabilization, diversity-aware score corrections, and online hyperparameter adaptation. GGEW produces a family of related methods, including Stable Gibbs weighting, Directional Gibbs-NCL, and Symmetric Gibbs-NCL. These variants share one core algorithm and differ only in the score used inside the exponential weighting rule. For sequential deployment, we adopt a UCB-style bandit mechanism, called online Local-UCB, to adapt the learning rate, diversity strength, and Gibbs variant without evaluating the full hyperparameter grid at every prediction step. We evaluate GGEW on official M4 competition forecast submissions and external rolling-origin deployment experiments using Monash Traffic Hourly, Electricity Hourly, and Solar Weekly datasets. Results suggest that Gibbs-style adaptive weighting is a useful and competitive tool across several benchmark settings, although its relative performance varies across datasets, forecast horizons, deployment protocols, and forecast disagreement groups. The contribution is not a universal dominance claim, but a framework and empirical study motivating further investigation of when adaptive Gibbs-style forecast combination is useful.

Modern time series are often long, serially dependent, and non-stationary. Existing change-point methods either target specific changes or become computationally intensive when using nonparametric costs on long series. Many also require thresholds to be carefully calibrated under serial dependence. We introduce SCAN, an offline method for detecting multiple distributional change-points in long, serially dependent univariate time series. SCAN compares adjacent windows using an integral probability metric, calibrates local discrepancies with a dependence-aware bootstrap, and refines candidate locations using a scaled 1-Wasserstein criterion, enabling detection of changes in mean, variance, and broader distributional structure within a unified framework. An ensemble over multiple window sizes reduces sensitivity to window size and threshold specification. We establish consistency of the estimated number and locations of change-points under exponential alpha-mixing dependence, and show that the localization statistic reduces to a CUSUM-type statistic under pure mean shifts. In simulations with up to one million observations, SCAN generally achieves higher covering and F1-scores than competing methods across mean and joint mean-variance shifts, particularly under serial dependence. On real data, SCAN identifies labeled activity transitions in sensor data and interpretable structural changes in hourly Bitcoin prices. Implementations are available in the Python package scan-cpd and R package scanr.

We present a suite of R packages for macroeconomic forecasting that leverages advanced Bayesian, structural, multivariate, dynamic, hierarchical, non-linear, and non-Gaussian models. The suite enables both structural and predictive analyses, and is adapted to time series data across various types, dimensions, and sampling frequencies. Each additional feature increases computational complexity. To address this challenge, our software design incorporates a carefully curated selection of models, efficient algorithms implemented in C++, advanced econometric and numerical methods, robust handling of complex input and output objects, and standardised workflows. This approach combines the computational efficiency of C++ with the convenience of working with data in R. We demonstrate that our packages facilitate original research contributions in forecasting, as illustrated by our example in which vector autoregressions with non-centred stochastic volatility enhance density and point predictions relative to models with centred stochastic volatility.

In this work, we explore particle learning strategies for the joint estimation of static parameters and latent states within conditional sequential Monte Carlo (CSMC) algorithms. Building on this idea, we propose the p(parameter)-CSMC algorithm, which incorporates both parameter learning and ancestor sampling, leading to much better mixing properties compared to (particle) Gibbs sampling in settings where strong internal correlations may challenge effective exploration. We also include two applications in the context of a branching process model: one using synthetic data, where we estimate the infectivity profile while assuming the reproductive number to be known, and another using real data, where we address the joint inference of the reproductive number and the infectivity profile based on daily hospital incidence from the arrival of the SARS-CoV-2 lineage B.1.1.7 (Alpha) in Norway in February 2021. We show that, in these settings, performance is dramatically enhanced, with substantially faster mixing and markedly reduced autocorrelation compared with standard particle Gibbs.

How much data must a fixed learner retain? Hanneke, Moran, Shlimovich and Yehudayoff (COLT 2025) posed this question for linear regression with the minimum-norm empirical risk minimizer. A selector sees a finite dataset $D\subseteq R^d\times R$, keeps at most $n$ examples with nonnegative weights, and $F_w(d,n)$ is the worst-case ratio between the full-data loss of the trained predictor and the optimal loss. The value is $\infty$ for $n<d$, $d+1$ at $n=d$ and $1$ for $n\ge2d$, and the regime $d<n<2d$ was left open. We settle several cases. For every $d$ we prove $F_w(d,2d-1)=1+1/d$, which confirms a claim stated without proof in the original note. We also prove $F_w(3,4)=5/3$, $F_w(4,5)=2$ and $F_w(4,6)=3/2$, the three smallest cells not covered by that formula. For every intermediate budget $n=d+k$ we prove the lower bound $F_w(d,d+k)\ge1+\Gamma_{d,k}$, where $\Gamma_{d,k}$ is an explicit harmonic quantity over balanced partitions of $d$. This bound is the exact minimax value on the class of datasets whose whitened systems split into orthogonal circuit blocks. All proved values equal $1+\Gamma_{d,k}$, and we conjecture that this holds throughout the open regime. Our upper bounds combine a rigidity theorem for positive spanning configurations of loss gradients with normal forms of the small positive bases in $R^3$ and $R^4$. These forms are special cases of the classification of Cornaz, Kerleau and Royer; we also control all gradients outside the basis. A dimension-free extremal-basis argument converts sign-cone geometry into selections of $d+1$ points. Explicit counterexamples rule out several shorter routes. Every upper bound is constructive, with selection procedures polynomial in the number of points for fixed dimension. Every numerical claim about a specific instance is an exact rational or algebraic identity, recomputed in exact arithmetic in the supplementary material.

Digital twins (DTs) and learned world models are increasingly used to generate synthetic data that augment the scarce real datasets available for training artificial intelligence (AI) models in engineering systems. Owing to the inevitable simulation-to-reality (sim-to-real) gap, however, augmentation may fail to improve the performance of the trained model on the real data distribution. This paper addresses the resulting decision problem: Given a real dataset, a candidate synthetic dataset, and a fixed learning algorithm, decide whether training on the augmented dataset improves the true, population-level performance, while consuming as few real test data points as possible. Two formulations are considered: a direct test on the mean loss difference between the two trained models, and a symmetry-based test on the paired loss difference, which trades a stronger null assumption for faster evidence accumulation. For the latter, we introduce the {adaptive e-process sign-flip test} (aeSFT), a doubly adaptive procedure that adapts both the number of Monte Carlo sign-flip rounds, and hence the computational cost, and the amount of real test data consumed. aeSFT yields anytime-valid Type-I error control, with no need to pre-specify the test-set size. Experiments on a synthetic-data classification task, a DT-aided wireless packet-scheduling task, and a radio-map prediction task show that aeSFT identifies useful synthetic data using substantially fewer real test samples than mean-based sequential testing, matches the power of fixed-sample sign-flip testing and the paired $t$-test, while keeping the false-positive rate below the target level.

The problem of sampling from a probability distribution arises in many applications such as posterior sampling in hierarchical Bayesian inverse problems and Gaussian processes for machine learning. Markov chain Monte Carlo (MCMC) algorithms are often used for sampling from a target probability distribution, but implementations can be computationally expensive, especially for large-scale problems. In certain applications, the target distribution naturally factorizes into a lower dimensional marginal distribution and a conditional distribution that allows exact sampling. We describe an MCMC algorithm called MarCo that exploits such a structure and generates a Markov chain via Metropolis-Hastings sampling from the marginal distribution, followed by sampling from the exact conditional distribution. By design, MarCo constructs a Markov chain on the joint space that inherits the convergence behavior of the marginal MCMC algorithm. This provides multiple theoretical and computational advantages. We prove that MarCo can achieve improved mixing time upper bounds compared to direct sampling from the joint distribution. Moreover, compared to one-block methods that also exploit marginal-conditional structure, we use the framework of Peskun-Tierney ordering to show that MarCo has a larger right spectral gap and smaller asymptotic variance, thus leading to superior convergence properties. Numerical results illustrate the performance benefits of MarCo and are provided for various problems, including a semi-blind image deblurring example.

We study $\ell_0$ isoperimetry for a convex body $K\subset \mathbb{R}^n$, $n\ge2$. For a Borel set $S\subset K$, let $\partial_0^K S$ be the set of points in $K \setminus S$ that can be reached from $S$ by changing at most one coordinate (i.e. the $\ell_0$ boundary of $S$). Suppose that, for some unconditional convex body $Q \subset \mathbb{R}^n$, numbers $r,R>0$, and possibly different centers $x_0,y_0$, \[ x_0+rQ \subset K\subset y_0+RQ. \] Writing $s=\text{vol}(S)/\text{vol}(K)$, we prove that whenever $0<s \le 1/2$, \[ \frac{\text{vol}(\partial_0^K S)}{\text{vol}(S)} \ge \frac{cr}{nR} \min\left\{1,\frac{\log(e/s)}{n}\right\}, \] where $c > 0$ is an absolute constant. Consequently, the associated $\ell_0$-isoperimetric coefficient is at least $cr/(n^2R)$. Previous direct lower bounds were only known for $\ell_2$ and $\ell_\infty$ regularity whereas our lower bound holds directly for any $Q$-regularity, where $Q$ is an unconditional convex body. Compared to $\ell_2$ and $\ell_\infty$ regularity, our lower bound result improves upon the previously best known lower bounds, for any $s$, by a factor of $n$. As an application of our result, we give improved mixing time bounds for the Coordinate Hit and Run walk (CHAR). Our proof of the lower bound is based on a modification of the method of canonical paths applied to a continuous Hamming graph over our convex body. Our construction of canonical paths can be viewed as a suitable coordinate discretization of certain mass transport maps from $S$ to $S^c$. We also give complementary upper-bounds for any $Q$-regularity, with an overall factor of $n$ gap between the two.

From a deck of cards, how many cards do I need to draw, until the first ace? I identify the distribution for this waiting time $T$, and its satisfyingly nice expected value ${\rm E}\,T=(N+1)/(n+1)$, with $N$ the number of cards and $n$ the number of aces; hence $53/5=10.6$ for the standard setup. After having solved this Question One I go on to certain alternative solutions and extensions, involving e.g. Beta approximations. I also consider the distributions and means for the 2nd, the 3rd, the 4th occurrences of aces, with generalisations, where there is a Dirichlet distribution in wait for us, with further links to order statistics for the uniform. Furthermore, an apparatus is developed for obtaining estimators and full confidence distributions for applications where one knows the number $n$ of aces, but not the deck size $N$; and correspondingly for inference about the unknown population size $N$ when $n$ is known. If you have 1000 people in a room, and need to interview 11 of them until you've found the first left-handed person, how may left-handed are there in the room – here we need both an estimate and a clear measure of uncertainty.

Artificial Intelligence trustworthiness scores are moving from research dashboards into compliance claims and procurement decisions. A compliance claim is a statistical decision based on the comparison between an estimated compliance metric and a set threshold. The recently proposed integrated SAFE AI metrics are based on three basic rank-graduation measures of accuracy, explainability and robustness, expressed on a common footing. The metrics are integrated into a single compliance score, so far reported as a point value. In this paper we propose to add an uncertainty layer to the SAFE AI compliance score. All component metrics are estimated on a shared test sample, so their errors covary. We estimate the full covariance of the component vector with a paired bootstrap, and quantify departures from the source-wise independence baseline suggested by the integrated-metrics framework's variability decomposition. A closed-form identity splits such departure into an uncertainty-weighted effective dimension and an exposure-weighted data-driven correlation, with both depending on the aggregator and the estimated uncertainty of the component metrics. The application of our proposal to both real and simulated data shows that the assumption of independence can either narrow or widen confidence bands, while the direction and magnitude of the effect depend on the aggregator type, machine learning model, and perturbation family. The resulting confidence region supports compliance decisions, which can be documented in a formal uncertainty certificate.

A released table is often treated as an i.i.d. sample, although its repeated rows may encode business frequency, repeated entities, joins, resampling, or extraction errors. We show that this ambiguity creates a hidden measurement layer with three consequences: feature-identical rows impose an attained evaluation ceiling, row-weighted AUROC is sensitive to replication, and row-trained detectors learn a multiplicity-size-biased law. An exact-row audit of all 690 OddBench datasets finds train-test overlap in 355, feature-identical label conflict in 147, and a test anomaly identical to a training normal in 137. Switching from row to support weighting changes AUROC by at least 0.05 on 50-61 datasets across four classical detector geometries. We introduce SCOUT (Support-Count Orthogonalized Unsupervised Testing), a factorized anomaly detector that separates replication-invariant support evidence from exposure-aware count evidence. Factorwise split-conformal calibration yields marginal false-positive-rate control, while the support channel is exactly invariant to arbitrary positive row replication. On 686 OddBench datasets and five seeds, support-only SCOUT is non-inferior to row-wise Isolation Forest in raw AUROC and improves replication-invariant AUROC. External normal-support evaluations track nominal false-positive levels, and four backbones remain exactly unchanged under controlled replication. Semi-synthetic interventions show that conditional count modeling helps materially only under strong rate heterogeneity. These results specify when multiplicity should be treated as signal, nuisance, or uninterpretable without additional information.

Public benchmark scores may reflect skill, prior exposure to the questions, or both, and for most models the training data are unknown. We present CleanScore, a black-box audit using scored outputs only. Each benchmark question becomes a parent item with one public form and two independently written fresh forms preserving its numbers, facts and answer. The audit reports an interval for the public-form advantage rather than a verdict, and a private negative-control bank with an explicit transport radius separates exposure from ordinary form mismatch. A registered controlled-exposure experiment detects planted exposure and stays quiet under fresh-form exposure. A registered audit of five open models on 200 GSM8K and 200 ARC-Challenge items finds no exposure-consistent advantage, bounding surface-form inflation below five points. Registered positive controls then bound what such a null can mean. Leaking an item raises accuracy on paraphrases the model never saw almost as much as on the leaked wording, leaving 52% to 110% of the effect invisible to a paraphrase audit. On ARC a planted 49-point advantage shows an observable gap of -0.020, and about 20 points survive rewriting stem and options, across four training seeds. A surface-form null bounds far less than the phrase contamination audit implies.

In the Western United States, snowmelt is essential to the agricultural industry in addition to being a key source of municipal drinking water. Consequently, accurate snowpack forecasting is critical for water policy and management. Automated Snow Telemetry (SNOTEL) stations provide accurate daily measurements of snow water equivalent (SWE) that exhibit strong correlations in space and in time. We tackle the problem of predicting future SWE values across the SNOTEL network. Specifically, we use a Gaussian Process-based linear transformation to remove spatial correlations before training a long short-term memory (LSTM) neural network on the decorrelated SWE data. This approach allows the LSTM to learn a clean temporal signal at each station. We show that this separation of spatial and temporal components yields better predictive success than multiple baseline models. Furthermore, we incorporate conformal prediction to quantify uncertainty in the resulting SWE forecasts, providing a distribution-free approach to illustrate a potential framework for establishing predictive intervals for spatiotemporal data. Together, accurate point forecasts and distribution-free uncertainty quantification provide a framework for SWE accumulation forecasting on subseasonal scales or projecting SWE with future data while motivating and supporting future work in predicting a large-scale, spatiotemporally complete SWE map.

This paper presents two interpretable machine-learning frameworks for quality screening of e-transaxle assemblies in electric vehicles: a Stagewise Wavelet Isolation Forest (SWIF) framework and a short-time Fourier transform (STFT)-based diagnostic framework. High-dimensional vibration signals acquired from front and back accelerometers are analyzed across multiple operating stages to capture stage-dependent vibration behavior. In the SWIF framework, signals are decomposed using a five-level Daubechies-4 discrete wavelet transform, and blockwise mean-squared coefficients are extracted from the selected wavelet detail level to obtain compact multiscale features. In the STFT-based framework, dominant-frequency trends are extracted from time-frequency representations and summarized through regression coefficients with respect to instantaneous motor speed. Anomaly detection models are trained using accepted production units under the assumption that only a small fraction of accepted assemblies contain latent defects, and their performance is evaluated using road-tested units with validated quality outcomes. Experiments on production and road-tested e-transaxle units show that both approaches provide interpretable diagnostic information, while SWIF achieves the most favorable balance between defect detection and false-positive control. Compared with the STFT-based method and alternative anomaly detectors, SWIF combined with Isolation Forest yields lower anomaly rates within the Accept population while identifying high-risk units from the Reject population. The stagewise structure further localizes anomalous behavior to specific operating conditions, supporting root-cause analysis and targeted process improvement.

Bayesian variable selection becomes computationally challenging when models contain many dependent parameters. We study Piecewise Deterministic Markov Process (PDMP) samplers as a continuous-time alternative to conventional Markov chain Monte Carlo for spike-and-slab variable selection. In sticky PDMP samplers, active parameters evolve continuously until they reach zero, where they may remain for a random duration before re-entering the model. While one parameter enters or leaves the model, the remaining parameters continue to evolve along the deterministic flow, offering a potentially advantageous mechanism for exploring posteriors with strongly dependent parameters. We make two methodological contributions. First, we extend existing sticky PDMP methods beyond independent spike-and-slab priors to dependent model priors and dependent slab distributions. Second, we investigate the use of unbiased stochastic gradients to reduce the computational cost of variable selection when the likelihood decomposes into many factors while retaining the same target distribution. We study these extensions to two psychometric models: a Gaussian random intercept cross-lagged panel model and an ordinal Markov random field. For the former, marginalization yields a fixed-dimensional sufficient-statistic representation that permits efficient model evaluation. For the latter, the model factorizes, which enables subsampling over person-node contributions. In simulation studies, we compare ZigZag, Bouncy Particle, and Boomerang dynamics with reversible-jump MCMC, and examine the effects of prior dependence and stochastic-gradient subsampling on sampling efficiency. We illustrate the methodology using data from an empirical study on mental well-being. Finally, we discuss the advantages and challenges when using PDMP samplers for Bayesian variable selection.

Recurrent fast-weight memories and selective state-space models compress an expanding context into a fixed-size recurrent state, making the state transition an online learning rule. We study this rule under read-after-write autoregressive semantics. For the prefix-prediction objective considered here, the local fast-memory example revealed at step $t$ is the prefix-aligned pair $(\mathbf{x}_t,\mathbf{y}_t)=(\phi(\mathbf{k}_{t-1}),\mathbf{v}_t)$. The common same-step association $(\phi(\mathbf{k}_t),\mathbf{v}_t)$ remains causal, but optimizes a different internal objective. We derive normalized first-order updates for squared-error regression and negative inner-product objectives. The regression family comprises Falcon-1 (a scalar NLMS update), Falcon-2 (its per-column extension), and Falcon-3 (a sliding-window mini-batch update); Falcon-1A/Falcon-2A/Falcon-3A are the corresponding inner-product variants. We provide recurrent, masked-parallel, and chunk-parallel forms, together with numerically stable positive-decay renormalization. Representative variants remain competitive in language modeling and improve length extrapolation on variable-digit addition. This framework separates temporal alignment, plasticity, forgetting, and bounded rehearsal in recurrent sequence models.

Searchless chess networks reach human master strength from a single forward pass by imitating a stronger teacher: the strongest, Leela Chess Zero's (Lc0) released Chessformer, distills the visit counts of an AlphaZero-style Monte Carlo Tree Search (MCTS). Imitating a search is a poor proxy for playing without one, so we fine-tune for single-pass strength with self-play reinforcement learning (RL). Its exploration is usually supplied by an entropy bonus, the reverse Kullback-Leibler (KL) divergence to uniform. We replace it with a forward, mass-covering KL toward the network's own MCTS prior (prior-directed exploration), so exploration covers the moves the prior judges promising, and pair it with an entropy-adaptive sampling temperature, set by the value head's outcome uncertainty, that sharpens once a position is decided. In about two thousand steps it raises puzzle accuracy from 93.9% to 94.9% on a 100,000-puzzle suite and mate-in-four accuracy from 77% to 81% while holding searchless strength at or slightly above the base. Measuring tactical accuracy and playing strength together across a matched-compute sweep, we find the two dissociate: accuracy gains fall in a one-point band while ratings straddle the base, and a control fine-tuned on puzzles alone posts the study's largest tactical gains while shedding roughly 260 Elo; a better puzzle-solver is not thereby a stronger player. Distribution-level measurements show what anchoring buys: without a regularizer self-play collapses onto a single line of play, and the puzzles newly solved are the near misses whose winning move the prior kept alive. The forward-KL prior tops the rating ladder, statistically tied with a reverse-KL anchor that concentrates twice as hard and drops the hardest solutions the mass-covering prior keeps in support.