Papers

Reference-based multiple imputation is used in longitudinal clinical trials to assess sensitivity to assumptions about outcomes unobserved after intercurrent events. Most existing methods target continuous outcomes and use multivariate normal working models. Scheduled count outcomes require a model that preserves integer support, skewness, overdispersion, longitudinal dependence, and an exposure-based rate interpretation. We propose visit-specific negative binomial (NB) margins linked by a Gaussian copula. Covariate-adjusted log rate models define the margins, while the copula captures longitudinal dependence. For missing outcomes in the active arm after a prespecified event, termed the trigger, assigned arm continuation retains the fitted active arm marginal mean, jump to reference uses the corresponding reference arm marginal mean, and the intermediate rule interpolates between these means on the log rate scale. Combined with the copula, the resulting NB margins determine an imputation distribution conditional on the retained history. We account for discreteness through randomized probability integral transform augmentation and fit the model with a custom Metropolis-within-Gibbs sampler. In targeted simulations, the model recovered the generating marginal and dependence parameters with little bias. In simulations with incomplete data, treatment effect estimates were closest to the corresponding complete data estimates when the imputation rule matched the mechanism governing outcomes after the trigger. We illustrate the method using repeated incontinence episode counts from a published trial in overactive bladder. Estimated rate ratios comparing active treatment with placebo remained below 1 under all reference-based assumptions, with modest attenuation toward the null and the greatest separation between rules at the final visit.

Validating an LLM-as-a-judge requires estimating its agreement with humans, yet annotation budgets rarely allow every item to be multiply labeled. We prove that this overlap sparsity is the first-order determinant of wrong deployment decisions: at 5% pairwise overlap, wrong-decision rates reach 25% and the probability of selecting the wrong best judge among ten candidates is 65%. The two actionable levers are overlap quantity and allocation. For quantity, we derive a minimum-overlap formula showing $\rho \geq 0.25$ suffices for non-borderline judges while borderline cases remain fundamentally hard. For allocation, a zero-cost stratified scheme halves false-rejection rates relative to random sampling when strata are informative. We validate on 10 LLM judges across four evaluation matrices spanning visual assessment, causal reasoning, and summarization.

Recent literature has shown a strong connection between optimization and sampling. We develop the corresponding first-order theory for diffusion models. First, the SDE-based reverse-time flows of overdamped and underdamped Langevin diffusions contract relative Fisher divergences at explicit exponential rates whenever the stationary potential of the forward process is strongly convex—a condition on the noising process one chooses, not on the data. This is a unique advantage of SDE-based reverse diffusion, absent in the reverse process based on ODEs. Second, we incorporate discretization and establish averaged first-order stationarity bounds—the sampling analog of averaged gradient-norm guarantees in nonconvex optimization—for samplers of both overdamped and underdamped diffusion models. As in nonconvex optimization, the convexity-free certificate is local: it guarantees score consistency, not global mode weights.

Generative AI systems are increasingly used, but aligning their outputs with user requirements poses a continuing challenge. Here, we aim to ensure that the distribution of an attribute of an AI-generated output aligns with a user-specified target. This is motivated by examples such as fairness, where we want to ensure that a protected attribute (e.g., gender, race, or age categories) follows a desired distribution, and synthetic data generation, where we want the generated data to be representative of a target distribution. We study the practically important black-box access setting, where a user can repeatedly query a generative AI model. The goal is to return $m\ge 1$ outputs whose joint attribute distribution is as close as possible to this target. For both exact and approximate alignment, we develop algorithms that minimize the expected number of queries to the generator, and we further demonstrate their optimality as the number of requested outputs $m \rightarrow \infty$. Experiments on text-to-image generation and geocoded persona generation tasks show that our post-processing algorithms improve statistical attribute alignment, complementing prompting-based interventions.

Quasi-Monte Carlo methods allow computer experiments to be run with far fewer simulations than crude Monte Carlo. A digital net in base two, such as Sobol', is however only balanced when the number of samples is a power of two, and Latin Hypercube Sampling (LHS) accepts any sample size but only controls the one-dimensional margins. This work proposes a space- filling design defined for any sample size, referred to as LAT for Latinized aperiodic tiling. The unit hypercube is cut recursively across its longest edge following the golden section into N cells of equal volume. One point is then placed in each cell, and the margins are made Latin while every point stays inside its own cell. The construction only uses integer splits and costs O(dNlog N). The recursion is shown to follow the Fibonacci word and its aperiodicity is analysed. LAT is assessed with four L2-discrepancies and with the integration error on analytical functions and engineering emulators, and compared to Monte Carlo, LHS, Halton, Sobol' and a rank-1 lattice. LAT is better than Monte Carlo and LHS as soon as the integrand has interactions. Sobol' remains more accurate at the powers of two, but its error is one to two orders of magnitude larger at other sample sizes. The accuracy of LAT does not depend on the sample size. Finally, the cells form a partition of the hypercube for any N. This allows one to refine the design locally, to search for an optimum by splitting cells and to sample non-rectangular regions.

Deep learning has substantially accelerated the calibration of complex stochastic-volatility models, but neural point calibration alone does not capture the uncertainty remaining after an implied-volatility (IV) surface has been observed. We develop a simulation-based inference framework for rough Heston (rHeston) calibration that learns the posterior distribution of the model parameters conditional on an IV surface. Using neural ratio estimation, we obtain calibrated posterior samples that can be propagated through heteroscedastic neural surrogate pricers for path-dependent exotic options. The resulting posterior-predictive distributions combine residual parameter uncertainty with conditional surrogate uncertainty and yield uncertainty-aware price intervals. We further introduce Hellinger-SHAP, an information-theoretic explainability method for posterior inference. Rather than attributing a single parameter point estimate, it applies local-background Kernel SHAP to a posterior-information functional measuring contraction from the prior to the posterior. This identifies maturity–moneyness regions associated with posterior information gain for individual rHeston parameters. In a simulation study, posterior-predictive intervals provide calibrated or conservative coverage across forward-start, barrier, and realized-variance claims, while point plug-in prices can be materially unreliable for selected contract regimes. Together, the UQ and XAI analyses provide a transparent framework for uncertainty-aware neural calibration and downstream exotic pricing under the specified prior-predictive model.

We study false-alert control when screening for text generated by artificial intelligence (AI). The screening procedure selects document prefixes and detectors from observed evidence and may stop before exhausting its inspection budget. We give two finite-sample constructions under document-level exchangeability between human calibration documents and a new null document, with no restriction on dependence among tokens within a document. Construction A registers a finite family of prefix-detector scores and allocates a false-alert budget across their conformal ranks. A union bound protects any executed subset of that family. Construction B calibrates the complete-path maximum of a development-fixed adaptive policy. Each partial-path maximum is bounded by the complete maximum, so a terminal conformal rank protects early stopping without splitting the error budget. We prove marginal control of any false alert across the permitted inspection path and derive necessary calibration counts for rejection. We also state oracle testing, distribution-shift, and independent-audit bounds with their additional assumptions. Both constructions protect stopping within their specified scope; neither proof constructs an e-process or justifies multiplying conformal ranks. Detection power and computational savings remain questions for empirical evaluation.

Bi-invariant geodesic regression generalizes linear regression to Lie groups. Its main feature is that it respects the symmetries of the group so that the resulting estimator is independent of arbitrary choices such as a reference frame. However, the local existence and uniqueness of the underlying estimator have not been shown until now. Furthermore, the convergence properties of the proposed algorithm for computing the estimator are not known. In this work, we investigate these questions. We prove that, locally, a unique estimator exists and give explicit bounds on the size of this neighborhood. We also show that the proposed iterative algorithm converges linearly to this estimator.

The decision problem is whether valence among the users who write reviews of an app has changed enough to warrant investigation of a release, outage, or support issue. We propose a statistical specification for that decision, applied to written Google Play reviews collected under a declared locale, language, sort order, retrieval cap, and window rule. That endpoint returns a selected collection rather than a random sample, so the index describes review writers under the declared protocol and not all app users. What is new is not a sentiment classifier but an auditable interface: an ordinal threshold model is the preferred representation of star ratings, a calibrated two-signal generalized least-squares estimator is retained as an interpretable linear approximation when held-out labels support its conditional-unbiasedness assumption, the estimand is declared before the estimator, and every downstream module–uncertainty, diagnostics, and regularization–is tied to that declaration. The framework separates the latent average of a fixed collected set from the mean of a protocol-defined population of review writers, so measurement and between-review variation are not conflated, and treats helpfulness and recency weights as a different policy target. Shrinkage, cross-app empirical Bayes, histogram and dependence diagnostics, and dynamic smoothing are specified as separate modules with defaults and mandatory sensitivity analyses. A reference implementation, a declared 6000-review three-app collection, and a synthetic stress test exercise the displayed equations: fusion reduced error in clean and small-window scenarios, coordinated contamination caused severe bias and interval failure, and the collected sample reproduces the abstention rules. No real-review validation is claimed.

Outliers are essential for evaluating and improving the robustness of machine learning systems, especially when future distributions may differ significantly from historical training data. In high-stakes applications, robustness often depends on rare cases that finite datasets fail to capture, making simple resampling or perturbation insufficient for stress scenario generation. Existing outlier synthesis methods typically rely on sparse neighborhoods, low support latent regions, or classifier boundary crossings, which can be heuristic, unstable, and tied to specific modalities or architectures. We therefore propose Sinkhorn Boundary Outlier Generation (SBOG), a structured framework for latent-space outlier generation that couples Sinkhorn optimal transport geometry with distributionally robust boundary modeling. The resulting Sinkhorn-induced support cost guides the sampler toward weakly supported boundary regions, while semantic constraints prevent uncontrolled drift from the intended context, yielding controlled deviations from the in-distribution reference measure rather than arbitrary sparse-region samples. Experiments on time series anomaly generation and image outlier synthesis show that our framework produces informative, semantically controlled outliers and improves downstream robustness evaluation across modalities, providing a foundation for stress scenario generation beyond empirical support.

The standard dependence summaries used in biomarker studies – Pearson's r, Spearman's rho, Kendall's tau – take values in [-1, 1] with 0 indicating no linear or monotone association. Zero does not distinguish independence from non-monotone dependence, so the scale cannot represent threshold effects, heteroscedasticity, and tail shifts common in biomarker practice. We formulate independence testing as a composite Bernoulli likelihood ratio: at each threshold t, comparing the Bernoulli laws of 1(Y <= t) conditionally on X versus marginally, aggregated over cut points. The resulting coefficient xi_cut lies on [0, 1] with 0 iff X and Y are independent (under continuity of Y) and 1 iff Y is a measurable function of X. Fisher weighting arises at second order from the Bernoulli likelihood, and xi_cut equals twice the threshold-averaged mutual information between X and 1(Y <= t), giving a distribution-free lower bound on I(X; Y). A second-order expansion recovers the Fisher-weighted Dette-Siburg-Stoimenov measure, which coincides under continuity with Chatterjee's rank correlation. Estimation uses a Nadaraya-Watson plug-in with a max-over-grid bandwidth; inference is by exact permutation. In biomarker-motivated simulations T_cut substantially outperforms rank-based coefficients on W-shaped non-monotone and heteroscedastic alternatives. We illustrate on the Seattle cohort (n=70, ages 21-88) of the aging plasma proteome dataset, screening all 1,305 proteins for age dependence: under Benjamini-Hochberg control at q<0.05, T_cut rejects on 70 proteins, six of which are missed by Pearson, Spearman, and Chatterjee at the same FDR level.

Transformers have become a central architecture for in-context learning (ICL), particularly through their state-of-the-art performance in large language models. This success motivates understanding how transformers exploit task-relevant structure in geometrically heterogeneous data. However, existing nonparametric ICL theory has largely focused on Euclidean domains or single-manifold models. To address this gap, we study the prediction problem under unknown local geometry, modeled by sample size-dependent mixtures of manifolds with heterogeneous dimensions, smoothness, and sampling masses. Under local separation and small-perturbation conditions, we establish a minimax lower bound capturing the aggregate difficulty of the components and construct an oracle tangent local-polynomial estimator with a matching upper bound. This estimator is connected to a structure-informed, two-stage softmax transformer with a geometric preconditioner and chartwise reduced local-polynomial solvers. The transformer achieves negligible approximation error relative to the minimax rate with logarithmic depth and polynomial size. Finally, we derive an in-context generalization bound for near empirical risk minimizers over this class. Together, these results identify conditions under which the resulting predictor exploits local geometry and attains the aggregate minimax rate.

Machine learning has become the standard tool for the design of interatomic potentials which balance efficiency and accuracy, but uncertainty quantification remains an open problem. Multiscale simulations introduce an additional challenge: robust uncertainty quantification across scales. Even within one scale, computations are often multistage, producing a sequence of target quantities, each dependent on the previous, and each with some uncertainty. Conformal methods have emerged as a model agnostic framework for recalibrating surrogate predictions to produce sets which contain the truth at a user-specified rate. For multistage workflows, we require uncertainty calibration for multiple chemical properties and atomistic configurations, and we want to propagate uncertainty sets to downstream quantities of interest. Such propagation should capture the error cancellations which occur in many downstream targets in materials science; for instance, an approximate energy difference is often more accurate than individual energy predictions. We present the first exploration of multivariate conformal methods for chemical properties, including Bonferroni-corrected hyperrectangles, hyperellipsoidal sets based on the Mahalanobis distance, and custom loss functions within conformal risk control. Calibration is applied directly to predicted energies, atomic forces, and virial stresses, then propagated to elastic constants and vacancy formation energies employing a variety of commonly considered approximate protocols in materials modeling. We highlight the benefits of building correlation predictions into the conformal procedure, making it possible to build sets which capture near symmetries and error cancellation. We conclude with a discussion of the interplay of the employed approximate computational protocol and conformal guarantees.

Tree-Adjoining Grammars (TAGs) have recently been introduced to Nonlinear System Identification (NLSI) as a means of encoding an entire model class as a finite set of grammatical rules, from which candidate models are assembled as trees. Existing TAG-based identifiers rely on evolutionary optimisation and return point estimates of the model structure. This paper instead proposes the TAG framework within a Bayesian setting. A generative prior is defined over tree structures and their parameters, and a Reversible-Jump MCMC sampler with structure-preserving tree moves is used to infer the joint posterior over model structure, parameters and predictions. Two training objectives are considered; that is, a one-step-ahead objective with conjugate parameter proposals, and a simulation-based objective handled by likelihood-free inference. The approach is validated on a simulated polynomial NARX system, the Silverbox benchmark, and wave-loading data from the Christchurch Bay Tower, where embedding Morison's equation as a fixed initial tree yields a grey-box model that outperforms the physics-driven baseline. The results demonstrate that Bayesian TAGs are well suited to quantifying uncertainty in equation discovery for dynamical systems and to fitting physics-informed models.

Distributionally robust optimization (DRO) provides a principled framework for learning under distribution shift, but its practical use is hindered by the difficulty of evaluating worst-case risks for nonconvex loss functions. We study a penalized DRO formulation in which the adversary may choose any distribution but incurs a Wasserstein penalty for deviating from the empirical distribution. We show that the adversary's problem can be reformulated as an optimization problem over transport maps that push empirical samples to adversarial ones, and we prove that optimal maps are cyclically monotone. We also show that standard adversarial training—based on per-sample local optimization—violates cyclical monotonicity and wastes transport costs unless the adversary is severely restricted. We propose two remedies. First, we introduce multi-start particle ascent, which alternates parallel gradient ascent with reassignment to enforce cyclical monotonicity across samples. Second, we parameterize adversarial maps as gradients of input-convex neural networks, which guarantees cyclical monotonicity by construction. Experiments on robust regression, image classification, and robust control show that our methods consistently outperform standard adversarial training and state-of-the-art baselines, achieving improved robustness and better generalization under distribution shift.

This article is concerned with the asymptotic shape of quantile surfaces, defined as the set of quantiles at a given level $\alpha$ generated by a controlled one-dimensional distribution. Specifically, when the distribution arises as a linear combination of log-normal random variables and the control is a vector of positive coefficients, we prove that quantile surfaces are globally concave in the left tail ($\alpha\to0$) and globally convex in the right tail ($\alpha\to1$). Moreover, these surfaces exhibit asymptotic separation of scale and shape.

Accurate modeling of dependent degradation processes is essential for credible reliability assessment and remaining useful life (RUL) prediction in complex systems. Existing dependent degradation models usually describe dependence using correlation-based methods with symmetric characteristics. However, they ignore inherent causal directionality between degradation paths, which may lead to biased reliability evaluation and RUL predictions when physical causality exists. To address this issue, this paper proposes a causality-driven framework for modeling dependent degradation data. Firstly, univariate degradation models with multi-source uncertainties are established for each performance indicator based on the Wiener process. Then, the stable Peter-Clark algorithm is employed to uncover inherent causal relationships between degradation processes, and an uncertainty-aware neural network is employed to quantify causal effects considering uncertainties. Next, univariate degradation predictions and causal predictions are integrated within a Bayesian framework to construct a causally dependent degradation model, and the corresponding loss function is derived for model training. Finally, system reliability and RUL predictions are derived via Monte Carlo simulation. The proposed methodology is validated on the C-MAPSS dataset. Results show that considering inherent causal directionality between degradation processes helps eliminate physically unrealistic degradation behaviors, yielding more accurate degradation and RUL predictions than independent and correlation-based dependent degradation models.

Many studies expose units to several binary treatments at once and record several correlated outcomes, yet analysts usually estimate one treatment's average effect on one outcome at a time – discarding how treatments interact and how their effects vary across units. We introduce the factorial multivariate Bayesian causal forest, a Bayesian nonparametric model that decomposes the factorial response surface over the treatment lattice into a prognostic sum-of-trees plus one sum-of-trees per main or interaction effect, each with correlated multivariate leaf parameters, estimated jointly with coherent uncertainty. A single indicator-weighted kernel samples every component – the prognostic term is the special case whose indicator is unity – so the two-treatment model, the single-treatment multivariate causal forest, and a general order-r truncation are one and the same sampler. We give the ANOVA/Möbius identification of each estimand, an efficient Rcpp engine, and an interpretability layer using value-suppressing uncertainty maps. In simulations the average-effect estimators are unbiased with nominal coverage, consistent, and robust under misspecification, failing only under unmeasured confounding, which we flag. We illustrate the method on clinical, agricultural and economic data and on a deeper application to the NHANES survey. Software is provided as an R package.

Unobserved common causes are pervasive in real-world time series and can induce spurious associations that causal discovery methods mistake for direct edges. We propose LUCID (Learning Under Confounding for Inference and Discovery, a regime-adaptive deconfounding layer that first estimates the confounding regime from data using a Marčenko–Pastur spectral router, then applies a deconfounding strategy matched to that regime. When the spectrum indicates pervasive factor confounding, LUCID attenuates factor-dominated variation and recovers contemporaneous (lag-$0$) structure from the resulting innovations, with edge selection calibrated against a data-driven edge-free null. Rather than being tied to a particular discovery algorithm, it can wrap existing discovery engines; we demonstrate consistent improvements across three such methods. On a diverse synthetic out-of-distribution benchmark spanning changes in confounder strength and sparsity, loading density, lag structure, volatility dynamics, edge heterogeneity, persistence, intermittency, and tail behavior, LUCID achieves the best family-weighted directed, lag-resolved graph $F_1$ ($0.60$), improving over the strongest baseline by $0.19$ absolute ($\approx\!46\%$ relative). Its advantage widens relative to looser lag-collapsed scoring, and remains robust under intermittent and heavy-tailed confounding. Code reproducing the method, the benchmark generators, and every reported experiment is available at https://github.com/bloomberg/causal-ts.

Certified defenses that incorporate differential privacy have proven effective on Convolutional Neural Networks (CNNs), furnishing rigorous robustness guarantees against norm-bounded adversaries. However, the certified robustness behavior of Pixel Differential Privacy (PixelDP) remains largely unexplored with the self-attention architecture now dominating the deep-learning landscape. Given that the Transformer has a profound impact on our daily applications from the digital world to the physical world, it is crucial to study certified robustness through differential-privacy-style stability. To fill this research gap, we revisit this construction in Vision Transformers and identify a failure mode that is largely hidden in the convolutional setting. When noise is injected after the patch embedding, the Laplace mechanism with the inherited grouped $\ell_1$ sensitivity bound collapses to chance-level accuracy across noise scales, whereas the Gaussian mechanism remains trainable. This contrast isolates the source of failure: not the injected noise itself, but the geometry of the sensitivity constraint. We show that the attenuation induced by the inherited $\Delta_{1,1}$ projection increases with layer width and kernel size according to a random-matrix scale $C/(\sqrt{M}+\sqrt{N})$. Replacing the $\ell_1$-type constraint with a spectral-norm constraint eliminates the collapse across datasets and architectures, but creates a fundamental obstacle: the repaired models no longer satisfy the sensitivity condition required by the standard Laplace certificate. We resolve this mismatch by deriving a dimension-free $(\varepsilon,\ \delta)$-privacy guarantee for the Laplace mechanism under $\ell_2$ sensitivity through concentration of the privacy loss.

We study geometric moment contraction (GMC) of the constant-parameter stochastic Nesterov recursion \[ Y_k=\Theta_k+\beta(\Theta_k-\Theta_{k-1}),\qquad \Theta_{k+1}=Y_k-\gamma G(Y_k,X_{k+1}). \] Under mean strong monotonicity and stochastic $L^p$ Lipschitz continuity, an explicit Perron comparison proves synchronous $L^p$ contraction when $\beta\gamma L_p<(1-\beta)(1-q_{\gamma,p})$. This direct criterion includes infinite-variance gradients for $1<p<2$, but its small-step regime requires $\beta<\mu/(\mu+L_p)$. A complementary power-Lyapunov argument establishes a positive, generally much smaller, step-size interval for every fixed $\beta<1$ and every $p>1$, using only a finite $p$th gradient moment. At $p=2$, a simpler explicit certificate gives \[ 0<\gamma<\frac{2\mu(1-\beta)^2}{L_2^2(1-\beta+2\beta^2)}. \] Its quadratic high-momentum scaling is a limitation of the chosen metric, not a sharp stability boundary. We quantify this loss, provide a general mean-only quadratic $S$-procedure, and exploit endpoint Lyapunov inequalities under stronger samplewise sector information. Verified endpoint certificates can be orders of magnitude less conservative than the explicit metric.

Gaussian process prediction is a central tool in spatial statistics, but standard implementations require dense matrix operations that become prohibitive for large datasets. We propose a scale-adjusted compactly supported working correlation for Gaussian process prediction, using the generalized Wendland family with a support radius $\phi_n$ that is allowed to decrease with the sample size $n$. Under fixed-domain asymptotics with quasi-uniform designs, a fixed support radius does not yield asymptotic sparsity, whereas a shrinking support radius can make the covariance matrix sparse. We show that $\phi_n$ and the regularization parameter can be jointly chosen so that the resulting predictor preserves the optimal integrated mean squared prediction error rate while reducing the number of nonzero covariance entries and the associated sparse matrix-vector multiplication cost. We also establish an analogous rate-preserving sparsification result for kernel ridge regression. Simulations and an ERA5 temperature application show that the proposed method achieves competitive prediction accuracy while retaining the computational efficiency provided by sparse linear algebra.

Reliable high-dimensional variable selection requires scalable error-controlling methods. The Terminating-Random Experiments (T-Rex) selector estimates the false discovery rate (FDR) by aggregating early-terminated forward-selection paths in which predictors compete with synthetic dummies. We address two remaining challenges: i) predictor dependence can bias dummy-predictor competition; ii) computation is wasted on recomputing terms shared across experiments. Building on memory-efficient virtual dummies, which sequentially sample projections from their exact conditional law, we estimate the conditional Gaussian law of inactive predictors and map draws onto the remaining sphere radius. A shared lazy Gram cache computes the response product and each requested Gram column once across experiments. Simulations across three covariance structures show that uniform spherical dummies can exceed the target FDR, whereas the proposed method empirically controls FDR. Caching yields more than a sixfold speedup, and the method remains feasible with 100000 predictors, where competing FDR-controlling methods become computationally impractical.

Large language models (LLMs) as a judge enable scalable evaluation, but their judgments can be sensitive to response order and, even after removing such position effects, can still diverge systematically from human preferences.We introduce DIAL, a unified framework that combines abundant LLM comparisons with limited human comparisons to separate judge-specific position effects, learn shared structure in position-debiased LLM preferences, and adaptively calibrate that structure toward the human preference target. Theoretically, we study three aspects of DIAL: (i) identification of latent LLM preferences, position effects, and human calibration; (ii) adaptive estimation that balances LLM anchoring against limited human evidence; and (iii) fixed-weight uncertainty quantification for the calibrated human preference. Empirically, we evaluate position debiasing and human alignment separately in controlled simulations and on three human-preference benchmarks, showing that DIAL remains robust to unbalanced response order, achieves strong human-aligned rankings with limited labels, and adapts toward human evidence when LLM information is imperfect. Our real-data study collects over 410K judgments from 21 LLM judges in both display orders, providing a resource for future studies of LLM-judge bias, heterogeneity, and human alignment.

This paper develops prediction models for population-level survival curves observed over time and sampled from a heterogeneous mix of populations. We consider a discrete-time setting where each curve is only partially observed and forecasts of the remaining trajectory are needed for downstream decision making. Our approach recasts cross-population heterogeneity into a multivariate sampling model. We propose two forecasting models for partially observed curves: a full factor analysis model that extends a general factor representation to incorporate the partially observed survival curve, and a double PCA model. The methodology is motivated by demand forecasting in short-term rental markets, where market-level occupancy paths can be viewed as survival curves over the booking horizon and where forecasts of future occupancy feed into dynamic pricing algorithms. We apply the models to the newly released Wheelhouse dataset, which contains time series of market occupancy curves for 500 markets from 2017 to 2022. Model performance is assessed using the integrated quadratic distance, and we compare the proposed PCA-based methods to Holt's linear trend model across multiple forecast horizons. The results show that the proposed models yield accurate and stable forecasts of the remaining survival trajectory and generally outperform Holt's method, particularly at longer horizons.

LLM-as-a-judge has become the de facto standard for scalable, subjective evaluation, yet current leaderboards compensate for systematic measurement bias by running ever more comparisons, an approach that is both statistically unsound and computationally wasteful. The root cause is an incomplete measurement model, treating LLM judges as neutral, interchangeable instruments ignores documented biases like position bias, verbosity bias, judge severity, and self-enhancement, that no volume of additional data can eliminate. We propose a unified latent variable framework that jointly models pairwise and ordinal data while explicitly correcting for these confounders, recovering reliable rankings from substantially fewer comparisons. Because fitting this model costs negligible compute relative to a single round of LLM inference, bias correction is not only more statistically rigorous but also a more sustainable approach to trustworthy evaluation.

To design systems that are protected against events much rarer than the observational record, extreme-value methods are needed to extrapolate distribution tails. Tail-index estimators such as the Hill estimator are central to this extrapolation, but overestimating the tail exponent can lead to substantial underestimation of rare-event probabilities. Motivated by this, we derive large- and moderate-deviation asymptotics for the Hill estimator and use them to construct estimators whose probability of exceeding the true tail index decays at a controlled exponential rate (the decay rate). In the large-deviations regime, we show that a simple rescaled version of the Hill estimator achieves an optimal balance between bias and decay rate among scale-invariant estimators based on the same top $k$ order statistics. Under a second-order condition, we quantify the effect of the Hill bias, analyze a bias-corrected estimator, and identify sufficient conditions for moderate deviations in the boundary case where the second-order parameter $\rho$ equals zero.

We study nonparametric multiple change-point detection for high-dimensional sequences, aiming to identify time points at which the underlying distribution changes. While many existing methods perform well when change-points are well-separated, their performance can deteriorate when structural breaks are densely clustered. To address this challenge, we propose gBottomup, a graph-based bottom-up framework for multiple change-point detection in high-dimensional settings. gBottomup constructs a hierarchical segmentation by proposing merges of adjacent segments and verifying them through an unmerge rule that combines absolute significance with relative local heterogeneity, thereby adaptively refining partitions and estimating the number of change-points. Simulation results demonstrate that gBottomup performs reliably across a range of structural configurations and is particularly effective in frequent change-point settings, where existing top-down procedures may lose sensitivity. Runtime experiments indicate favorable computational performance relative to graph-based top-down alternatives. We illustrate the proposed method through an analysis of a S&P 500 dataset.

The flatness of the loss landscape at a minimizer is a widely used heuristic for reasoning about neural-network generalization, yet evidence for this relation is mostly empirical and controversial. We study this relation in a teacher-student tree committee machine, where both the ERM estimator and the Hessian spectrum are analytically tractable in the proportional high-dimensional limit. First, we use a zero-temperature Gibbs formulation to obtain predictions for the observables of the typical minimizers of the empirical loss. Secondly, we use Edwards-Jones formalism to derive the limiting Hessian resolvent around these typical minimizers. All predictions agree with finite-size gradient-descent simulations. Finally, we study three measures of flatness, namely the left and right edges and the spectral mean, and check if a decrease in generalization error as the dataset size is increased corresponds to an increase in flatness. We find that the answer strongly depends on the learning task and on the ratio of the number of parameters to the number of data points. In regression, the spectral mean and right edge correlate with the generalization error, while the left edge does so only in the overparametrized regime. In classification this correlation reliably holds only in the highly overparametrized phase, while for underparametrized networks it can even reverse.

Knowing where species occur is fundamental for biodiversity research and conservation. Species distribution models (SDMs) link species observations to environmental conditions to estimate their spatial distribution. However, accuracy varies with the underlying data and models, making it essential to know for which species models can be trusted. Deep-learning-based SDMs ("DeepSDMs") now jointly model thousands of species, drawing on hundreds of millions of community-science records. At this scale, averaging performance hides substantial species-level variability, particularly for rare species, often of greatest conservation concern. Records are also strongly biased, making occurrence counts misleading. Accounting for these factors is essential for a reliable and informative evaluation of multi-species SDMs. Here, we introduce a Sampling-Aware Global Evaluation (SAGE) benchmark, combining GBIF records for training with sPlotOpen vegetation plots for presence-absence evaluation across 5771 plant species. We propose an evaluation framework that groups species based on two properties, sampling effort and relative prevalence, which describe how densely a species' range is sampled and how frequently the species is recorded. Evaluating single-species SDMs and multi-species DeepSDMs, we find that Random Forests and DeepSDMs perform best overall, but neither dominates: DeepSDMs outperform single-species SDMs for infrequently recorded species while offering no consistent advantage for well-sampled ones. Crucially, this advantage emerges only when established bias-correction practices, such as spatial thinning and reweighting, are carried over to the deep-learning setting. SAGE helps identify the species and data conditions for which a given approach is beneficial, thereby supporting the development of more transparent and ecologically credible SDMs. Data and code: https://earens.github.io/sage/