Papers

Forest managers need timely stand-level information to support operational planning, particularly in mixed-species, structurally heterogeneous forests facing climate-related disturbance. Model-based estimation combines sparse field data with remotely sensed predictors to estimate growing stock volume (GSV) for small areas. While uncrewed aerial vehicle laser scanning (ULS) offers flexible, high-resolution LiDAR acquisition, its advantages over conventional airborne laser scanning (ALS) remain unclear. We compared publicly available ALS and newly acquired ULS data using Bayesian change-of-support models to estimate GSV in a mixed-species forest in north-eastern Germany. We evaluated distributional LiDAR metrics and spatial random effects. ULS consistently outperformed ALS, achieving cross-validated RMSPEs of 68.5 m^3/ha and 79.5 m3/ha, respectively-a 13.8 % reduction in prediction error. Distributional metrics improved ULS models more strongly, reducing RMSPE by up to 10.1 %; spatial effects provided only minor gains at substantially higher computational cost. ULS also produced lower uncertainty in latent stand-mean GSV estimates. The ULS advantage may reflect both finer-scale canopy information and closer temporal alignment with field measurements. Timely, information rich LiDAR may therefore be more valuable for stand-level GSV estimation than increasingly complex spatial models. Temporally matched ALS-ULS comparisons are needed to isolate platform effects.

Predicting patient-specific survival functions is crucial for clinicians in making informed decisions about patient care and treatment strategies. Among the various models available, the Survival Forest has demonstrated significant effectiveness in numerous scenarios. In this work, we propose an ensemble method that leverages the strengths of the Survival Forest as the master model, complemented by several base models. This ensemble incorporates the Beran estimator, a type of kernel estimator, to enhance predictions of patient-specific survival curves. We evaluated the performance of our proposed model using four distinct healthcare datasets. The results highlight the superiority of our ensemble method over baseline models in both calibration and ranking across most datasets. The findings suggest that our approach offers a more accurate and reliable estimation of patient-specific survival functions, providing a valuable tool for clinical decision-making.

Numerous agentic workflows are based on a generator-verifier loop: a generator proposes candidates, a cheap verifier scores them, and the workflow terminates when a proposal is verified as good enough. The verifier typically proxies a more costly ground-truth oracle, and as the generator searches adaptively against it, false acceptances may accumulate. Proposals can pass the proxy but fail under the costlier ground-truth check. We study when to stop these loops while controlling the false discovery rate of the accepted proposals. Our construction introduces tools of independent interest in distribution-free statistical testing and conformal risk control, including analysis of $e$-values constructed through index betting and a novel conformal risk control procedure for non-monotone losses. We validate the approach in synthetic settings and on a protein-design benchmark.

Data imbalance is pervasive in machine learning, from rare words and anomalies to underrepresented patterns in heterogeneous or cross-tabulated data. We study idealized optimizers geometries in continuous time to model small-step training in deep learning. We assume that the source of imbalance is unobserved: the optimizer has only access to the aggregate training loss ignoring the exact contributions of the majority and minority groups. In this setting, we characterize a region where majority losses are optimized regardless of the admissible minority structure. We derive explicit equations of this zone and bounds on the time needed to leave it. These bounds exhibit a milder dependence on minority amplitude for sign, spectral, and Newton descent than for Euclidean gradient descent. Experiments with AdamW and Muon suggest similar advantages over SGD across language, tabular, and image tasks.

We consider the stability of multi-step reasoning processes, which have extensive applications in language models, including chain-of-thought and algorithmic reasoning. While longer sequences of reasoning can improve a model's generation capability at test time, the errors due to intermediate reasoning steps can accumulate in autoregressive generation, and thus grow substantially at the end. In this paper, we ask: What are the key factors determining the stability of multi-step reasoning? First, we show an inference error bound governed by the product of spectral norms of the Jacobians taken through the input space across generation steps. This product can be viewed as an error amplification factor, which could scale exponentially with the number of reasoning steps, serving as a quantitative measure of reasoning stability. Second, we analyze this measure in transformer models trained to predict simple tasks like linear and quadratic functions. We theoretically prove that the transformer model converges to a solution where the stability measure decays, thus yielding nearly zero inference loss over (arbitrarily) long steps. Finally, the stability analysis leads to several algorithmic implications for controlling the stability, through (i) chain-of-thought length compression that reduces the sensitivity of each step, and (ii) quantization-aware training that regularizes the input Jacobian norms. We validate the proposed algorithms by fine-tuning language models on graph-algorithmic reasoning tasks and symbolic state-tracking tasks. Across seven evaluations, our algorithms improve over baseline comparisons by 3.5% on average, and by 8.2% for longer-length inputs. Ablation analysis validates that the stability measure is drastically reduced by 3-8$\times$, confirming the regularization effect on the spectral norms of the (input space) Jacobians.

Gliomas are the most common type of primary brain tumors. Diffuse low-grade gliomas (DLGGs) are slow-growing tumors that are often minimally symptomatic for a long period of time. They progress to a higher grade, resulting in the patient's death. Treatments include surgery, chemotherapy and radiation therapy to control tumor progression. Responses to treatments are highly variable among patients. Furthermore, the diffuse component of this tumor entity has been observed but is not yet well measured. Here, we propose a new variable to quantify glioma morphology, called ESVR (Extra Sphere Volume Ratio). We use then a machine learning approach to study the importance of different variables for discriminating patterns of patients: patient-specific variables, genetic alterations of tumor tissue, and some image-based variables like ESVR and the volume of the tumor, obtained by MRI analysis. Our machine learning approach shows that the patient's age and ESVR at diagnosis, as well as the pathology results seem to play an important role. Taking the highlighted variables into account could thus help to model the tumor behavior. In association with other classical biomarkers, our new ESVR feature could help the clinician to manage the treatment, as it carries significant information in terms of aggressivity of the DLGG.

Background: The Expected Value of Sample Information (EVSI) quantifies the value of collecting additional evidence to inform a health economic model. Existing EVSI methods typically assume idealized data collection mechanisms, most commonly randomized controlled trials (RCTs). However, in many realistic contexts, additional evidence comes from observational studies, which are subject to confounding or other bias. In this work, we define a methodology to calculate EVSI when additional data are observational and confounded. Methods: First, we define a simulation-based framework in which confounded observational data are generated through Inverse Target Trial Emulation (ITTE), a methodology that generates observational data with controlled levels of confounding starting from initial level data or prior information on population structure. Then, we apply inverse probability weighting (IPW) to obtain an adjusted summary statistic of the data targeting the corresponding randomized estimand. EVSI is finally computed using a regression based approach. Moreover, we propose a computationally efficient method to determine the sample size required to recover the EVSI achievable under an idealized randomized design. Results: We apply the methodology to two health economic models: a Normal Normal conjugate model and a chemotherapy treatment model combining a decision tree and Markov structure. We show that EVSI computed from observational data, even after adjustment, is lower than EVSI based on randomized data. The loss in EVSI increases with the level of induced confounding. Conclusions: This methodology extends EVSI when future evidence is expected to be observational and affected by confounding, enabling value-of-information analysis in more realistic and feasible data collection scenarios. It also provides a principled approach to sample size planning when observational evidence is anticipated.

Forecasting suicide risk is difficult due to the high heterogeneity of patients and the low base rate of suicide-related events (SREs). We present Latent Similarity Gaussian Processes (LSGPs), which embed patients in a continuous latent space to jointly model similarity and forecast risk. By selectively drawing information from latent peers, LSGPs better capture individualized risk trajectories, generalizing nomothetic (pooled), idiographic (per-patient), and hierarchical frameworks. Our contributions are: (1) an identifiable two-channel Similarity Kernel; (2) proof that the standard model-fitting algorithm, mean-field variational inference, collapses LSGPs to nomothetic models, along with a fix; and (3) empirical results on intensive longitudinal suicide data showing LSGPs outperform nomothetic, idiographic, and hierarchical models for next-week risk forecasting, with the largest gains in forecasting first-occurrence SREs.

Article 50 (2) of the EU Artificial Intelligence Act requires providers of generative systems to make synthetic outputs machine-readable and detectable, while qualifying the effectiveness, interoperability, robustness, and reliability by technical feasibility, cost, content-specific limits, and the state of the art. For free-form text, one important implementation route is the implementation of a generative watermarking procedure, which poses a compliance problem that is hard to address. Strong watermarking is impossible against adaptive removal, while ordinary edits attenuate statistical evidence, and unmarked human text may overlap distributionally with machine output. This article develops an auditable alternative. First, it defines a description-length robustness profile. A finite-sample bound shows that detectable bias decays and that the required sample size grows with the inverse square of the decay rate. This replaces an unidentified Shannon-entropy constant with collision entropy. Second, it constructs label-conditional conformal prediction sets with separate false-attribution and false-exclusion levels, reporting “watermark supported,” “not supported,” or “inconclusive”. Coverage is obtained as a finite-sample result and is class-conditional under exchangeability. A small reproducible simulation of a tournament watermark confirms both claims and shows that the surviving-token rule overstates the tolerable edit rate roughly twofold. The resulting premarket certificate, signed detector report, and postmarket recalibration protocol operationalize the Commission's 2026 Code of Practice without claiming universal robustness.

We study deterministic and randomized midpoint discretizations of Langevin dynamics for a target $\pi \propto e^{-V}$, where $0 \prec \alpha I\preceq\nabla^2V\preceq\beta I$ and $\kappa=\beta/\alpha$. To achieve $\sqrt\alpha\,W_2\leqslant\varepsilon$, we show that deterministic Heun uses at most $\widetilde O(\kappa^{4/3}d^{1/3}\varepsilon^{-2/3})$ gradient queries, and underdamped exponential midpoint uses $\widetilde O(\kappa^{5/4}d^{1/4}\varepsilon^{-1/2})$. The proofs exploit cancellation at stationarity and smoothing using techniques from Malliavin calculus, outperforming previous upper bounds based on standard couplings. At bounded condition number, a lower bound matches the $d$ and $\varepsilon$ powers of both deterministic methods. To contrast, for the randomized midpoint methods and Poisson midpoint with at least two grid points (both overdamped and underdamped variants), a simple Gaussian calculation yields a lower bound $d^{1/3}\varepsilon^{-1/3}$ to get an $\varepsilon$-close sample despite starting at a benign initialization. This shows surprisingly that in high dimensions, deterministic discretizations can outperform their random counterparts.

Recovering the forward operator of an imaging system from unpaired data avoids both calibration hardware and the clean/degraded pairs that supervision requires-pairs that, for a real lens, are often impossible to acquire. Existing unpaired approaches that explicitly estimate the forward operator by distribution matching evaluate a candidate only through the measurements it generates, whose distribution should match that of the real ones. Components suppressed by the operator are barely present in the degraded images, and therefore barely constrain the operator under such a criterion. Yet inversion precisely tries to recover them. As a result, two operators that are nearly indistinguishable as forward models can invert very differently. We address this by adding a comparison on the clean side: real degraded images, once restored, should be distributed like clean ones. Restorations are computed by a differentiable plug-and-play algorithm parameterized by the operator being learned. On spatially varying PSF calibration and blind super-resolution, the method recovers more accurate operators than degraded-side matching alone, and closes much of the gap to restoration with the true operator.

Concept bottleneck models (CBMs) are neural classifiers that allow to explain their decisions via high-level concepts, potentially enabling understanding, steering and debugging. However, their explanations are often derived heuristically. Building on formal explainability, we argue they should also be faithful, i.e., not misreport which concepts actually matter. We show that, for widespread CBM architectures, including recent VLM-based variants, faithful explanations must include all concepts in the bottleneck, compromising interpretability when this is large. This result applies to both heuristic and faithful-by-construction formal explanations. To encourage the existence of compact faithful explanations, we suggest i) modeling concepts probabilistically as binary or categorical random variables (rather than logits), and ii) employing per-concept training-time sparsification via group lasso (rather than regular elastic net). We also extend algorithms from formal explainability to CBMs, and show they outperform natural heuristics in terms of guarantees and explanation size. Overall, our work warns against naive interpretability claims and provides formal conditions and practical strategies for ensuring CBMs are as interpretable as advertised.

The Bradley-Terry model is a parametric model for ranking from pairwise comparisons. Existing asymptotic theory for the maximum likelihood estimator (MLE) in regimes where the number of objects grows often requires homogeneity assumptions or compatibility conditions on comparison graphs, which limits its applicability to many practical settings. In this work, we establish uniform consistency of the MLE under general deterministic comparison designs. Our pairwise error bound consists of a pair-specific term governed by the effective resistance between the corresponding objects and a global term governed by the spectral gap of the unnormalized graph Laplacian. The bound is tight up to logarithmic factors for certain graph sequences. For any prespecified sequence of pairs satisfying an additional balancing condition, we further establish asymptotic normality of the corresponding estimated utility differences. As an application, we obtain uniform consistency for independent-edge random graph designs whenever the minimum edge probability exceeds the Erdős-Rényi connectivity threshold by a logarithmic factor, as well as asymptotic normality under additional balancing conditions.

Although the names significance test, p-value, and confidence interval came into use only in the 20th century, the methods they name were already used and abused in the 19th century. Knowledge of this earlier history can help us evaluate some of the ideas for improving statistical testing and estimation currently being discussed. This article recounts first the development of statistical testing and estimation after Laplace's discovery of the central limit theorem and then the subsequent transmission of these ideas into the English-language culture of mathematical statistics in the early 20th century. I argue that the earlier history casts doubt on the efficacy of many of the competing proposals for improving on significance tests and p-values and for forestalling abuses. Rather than further complicate the way we now teach statistics, we should leave aside most of the 20th-century embellishments and emphasize exploratory data analysis and the idea of testing probabilities by betting against them.

Establishing ordinary differential equations (ODEs) describing population data is a fundamental part of mathematical modeling in pharmacology, crucial to developing digital twins. However, doing so from sparse, noisy data is a slow, expert-driven task. Existing automated methods either search a restricted model space or ignore population inter-individual variability. Here we introduce APOD (Agentic Population ODE Discovery), a language-model agent that iteratively reasons over biological knowledge and fit diagnostics in an open-ended search space to discover a population digital twin (PDT), i.e., a shared ODE system with between-subject variability. On synthetic pharmacokinetic and tumor-dynamics benchmarks, APOD recovered ground-truth structures in 94-100% of runs, 12-fold faster in median than an established library-based search. On real cohorts it converged to valid structures, and proposed a PDT of radioligand-therapy-induced platelet dynamics that predicts thrombocytopenia from first-cycle data and simulates alternative dosing schedules that lower the predicted risk of toxicity.

We study the sampling allocation of LinUCB in the small-gap regime, where the reward gaps are of order at most $n^{-1/2}$ over the decision horizon $n$. This scaling captures the hard instances underlying worst-case regret lower bounds, for which LinUCB is known to be near optimal up to logarithmic factors in $n$. Using a mean-field perspective, we characterize this allocation through the empirical sampling distribution, a macroscopic object that averages the effect of adaptive decisions over the horizon, and identify its limit as $n\to\infty$. We establish that in this regime, the empirical sampling distribution induced by LinUCB converges to the set of D-optimal designs. This central result reveals that, in the small-gap regime, LinUCB not only achieves near optimal minimax regret but also allocates samples in a way that is asymptotically efficient for learning the reward parameter, thereby connecting regret-driven online learning with information-efficient experimental design. Building on the optimal design limit, we obtain two useful consequences. First, we refine the asymptotic regret analysis of LinUCB in the small-gap regime by characterizing its leading-order constant in the limit. Second, we show that, despite LinUCB's adaptive sampling strategy, the regularized least-squares estimator satisfies a central-limit-type theorem in the small-gap regime, thereby enabling valid statistical inference for the reward parameter.

In high-dimensional factor pricing models, the power of regularized alpha tests depends on the ridge parameter, whose optimal value varies with the unknown direction of pricing errors. We address this tuning uncertainty by combining ridge-specific p-values using the Cauchy rule. The resulting test retains the least-squares alpha estimator and residual sample covariance and accommodates more assets than observations. We establish the joint Gaussian limits of the component statistics under the null and local alternatives and derive an explicit covariance formula across ridge parameters. These results characterize the combined test's asymptotic distribution and local power and justify its tail calibration. Simulations show empirical rejection rates close to the nominal levels and power gains over the fixed-ridge benchmark, with power approaching that of signal-informed ridge benchmarks across the simulated settings.

Spatial prediction maps are crucial for environmental management yet highly sensitive to subjective modelling choices such as, e.g., covariates, spatial dependence structures, or mesh resolution. We develop a workflow that attributes the resulting map uncertainty to these choices and is applicable to any spatial model, since it operates only on an ensemble of maps produced by propagating the choices through spatial prediction. This ensemble is then filtered to retain only models with acceptable predictive performance, reduced in dimension by principal component (PC) analysis, and the sensitivity of the resulting scores to each choice is quantified by global sensitivity analysis based on optimal transport (OT) metrics. We demonstrate the framework with Bayesian geostatistics applied to the spatial mapping of sulphate concentrations in groundwater of Paris Basin (France), which is key for assessing groundwater chemical quality and establishing the natural geochemical baseline of aquifers. For this application, the covariates, mesh resolution, covariance models, and priors are combined into 18000 candidate configurations. These are filtered by cross-validated root mean square error (RMSE) and 95% coverage of the prediction interval, and the retained configurations are then inferred on a high-resolution grid and reduced to its three PCs. The OT analysis identifies covariate selection (under 95% coverage) and mesh resolution (under RMSE) as the dominant sources of uncertainty to the PCs, and a negligible one for the choice of the covariance model.

Learning directed acyclic graphs (DAGs) to uncover causal mechanisms has attracted substantial attention in machine learning. While most existing methods focus exclusively on observed variables, many variables of substantive interest are latent constructs defined by statistical measurement models. Such constructs are particularly common in the social and behavioral sciences. In this paper, we propose a general statistical framework for DAG learning when some or all nodes of the graph are latent variables, accommodating non-Gaussian manifest variables such as binary and categorical data in the measurement model. To overcome the computational burden of high-dimensional integration in standard marginal likelihoods, we develop DAG learning via Composite-Likelihood-based screening and Iterative Pruning (DAG-CLIP), a two-step composite-likelihood-based learning algorithm. This algorithm first solves a smooth acyclicity-constrained optimization problem to screen out misspecified DAG structures, and subsequently performs BIC-guided composite-likelihood backward deletion within the Markov equivalence class (MEC) space to identify a sparse DAG. We establish the statistical consistency of the algorithm in recovering the MEC of the true DAG, and demonstrate its effectiveness through extensive simulation studies and a real-world application to large-scale educational survey data.

The use of run-off triangles (ROTs) is a common industry practice in estimating the loss given default (LGD) risk parameter when predicting credit losses in banking. We benchmark this industry practice using credit card data against a more sophisticated (though classical) regression-based approach, which is able to leverage various types of input variables in producing loan-level LGD-estimates. This regression-based approach can demonstrably recover the typical characteristics of the 'U-shaped' empirical LGD-distribution, which the ROT-based approach cannot do. First, we critically review the ROT-based approach and identify multiple demerits using data-driven diagnostics. We then estimate a two-stage regression-based LGD-model and favourably assess the model performance of each component (or 'stage'). Finally, we aggregate the LGD-estimates produced by each approach over time, and compare each time series to the mean empirical loss rate over time. The ROT-based aggregates diverge substantially from the empirical rate over most time periods, whilst the regression-based aggregates follow the empirical trends much closer. These results underscore the greater prediction accuracy of the regression-based LGD-model, relative to the ROT-based one. By implication, the former approach is probably better than the latter ROT-based approach when estimating the LGD under the IFRS 9 accounting framework, which prioritises accuracy.

Scalable Graph Transformers are commonly trained and evaluated on static large graphs in a transductive setup. Many scalable Graph Transformer components can be formulated as a constant-size shared memory, similar to virtual nodes, providing compressed information about the whole graph. The counterpart of these models in language models and other domains is justified as the input changes, and this mechanism learns to compress some useful information about the input. In transductive learning on a single fixed graph, however, any shared memory can be seen as a constant at test time. This raises the question of what exactly this shared memory does in this static setup. We give preliminary evidence that optimizing a shared memory directly performs similarly to global communication methods, and so normal local message-passing models can embed similar information in their weights. Thus, these settings may be a poor fit for evaluating global communication in graph neural networks.

This paper studies online quantile regression for large-scale and streaming data using Stochastic SubGradient Descent (SSGD) with constant learning rates. Classical offline inference for quantile regression is computationally and memory intensive. Existing works of online inference for quantile regression provide only asymptotic guarantees and typically require sub-exponential tail conditions for distribution theory. To bridge these gaps, we introduce new techniques to prove a quenched central limit theorem (CLT) and finite-sample Gaussian approximation for SSGD under a finite-moment assumption. We further show that Ruppert-Polyak averaging with a constant learning rate has a non-vanishing bias and fails to satisfy CLT centering at the population target. Hence we propose suffix averaging to address this issue and establish its finite-sample Gaussian approximation. Based on these results, we provide an efficient online inference method for quantile regression that avoids covariance estimation. Numerical experiments show that our method achieves desirable empirical coverage rates and competitive performance compared to other inference methods. We also apply our approach to U.S. wage data to demonstrate its practical effectiveness.

We study exact support recovery under $(\epsilon,\delta)$-differential privacy in sparse high-dimensional linear regression. We introduce Saturated Propose-test-release, a general mechanism that privately releases the output of a discrete selector with probability one once its stability certificate reaches a finite threshold. Exploiting the coordinatewise geometry of the LASSO, we construct a computable support-stability score. The resulting computationally efficient Saturated LASSO satisfies worst-case $(\epsilon,\delta)$-differential privacy and achieves exact support recovery with high probability under explicit regularity and beta-min conditions. Maximizing sparsity-indexed certificates yields an adaptive procedure requiring no sparsity knowledge and having exactly the same finite-sample exact-recovery risk as the oracle fixed-sparsity procedure under common public tuning parameters. We also establish a minimax lower bound explicitly tracking $\delta$: under its recovery conditions, Saturated LASSO is minimax optimal up to logarithmic factors in $n$ and $1/\delta$ uniformly over $0 < \delta \leq \epsilon/16$; in the broad moderate-$\delta$ regime, it further matches the lower-bound $\delta$-dependence. A complementary information-theoretic construction with known sparsity attains the lower-bound rates up to constant factors under independent Gaussian design, at exponential computational cost. Simulations and a semi-synthetic study using public American Community Survey covariates illustrate the numerical performance of the proposed procedures.

We construct a feasible two-step estimator for the elasticity parameter in small-noise CEV-type diffusions. Under joint small-noise and high-frequency asymptotics, we establish its consistency and an $\varepsilon^{-1}$ central limit theorem with an explicit asymptotic variance. We adapt a Lamperti-based transformation strategy to elasticity inference for a CEV process with an attainable, absorbing $0$ boundary. Under a local-to-CEV scaling, an auxiliary CKLS process and a Girsanov change of measure yield a strictly positive CIR-type benchmark in which the elasticity is recast as a linear-drift parameter. A preliminary elasticity estimator based on local realized variance supplies the unknown parameter in the state mapping, yielding a feasible LSE-type estimator. The asymptotic theory combines control of the CKLS-to-CEV path-replacement error, total-variation closeness between the original and changed measures, and asymptotic negligibility of the preliminary plug-in error, thereby transferring the auxiliary CIR limit theory to the feasible estimator under the original measure.

We study kernel functions induced by a linear time-invariant (LTI) stochastic differential equation (SDE), an approach that embeds prior knowledge about the function to be estimated directly into the state-space description of the SDE. This kernel-design perspective is relevant across the many settings where kernels play a central role, including kernel methods in statistics, Gaussian process (GP) regression in machine learning, and kernel-based regularization methods in system identification. The resulting class of SDE-induced kernels includes several kernels of practical interest, such as Matérn kernels with half-integer smoothness, spline kernels, and related kernels used in system identification. In contrast to existing linear-time GP regression methods for these kernels, which are typically based on Kalman filtering and Rauch–Tung–Striebel smoothing on the latent state, we work directly with the SSS representation of the observed covariance matrix. This yields linear-complexity recursive algorithms for the matrix operations required in GP regression, including factorization, linear solves, log determinants, posterior covariance, log-marginal-likelihood gradients, and posterior sampling; the same generator-level recursions extend, with only minor modifications, to the analogous computations in kernel-based regularization methods for system identification. Compared with previous uses of SSS representations in GP regression, we derive efficient recursive algorithms for analytic marginal-likelihood gradients in three application-relevant cases, and we develop new recursions for posterior computations and Matheron-type sampling. Numerical experiments verify the accuracy of the proposed recursions and illustrate posterior inference and sampling for representative SDE-induced kernels.

Monitoring concept drift from an adaptive classifier's error stream creates an operational conflict with the model's own update loop. When internal adaptation outpaces evidence accumulation, accuracy recovers before cumulative detectors (CUSUM, Page-Hinkley) can reach threshold. Instrumenting an Adaptive Random Forest (ARF) shows that surviving trees absorb 98.6% of the post-drift error transient through incremental leaf updates alone. The first background tree swap accounts for just 0.71% of this erased error volume, but drops external detection rates by 31 percentage points. We derive the finite-horizon boundary where cumulative evidence fails to cross threshold and measure a critical magnitude floor ($\Delta e_c = 0.120$) below which false-alarm budgets preclude detection. This failure manifests as missed shifts on stationary streams and false-alarm flooding triggered by internal tree swaps on noisy baselines. We validate on synthetic shifts, ARMA-GARCH series (ProteuS), and tabular benchmarks (BAF, INSECTS); on the synthetic sweep at a standard threshold, the blind spot appears at $\Delta e \approx 0.25$, showing why classical benchmarks like SEA ($\Delta e \le 0.21$) failed to reach it.

Estimating causal effects in climate science, such as the effect of anthropogenic warming on crop loss, is challenging because of complex spatio-temporal dependence and the high-dimensional nature of the treatment. To address this dependence and the resulting poor overlap between observed and counterfactual scenarios, we develop a spatio-temporal stochastic-intervention framework for estimating causal effects from climate observations. We introduce a regularized estimator of the stochastic-intervention treatment effect that trades a controlled bias for a reduction in the weight variance caused by poor overlap. Simulation studies show that this estimator attains lower mean squared error than alternative weighting estimators and removes the confounding bias of an unadjusted estimator. We apply the framework to estimate the effect of historical warming on vapor-pressure deficit, a driver of crop stress, adjusting for precipitation, which confounds the effect by affecting both temperature and humidity. In GISS-E2-1-G climate-model simulations, the global effect is distinguishable from zero in every year from 1995 onward, and omitting the precipitation adjustment inflates the global estimate by 47%. Adjustment reverses the sign of the estimate over 8% of global cropland (125 million hectares), where an unadjusted analysis could misdirect adaptation between heat-focused and moisture-focused measures.

Classification problem in the context of highly imbalanced data is a major challenge in many real-world applications (e.g., FinTech, healthcare, etc.). In these cases, the vast majority of instances belong to a single class and a small fraction represent the minority class (often the most critical class). Recently, diffusion models have emerged as powerful approaches to reduce the degree of “imbalanced-ness” in the dataset; they work by generating synthetic data by capturing complex data distributions using iterative transformations. However, standard diffusion models are not inherently suited to highly skewed or heavy-tailed data, due to inbuilt quadratic error loss, which lacks the structural sensitivity to capture rare, extreme values, and minority-class nuances. We propose a novel approach, namely, Quantile-TabDDPM, based on a quantile-regularized denoising objective that combines the standard quadratic error loss with a quantile loss term to explicitly capture rare events while preserving the theoretical grounding of the original denoising objective. We extensively evaluated our approach on a real-world credit card transaction dataset characterized by extreme class imbalance. The results demonstrate that the integration of diffusion-based synthetic data generation with a quantile-regularized denoising objective provides a robust and effective framework for fraud detection in highly imbalanced datasets.

High-dimensional Bayesian optimization (BO) often fits Gaussian process (GP) surrogates from far fewer observations than input dimensions. Modern Vanilla BO can perform well in this regime with dimension-aware priors, initialization, and acquisition optimization, but it typically retains automatic relevance determination (ARD), fitting one lengthscale per input coordinate. We study this modeling choice and propose Iso-BO, a controlled modification that replaces the ARD GP with an isotropic GP using one shared lengthscale while keeping the surrounding BO pipeline matched. For radial kernels, we show that the marginal log likelihood (MLL) depends on the inverse-squared ARD lengthscales only through weighted pairwise distances among the observed inputs. The current design can therefore leave some ARD directions exactly invisible or only weakly constrained by the MLL. Iso-BO removes coordinatewise reweighting and fits a single shared scale instead. Lengthscale-fitting and predictive-density diagnostics show that this finite-data effect appears in practice, including when the data-generating process is anisotropic. Across GP-prior, synthetic, and real-world benchmarks, Iso-BO often improves over matched modern Vanilla BO and remains competitive with the included high-dimensional BO baselines under the tested budgets. Stress tests also show the expected boundary wherein sufficiently strong, learnable anisotropy can favor the more flexible ARD model.

We construct computable error estimators, which double as loss functions for neural networks, for a class of parametric nonlinear partial differential equations with a monotonicity property, and prove that they are globally reliable and efficient. The value of such a loss function is bounded above and below by the squared error in the natural trial norm, for every trial function, not merely for those near the exact solution; this global property rests on monotonicity. The construction rests on splitting the nonlinear operator into a linear part and a strongly monotone closure, and on measuring the linear residual in a discrete dual norm. Since the closure contributes a dual norm that admits no closed form when the trial norm is stronger than an $L_2$ norm, the estimator is built around a computable surrogate for it, required only to satisfy a pairing bound and a Lipschitz bound. The main theorem then yields two-sided bounds with explicit constants and covers two instances. A first-order system least-squares estimator on conforming trial spaces is the first instance studied: its two-sided bound holds on the whole trial space and therefore applies to arbitrary approximations, including those not in a discrete finite element space. The second instance is a discontinuous Petrov-Galerkin estimator on trial spaces of finite element functions for each parameter value, built with broken test spaces, for which no conformity is required and the dual norm is computed by independent element-local problems. All assumptions are verified for a model class of nonlinear fluxes, with the constants tracked explicitly in terms of the parameter range. Being computable for an arbitrary input, both estimators serve as variationally correct loss functions for neural network approximations of parameter-to-solution maps.