Papers

We study the query complexity of obtaining a relative Fisher information guarantee for sampling from a log-smooth non-log-concave distribution; this is a sampling analog of finding an approximate stationary point in optimization. Our algorithm is based on the proximal sampler, which is an implicit discretization of the Langevin diffusion, and requires an implementation of the backward step known as the restricted Gaussian oracle (RGO). We show that by leveraging the recent results for log-concave sampling with high-accuracy guarantees in Rényi divergence, we can obtain an approximate RGO implementation that – when used with the proximal sampler – yields a complexity guarantee in relative Fisher information that inherits the same dimension dependence as log-concave sampling, and improves upon prior work for non-log-concave sampling. We also show a converse reduction that any improvement in the dimension dependence in relative Fisher information for non-log-concave sampling will yield an improved dimension dependence for high-accuracy log-concave sampling.

Cross-fitting is a key ingredient in many semiparametric estimation procedures, such as double/debiased machine learning (DML), enabling valid estimation of low-dimensional targets in the presence of high-dimensional nuisance functions by enforcing out-of-sample use of nuisance predictions. crossfit is an R package that provides a general-purpose, estimator-agnostic cross-fitting engine. Users specify (i) a target functional and (ii) a directed acyclic graph (DAG) of nuisance models, with node-specific training fold widths and target-specific evaluation windows. The engine executes a reproducible schedule over folds, panels, and repetitions, returning either a scalar estimate (mode="estimate") or a cross-fitted predictor function for application to new data (mode="predict"). Beyond standard cross-fitting, crossfit implements fold-allocation modes that control how training data are shared across nuisance components, including disjoint and independence-enforcing allocations that duplicate reused nodes to reduce dependence between nuisance branches. The implementation targets simulation-heavy benchmarking and method development, with explicit and auditable schedules, defensive validation of specifications and nuisance dependencies, reuse-aware caching to avoid redundant refits, and failure isolation policies for large experiment grids. The crossfit package is available on CRAN, openly developed on GitHub under GPL-3, and is intended as a lightweight, tested foundation to prototype and empirically evaluate cross-fitted estimators with explicit control over fold geometry, dependence, and computation.

The distance dependent Chinese Restaurant Process (ddCRP) provides a flexible prior distribution for clustering observations, incorporating covariate information through pairwise distances and accommodating a rich variety of cluster structures. When cluster parameters are conjugate to the likelihood, Bayesian inference is straightforward. In the non-conjugate setting, however, inference becomes substantially more challenging due to the trans-dimensional parameter spaces that arise as cluster assignments change. We develop a reversible jump Markov chain Monte Carlo (RJMCMC) framework to address this challenge, targeting the dimension-changing nature of cluster parameter vectors when observation assignments are updated. We introduce and compare several proposal strategies for birth and death moves, including prior-based, independence, and data-driven moment-matching proposals that target regions of high posterior density. For fixed-dimensional moves, we propose a posterior resampling strategy that improves acceptance rates while maintaining computational efficiency. Through a simulation study and an application to Old Faithful eruption durations, we demonstrate moment-matched proposals offer a principled, data-driven alternative to prior-based proposals. The resulting methodology provides a general RJMCMC framework for ddCRP models with non-conjugate likelihoods, demonstrated here on both discrete and continuous observation models.

Researchers and practitioners in the field of reliability engineering and optimization frequently use active redundancy techniques to intensify the performance of systems. In this article, we study allocation strategies of non-matching active redundancies (spares) in coherent systems consisting of possibly dependent and identical components for achieving better system reliability. The dependence of the components is modeled through copulas using the distortion function. Sufficient conditions are derived to establish optimal allocation strategies for two heterogeneous active redundancies at the component or system levels. Moreover, the results are true for the component lifetimes following a general family of parametric distributions. The results guarantee the likelihood ratio (reversed hazard) ordering between the coherent systems at the component level (system level) active redundancies. Some aging properties are also established in this endeavor. Several examples are provided to demonstrate the theoretical results.

Score-based generative models are trained in high-dimensional ambient spaces, yet many data distributions are supported on low-dimensional nonlinear structures. We prove that, for compact $d$-dimensional smooth manifolds $\mathcal{M} \subset [0,1]^D$ with $d > 2$ and $\beta$-Hölder densities strictly positive on $\mathcal{M}$, a variance-preserving SGM estimator attains the intrinsic Wasserstein–1 sample exponent $\tilde{\mathcal{O}}(D^{\mathcal{O}_\beta(d)}n^{-(\beta+1)/(d+2\beta)})$, up to logarithmic factors and explicit geometry and density factors. The full nonasymptotic bound explicitly isolates the finite-order geometry envelope, Hölder radius, density lower bound, ambient dependence, and finite-order correction terms. The analysis separates score approximation into a large-noise tangent-cell regime and a small-noise projection-centered, de-Gaussianized Laplace regime. The key technical ingredient is a ReLU implementation of nearest-projection coordinates via finite intrinsic anchors and Gauss–Newton iterations, rather than approximating the manifold projection as a black-box high-dimensional smooth map. Consequently, for families with polynomially controlled geometry and density lower bounds, the constructed score-network parameters have polynomial ambient dependence.

Suppose we have an observed path from a point process counting event occurrences in a large population. Based on the observed path, we would like to test the null hypothesis that the conditional intensity of the point process belongs to a particular parametric family. We propose a novel approach to conducting such goodness-of-fit tests. The idea is to construct a unitary transformation of a natural parametric testing process such that it converges weakly to a “standard” target process, independent of the particular parametric form assumed under the null hypothesis. This transformation therefore paves the way for asymptotically distribution-free goodness-of-fit testing of parametric point processes. We demonstrate the good finite-sample performance of our approach through Monte Carlo simulations of Aalen-type survival processes, without and with censoring, mixture cure models, and software reliability models, and we illustrate its applicability with observed human lifetimes as well as real software failures.

The Chain-Ladder (CL) method remains the dominant macro-level technique for claims reserving in non-life insurance, yet its classical formulation lacks a coherent probabilistic foundation. Existing stochastic extensions-including the Mack model and the Over-Dispersed Poisson (ODP) framework-provide measures of uncertainty but rely on second-moment assumptions or quasi-likelihood variance structures without clear generative interpretations. This paper develops a Negative Binomial Chain-Ladder (NB-CL) model that embeds the CL method within a full likelihood-based framework. The key contribution is a micro-level derivation showing that the negative binomial distribution arises naturally from a Poisson-Gamma construction: claims arrive according to a Poisson process with Gamma-distributed accident-year heterogeneity, and aggregation yields negative binomial incremental counts. This derivation gives the dispersion parameter $\kappa$ a structural interpretation as accident-year heterogeneity, rather than an ad-hoc overdispersion adjustment. The NB-CL model generalises the Poisson Chain-Ladder model in the limit $\kappa \to \infty$, shares the point estimates of the ODP model while differing in its variance function (quadratic vs. linear), and unifies the Chain-Ladder family within a single probabilistic hierarchy. A parametric bootstrap procedure is developed to incorporate both process and parameter uncertainty. Simulation studies confirm near-nominal coverage under correct specification once the dispersion parameter is bias-corrected, and a controlled degradation under model misspecification. Empirical illustrations on claim count data (Australian motor bodily injury) and paid amounts (Taylor-Ashe) document both the structural reading of $\kappa$ and the working-approximation status of the model in the amounts case.

In regression models fitted to data from complex survey designs, sampling weights often incorporate non-essential variation, inflating variance estimates. Stabilized weights mitigate this issue by adjusting sampling weights to account for variation explained by covariates. In the context of two-phase sampling, we evaluate the performance of optimal stabilized weights and propose combining the stabilized weight estimator with generalized raking, a class of efficient design-based estimators. This combination improves efficiency by reducing unnecessary weight variation and leveraging information from auxiliary variables. We show this combination can be implemented using the standard statistical package that handles two-phase samples and generalized raking. Simulation studies demonstrate that the proposed estimator enhances precision under realistic two-phase designs, though efficiency gains may be limited in highly informative designs. The developed methods were applied to a large multinational two-phase study of Kaposi sarcoma among people living with HIV.

Uncertainty quantification is essential in safety-critical settings–from autonomous driving to aviation, finance, and health–where decisions must rely on conservative bounds rather than point estimates. Predictor-level intervals (e.g., from quantile regression, conformal prediction, variance networks, or Bayesian models) generally do not compose: adding two per-variable intervals need not yield a valid interval for their sum or preserve coverage. In aviation, Gaussian overbounding replaces complex error distributions with a conservative Gaussian whose tails dominate the truth, so conservatism propagates through linear operations. Yet classical overbounds are global, often overly conservative, and hard to adapt to feature-conditioned errors. We propose a unified learning framework that trains neural networks to produce context-aware Gaussian overbounds–mean and scale–with provable conservatism on a finite quantile grid and, under three explicit regularity assumptions, continuous-tail conservatism on a certified interval. Our overbounding loss enforces conservativeness at selected quantiles while penalizing distributional distance with a Wasserstein-style term. The learned bounds support conservative linear-combination and convolution analysis on the enforced grid, and on the certified interval when assumptions hold, while being less redundant than traditional methods. We provide a scoped analysis of discrete-to-continuous conservatism and compact-domain objective regularity, and validate on synthetic data and real-world datasets, including multipath, ionospheric, and tropospheric residual errors. Across these settings, the method yields tighter bounds while maintaining conservatism on the enforced grid and in experiments. The framework is modality-agnostic and applicable to learning systems that require conservative, feature-conditioned uncertainty estimates in dynamic environments.

Acute psychological stress occurs in a wide range of everyday contexts, including transportation, occupational settings, and physical activity, where its reliable detection could enable adaptive system responses and support human well-being. A persistent challenge in automated stress recognition is disentangling the biometric signatures of acute psychological stress from those of concurrent physical exertion. This study examined how five physiological signals (tonic electrodermal activity, trapezius electromyography, heart rate, heart rate variability, and respiration rate) respond to cognitive stress and physical activity, independently and in combination. Nineteen participants completed a 2x3 within-subjects design in which acute psychological stress was induced via an n-back arithmetic task combined with social pressure and financial reward, across three activity conditions: idle sitting, walking, and stationary cycling. Multilevel linear mixed models and repeated-measures ANOVA were used to decompose main effects and interactions for each sensor. Tonic electrodermal activity showed a robust, additive response to both cognitive stress (r=0.48) and physical exertion (r=0.67), with no interaction, making it the most promising candidate for stress detection during physical activity. Heart rate and trapezius electromyography were driven almost exclusively by physical exertion, with no reliable sensitivity to the stress task. RMSSD was strongly suppressed by physical activity and showed only marginal sensitivity to cognitive load. Respiration rate was dominated by physical activity, with no reliable stress effect in the primary analysis. These findings provide a sensor-specific hierarchy for real-world stress detection and highlight tonic electrodermal activity as the most informative channel when cognitive stress must be identified in physically active populations.

Causal inference with time-to-event outcomes is fundamental in various scientific studies. In a static setup with fitted propensity scores, weighted Kaplan-Meier estimation for survival probabilities and weighted Breslow-Peto estimation for hazard ratios have been widely used, but their statistical properties have been overlooked or studied only to a limited extent. We re-examine the weighted Kaplan-Meier method by formally linking it with the general framework of augmented inverse probability weighted estimation including both point and variance estimation. Furthermore, to address limitations of existing weighted methods for survival analysis, we develop new methods and associated theory through calibrated estimation in both low-dimensional and high-dimensional settings. We present a simulation study and an empirical application on the effectiveness of adjunctive psychotropic treatments for patients with schizophrenia. The calibrated methods yield coverage proportions closer to target ones in the simulation study, and produce shorter confidence intervals in both simulation and empirical studies.

We study episodic reinforcement learning with fixed reward and transition functions, but with episode-dependent admissible action sets that are observed at the start of each episode. Performance is measured by cumulative regret against the episode-wise optimal value, $\sum_{k=1}^K [V^{*,M^k} - V^{\pi^k,M^k}]$, where $M^k$ represents the action context in the $k$-th episode. We show that the MVP algorithm naturally extends to this framework and enjoys strong theoretical guarantees. In particular, we establish a minimax regret bound of $\widetilde{O}(\sqrt{SAH^3K\log L})$ for adversarial contexts, where $L$ denotes the number of possible contexts. This result implies a regret bound of $\widetilde{O}(\sqrt{SAH^3K})$ for stochastic contexts. We further translate the stochastic regret guarantee into a sample complexity bound of $\widetilde{O}(SAH^3/\epsilon^2)$ for a fixed context distribution. In addition, we derive a gap-dependent regret bound of \[ \widetilde O\left( \inf_{p\in [0,1)} \left( \frac{1}{\Delta_{\min}^{p}} + pK\Delta_{\min}^{p} \right)\log K \cdot \mathrm{poly}(S,A,H) \right), \] where $\Delta_{\min}^{p}$ is the global $p$-trimmed positive-gap floor over suboptimal $(h,s,a)$ triples. This bound can substantially improve upon the minimax rate when the relevant suboptimality gaps are large.

Concept Activation Vectors (CAV) and the Testing with CAVs (TCAV) method are fundamental tools for concept-based explainability in deep learning, yet their practical utility is limited by the variability across different samples of concept and non-concept examples. We analyze this stochastic nature of CAVs, and identify a fundamental flaw in the standard TCAV score, its instability by using a discontinuous indicator function. To address this, we introduce $\alpha$-TCAV, a parameterized unified framework that replaces the discontinuous indicator with a smooth function, which recovers TCAV as a limiting case. Under realistic assumptions, we characterize the score distributions and derive principled parameter choices: one matches the mean of its averaged counterpart, Multi-TCAV, with no larger variance using a single CAV; the other provides a calibrated probability that the concept positively influences the model output. Our analysis and experiments provide practical guidance and challenge the established practice of splitting the sampling budget across multiple CAVs.

We propose a joint order-based scoring framework for causal structure learning of directed acyclic graph (DAG) models under heterogeneous data settings. We show that leveraging heterogeneity improves the accuracy of causal ordering estimation. In the most favorable case, the causal ordering is identifiable up to two permutations. Building on this framework, we propose an order-based Bayesian method for Gaussian DAG models and establish its theoretical properties in the high-dimensional regime. For posterior inference over the space of orderings, we introduce a random-to-random (R2R) proposal neighborhood for the Metropolis-Hastings algorithm, which is theoretically motivated and exhibits efficient mixing behavior. Simulation studies confirm the strong empirical performance of the proposed method, and an application to single-nucleus RNA sequencing data from major depressive disorder demonstrates practical utility.

Background: Survival prediction models are often less reliable in clinical groups with limited sample sizes or few outcome events. Target-only models may be unstable, whereas models from larger cohorts may transfer poorly when risk-factor effects differ across populations. We evaluated whether structured transfer learning can improve survival risk stratification in data-sparse cohorts while allowing cohort-specific adaptation. Methods: We developed the COhort-shared Rank-rEduced Cox model (CORE-Cox), a two-stage framework for multi-outcome survival prediction. CORE-Cox learns shared risk-factor patterns across related outcomes in a larger source cohort via a low-rank Cox coefficient structure, then adapts these patterns to a smaller target cohort through regularized residual correction. We evaluated CORE-Cox in UK Biobank (White source, n=150,093; Asian target, n=2,534) and MIMIC-IV (White ICU source, n=15,997; Asian ICU target, n=672), comparing against target-only Cox, penalized Cox, low-rank multi-task, naive pooling, direct transfer, and single-outcome residual transfer under repeated nested cross-validation. Results: CORE-Cox achieved best or near-best discrimination across most outcomes. Mean C-index improved from 0.733 to 0.766 in UK Biobank and from 0.628 to 0.658 in MIMIC-IV, with gains in eight of nine outcomes. CORE-Cox also improved top-15% risk enrichment, with hazard-ratio estimates typically intermediate between source-only and target-only models. Discussion: CORE-Cox offers an interpretable transfer-learning framework for survival risk stratification in data-sparse cohorts, combining shared cross-outcome structure with cohort-specific adaptation. Further validation is needed before use in calibrated absolute-risk prediction or clinical decision-making.

We study risk-aware offline policy learning, aiming to learn a decision rule from logged data that is optimal under general risk criteria. This problem is crucial in high-stakes domains where online interaction is infeasible and adverse outcomes must be carefully controlled. However, existing literature on offline contextual bandits either centers on expected-reward criteria or restricts risk considerations to policy evaluation instead of optimization. In this work, we propose a unified distributional framework for optimizing Lipschitz-continuous risk functionals, a broad class of risk measures encompassing mean-variance, entropic risk, and conditional value-at-risk, among others. By developing novel empirical concentration inequalities for importance sampling-based distributional estimators, our analysis derives data-dependent suboptimality bounds with an $\tilde{\mathcal{O}}(1/\sqrt{n})$ rate, without relying on restrictive uniform overlap assumptions. This rate is minimax optimal and matches that of risk-neutral offline policy optimization, indicating that optimizing general Lipschitz risk criteria incurs no additional statistical cost relative to the expected-reward.

We formulate and study a statistical version of Katona's two-round search problem of finding at least one excellent element in a set. A population of $n$ elements is considered, where each element is independently excellent with probability $\lambda/n$, $\lambda > 0$. A subset test is noiseless: it returns positive exactly when the queried subset contains at least one excellent element. The goal is to minimize the expected number of tests subject to finding one excellent element with probability at least $1-\alpha$, where $0<\alpha<1$, under the restriction that testing is performed in two rounds. Unlike classical group testing, the objective is not to recover the full set of excellent elements, but only to identify one of them. We first show that success is fundamentally limited by the possibility that no excellent element exists. In the sparse Poisson regime, this imposes the necessary feasibility condition $\alpha\ge e^{-\lambda}$. When the target success probability is feasible, we prove that the optimal expected number of tests grows logarithmically with the population size. The upper bound is obtained by combining an initial existence test with a second-round separating design; the lower bound follows from an information-counting argument. Numerical illustrations show the feasibility boundary and the resulting logarithmic scaling.

Prewhitening is a common approach to deal with strong autocorrelation. In this article, we propose a new approach called tail postcoloring, motivated by it. It uses parametric models to project, or color back, the neglected tail autocovariances in nonparametric estimators onto the final estimator. This approach bridges the non-parametric variance estimator and the parametric coloring model through a scaling factor. It automatically switches between these two arms using a bandwidth parameter, without the need to transform the entire dataset into residuals, as in the standard prewhitening approach. When the coloring model is well-specified, a parametric rate can be achieved. In finite samples, it is also more robust to misspecification of the coloring model compared to the whitening model in the standard approach. Besides, it avoids severe potential variance inflation or power reduction caused by the recoloring factor in the standard approach. We show that multiple parametric models can be used to construct a multiply robust tail postcolored estimator. It also naturally works for multivariate time series. A real-data example in Markov chain Monte Carlo output analysis is provided.

Estimating the number of distinct elements in a data stream is well understood when repeated elements are identical. In modern settings, however, observations are high-dimensional and noisy, so repeated instances of the same object are only approximately similar – for example, different images of the same individual may vary significantly at the pixel level. Classical sketches such as HyperLogLog rely on consistent hash values for identical elements and break down in this regime. Recent work on robust distinct counting in general metric spaces achieves $\widetilde{\Theta}(\sqrt{n})$ memory, which is tight in the worst case. We show that substantially improved memory guarantees are possible under geometric structure common in learned representations. We introduce MaxSketch, a simple max-linear sketch built from random Gaussian projections, and prove that it succeeds in estimating the number of distinct latent objects. Concretely, we show that under this assumption $m = \widetilde{O} (\log n / \varepsilon^2)$ random projections (and hence $\widetilde{O} (\log n/\varepsilon^2)$ memory) suffice to recover the true distinct count within a $(1+\varepsilon)$ factor. Experiments on image streams confirm that MaxSketch accurately estimates distinct counts and generalizes beyond the training regime. Our results bridge classical streaming algorithms and modern representation learning, showing how geometric structure can fundamentally reduce the complexity of distinct counting.

We derive explicit upper bounds for the number of nondegenerate critical points of a $k$-component Gaussian mixture density in $\mathbb{R}^d$, and the number of modes when the modal set is finite, together with lower bounds. By normalizing the critical-point equations by a reference component, for $k\ge2$ we get the direct Pfaffian bound \[ U_{\mathrm{het}}(d,k)=2^{\,d+\binom{k-1}{2}}\left(d+2\min(d,k-1)+1\right)^{k-1}. \] For the same parameter range, an exact elimination augmented by an algebraic reciprocal variable gives the alternative bound \[ U_{\mathrm{aug}}(d,k)= 2^{\binom{k-1}{2}}(d+1)\left((2k-1)d+2k-1\right)^{k-1}. \] Thus, for $k\ge2$, the best critical-point bound is their minimum. A Morse-theoretic argument improves the corresponding finite-mode upper bound to \[ \left\lfloor \frac{\min\{U_{\mathrm{het}}(d,k),U_{\mathrm{aug}}(d,k)\}+1}{2}\right\rfloor. \] In the homoscedastic case, for $k\ge2$, the direct bound improves to \[ U_{\mathrm{hom}}(d,k)=2^{\,d+\binom{k-1}{2}}\left(d+\min(d,k-1)+1\right)^{k-1}, \] an affine-rank reduction replaces $d$ by the affine rank of the component means, and an augmented homoscedastic reduction gives the dimension-free bound \[ U_{\mathrm{aug,hom}}(k)=2^{\binom{k-1}{2}+1}(2k)^{k-1}. \] On the lower-bound side, for $d,k\ge 2$ we obtain \[ L_{\mathrm{bin}}(d,k)=k+\max_{2\le r\le \min(d,k)}\binom{k}{r}, \] together with a padding-product family that in particular implies the linear lower bound $d+k-1$, and a seed-closure principle that packages product and padding constructions. We further give explicit bounds for the number of connected components of the critical set.

Point cloud learning often rests on the premise that observed samples are noisy traces of an underlying geometric object, such as a manifold embedded in a high-dimensional feature space. Yet much of this geometry is not captured directly by coordinates, pairwise distances, or learned graph neighborhoods alone. In the smooth setting, differential forms are devices to encode higher order tangency information. In this work, we introduce a new family of principled learnable geometric features for point clouds called neural point-forms (NPFs). In the absence of a natural tangency structure, we instead use Laplacian-based techniques from Diffusion Geometry to build a discrete model for comparing differential forms on point clouds via inner products. In the continuum, submanifolds of a shared ambient feature space are represented as comparison matrices, whose entries describe how pairs of feature forms interact with extrinsic tangency information. We make this intuition precise by proving the long-run consistency of comparison matrices under standard sampling, bandwidth, density, and manifold-hypothesis assumptions. This yields a compact, efficient and permutation-invariant neural layer whose output is a learned form-comparison matrix. Across synthetic and biologically relevant experiments, we show that NPFs provide a competitive, and interpretable representation, with the strongest benefits appearing when labels depend on sampling density, manifold-like structure, or response-relevant population geometry.

Liquid-cooled exascale supercomputers dissipate heat through cooling plants organized as multiple parallel subloops, but how to allocate coolant distribution units (CDUs) across subloops and how to distribute flow among them has not been systematically addressed for facilities at this scale. This paper presents a three-layer optimization framework that jointly determines the integer partition of CDUs across subloops, the continuous flow fraction allocation, and the per-timestep co-design optimization of total flow rate and supply temperature subject to per-subloop thermal safety constraints. The Modelica simulation model is built based on the data of the Frontier exascale supercomputer at Oak Ridge National Laboratory. By developing a reduced-order surrogate model, all 611 feasible partitions of 25 CDUs are evaluated across the full year operational dataset of 49,353 timesteps. Three progressively richer operational strategies are compared, ranging from flow control optimization to full three-layer co-design optimization with dynamically adjusted flow fractions. The optimal design within the surrogate optimization problem is a two-subloop plant achieving 35.48% annual cooling energy savings, only 0.18% above the current three-subloop design at 35.30%. Most of the savings are delivered by supervisory co-optimization of total flow rate and supply temperature; the distinct role of flow fraction optimization is design robustness rather than additional raw savings. Flow fraction optimization compensates for any feasible CDU-to-subloop assignment, reducing the design sensitivity by 93% and providing a low-cost software-only pathway to near-optimal performance on the existing Frontier hardware. The framework is transferable to other liquid-cooled high-performance computing plants.

Survival analysis provides a powerful statistical framework for modeling time-to-event outcomes in the presence of censoring. However, selecting an appropriate estimator from the many specialized survival approaches often requires substantial methodological and domain expertise. We introduce SurvivalPFN, a prior-data fitted network that amortizes Bayesian inference for censored observations through in-context learning. SurvivalPFN is pretrained on a diverse family of synthetic, identifiable, and right-censored data-generating processes, enabling it to amortize survival analysis in a single forward pass during inference. As a result, the model adapts to the effective complexity of each dataset without task-specific training or hyperparameter tuning, avoids restrictive parametric assumptions, and produces calibrated survival distributions. In a large-scale benchmark spanning 61 datasets, 21 methods, and 5 evaluation metrics, SurvivalPFN achieves strong predictive performance and often improves upon established survival models. These results suggest that SurvivalPFN offers a principled and practical foundation model for survival analysis, with potential applications in high-impact domains such as healthcare, finance, and engineering (https://github.com/rgklab/SurvivalPFN).

Distributed systems must frequently keep track of many different types of performance metrics across many different computers. For example, the latency distribution of certain operations may be computed for a large combination of computers, users, and operations. These empirical distributions need to be collected at minimal expense on the individual software components, efficiently aggregated across multiple dimensions, and stored in a compact representation for a variety of downstream data analysis applications. We describe an information loss metric for binned data that allows us to optimize cost of information loss from different histogram representations. We explore the use of polynomial histograms where each bin of a histogram is annotated with moments of the underlying distribution in that bin. These polynomial histograms are compared to traditional histograms using the same storage cost for additional bins instead of annotations in each bin. We describe an application of these techniques for file system metrics for a large production system, and analytically characterize when polynomial histograms offer more information at lower cost.

The operational reliability of a high performance marine vessel depends critically on the health of its marine propulsion systems, which are increasingly subjected to diverse operational loads and environmental stressors. This paper proposes a robust mathematical framework for non-linear state-space forecasting of marine engine parameters using adaptive-window multi-particle stochastic differential equations. Traditional time-series models such as Vector Autoregressive Integrated Moving Average, often fail to capture the inherent stochasticity and transient dynamics of complex systems due to their reliance on fixed-window linear assumptions. To address this, we develop a dual-layered estimation approach: first, an adaptive lookback mechanism dynamically adjusts the learning window size based on the instantaneous drift magnitude, ensuring responsiveness during non-stationary regimes. Second, a Multi-Particle ensemble is evolved via Euler-Maruyama discretization, where each particle trajectory represents a stochastic realization of the system state. To refine the ensemble mean and mitigate the "noise-chasing" behavior of raw estimators, a Girsanov transform induced change of probability measure is implemented, assigning higher probabilistic weights to particles that align with the physical drift. Theoretical evaluation and empirical benchmarking demonstrate that the proposed adaptive SDE framework significantly outperforms classical statistical baselines in multi-step prediction stability and computational efficiency. The model provides a scalable, "grey-box" solution for real-time risk quantification in systems characterized by high-frequency volatility and non-linear transitions.

Probabilistic prediction systems often aggregate probability estimates from multiple models into a single decision. A common assumption is that if each model is individually calibrated, the aggregate prediction will also be well calibrated. We show that this assumption fails in multi-agent settings: individually calibrated predictors can become collectively miscalibrated when their predictions interact strategically, in the game-theoretic sense of Brier-optimal local response, even without deliberate coordination. This phenomenon arises naturally when agents are independently trained on overlapping data. We prove that under Brier-score-based aggregation with positively correlated beliefs, each agent's individually optimal report systematically underestimates the positive-class probability, yielding a Price of Anarchy greater than one whenever Cov(b_i, b_j) > 0. In a canonical setting (n = 5 agents, pairwise correlation = 0.5, base rate = 0.3), the empirically measured PoA in false-negative rate reaches 7.25x. In contrast, VCG-based aggregation aligns incentives by rewarding marginal contribution, achieving dominant-strategy incentive compatibility and near-optimal performance. Experiments on three real-world datasets (NSL-KDD, UNSW-NB15, Credit Card Fraud) show that VCG provides strong robustness while maintaining comparable accuracy. It performs particularly well in data-sparse and adversarial settings, and adaptive weighting further improves performance under distribution shift.

Subgroup analyses within randomized controlled trials are often underpowered due to limited sample sizes. We address this challenge by leveraging trial participants outside the subgroup of interest to augment estimation within the subgroup. Specifically, we study two Targeted Maximum Likelihood Estimators (TMLEs) that borrow information from non-subgroup participants within the same trial: a TMLE with pooled regression (TMLE-PR) and an Adaptive Targeted Maximum Likelihood Estimator (A-TMLE). Both estimators enable information sharing without relying on any external real-world data, thereby capitalizing on key strengths of the trial: most importantly, the protection against bias afforded by the randomized treatment, but also harmonized data collection, and consistent treatment and outcome definitions. The general strategy proposed here directly advances the priorities of key regulatory agencies, including the FDA, by improving the precision of subgroup-specific treatment effect estimates without introducing external sources of bias, thereby facilitating rigorous inference to support equitable labeling, access, and post-market evaluation. In a case study based on analysis of data from a cardiovascular outcome trial (LEADER, NCT01179048), we estimate the risk reduction of major adverse cardiac events (MACE) under liraglutide treatment among Black and Asian subgroups – each comprising less than 10% of the trial population – using the proposed estimators that borrow information from the remainder of the trial. Using A-TMLE, in particular, we find estimated absolute MACE risk reductions of 1.6, 1.5, and 1.5 percentage points among Asian participants and 2.1, 2.0, and 2.1 percentage points among Black participants at 365, 540, and 730 days, respectively, with 95% confidence intervals excluding the null at each time point.

Compositional covariates in microbiome studies are often measured with error and organized by a biological hierarchy. Tree aggregation can improve multiresolution interpretation, but it also combines leaf-level errors into correlated contamination whose scale varies across the hierarchy. Existing tree aggregation and compositional measurement-error correction do not combine directly in redundant tree coordinates because a generic positive semidefinite projection can make the corrected criterion depend on the chosen representation. TARCO resolves this mismatch by normalizing tree coordinates by descendant leaf counts and applying a kernel-preserving positive semidefinite projection to the corrected tree-space Gram matrix. The resulting criterion is constant across equivalent tree representations, and the tree-coordinate estimator is exactly equivalent to an estimator on the identifiable coefficient space. For this estimator, we establish finite-sample prediction and coefficient-estimation bounds and, under sufficient separation and an appropriate grouping threshold, exact recovery of the maximal constant subtrees of the identifiable coefficient. These guarantees extend, with additional covariance-estimation terms, when the measurement-error covariance is estimated from independent auxiliary technical replicates. In a longitudinal gut microbiome analysis, correction changes the displayed taxonomic resolution of some associations with body mass index while preserving their directions, illustrating why the hierarchy should guide both signal aggregation and error correction.

The minima of modern neural network loss functions are typically not isolated, rather they form connected components of reparameterization invariant solutions on the training data. Analytically characterizing these solutions is a hard problem, but sampling approaches are feasible. By construction, existing methods either spread over low-loss regions, and thus do not sample reparameterization invariant solutions exactly, or are inherently local, which limits exploration of other minima valleys. We propose sampling such reparameterization invariant models using a dynamical system based on kinetic energy, subject to a gravitational pull and a friction term that dissipates energy from the system. Our proposed sampler, DiMS, is guaranteed to sample exactly from the minimum level sets and depends on physically motivated hyperparameters which allows control over the exploration capabilities of the sampler. We consider uncertainty quantification in Bayesian inference as the motivating problem and observe improved performance compared to previously proposed approaches.

Reasoning-trained language models often spend more tokens on harder problems, but longer chains of thought do not show whether a model is merely computing for more steps or following a different internal trajectory. We study this distinction through hidden-state trajectories during chain-of-thought generation across competitive programming, mathematics, and Boolean satisfiability. Raw trajectory geometry is strongly shaped by generation length: longer generations mechanically alter path statistics, so difficulty-dependent comparisons are misleading without adjustment. After residualizing trajectory statistics on length, difficulty remains systematically coupled to corrected trajectory geometry across all domains studied. The clearest reasoning-specific separation appears in the code domain, where harder problems show more direct corrected trajectories and less heterogeneous local curvature in reasoning-trained models than in matched instruction-tuned baselines. Corrected difficulty-geometry coupling is weaker, but still present, in mathematics and Boolean satisfiability. Prompt-stage linear probes do not mirror the code-domain separation, and behavioral annotations show that stronger corrected coupling co-occurs with strategy shifts and uncertainty monitoring. Together, these findings establish length correction as a prerequisite for generation-time trajectory analysis and show that reasoning training can be associated with distinct corrected trajectory geometry, with the strength of the effect depending on the domain.