Papers

Robust principal component analysis (RPCA) is a widely used technique for recovering low-rank structure from matrices with missing entries and sparse, possibly large-magnitude corruptions. Although numerous algorithms achieve accurate point estimation, they offer little guidance on the uncertainty of recovered entries, limiting their reliability in practice. In this paper, we propose conformal prediction-RPCA (CP-RPCA), a practical and distribution-free framework for uncertainty quantification in robust matrix recovery. Our proposed method supports both split and full conformal implementations and incorporates weighted calibration to handle heterogeneous observation probabilities. We provide theoretical guarantees for finite-sample coverage and demonstrate through extensive simulations that CP-RPCA delivers reliable uncertainty quantification under severe outliers, missing data and model misspecification. Empirical results show that CP-RPCA can produce informative intervals and remain competitive in efficiency when the RPCA model is well specified, making it a scalable and robust tool for uncertainty-aware matrix analysis.

We study global inference for regression coefficients in high-dimensional linear models under potentially heavy-tailed errors. While sum-type tests are powerful for dense alternatives and max-type tests excel for sparse alternatives, practical applications rarely reveal the sparsity level, and many existing procedures rely on light-tail assumptions. Motivated by the Wilcoxon-score sum test of Feng et al. (2013) and the two Wilcoxon-score maximum tests of Xu and Zhou (2021), we establish under $H_0$ the asymptotic independence between the rank-based sum statistic and each max statistic. These joint limit results justify principled $p$-value aggregation, and we propose two adaptive rank-based maxsum tests via the Cauchy combination method (Liu and Xie, 2020). The proposed procedures inherit robustness from rank-based construction and adaptivity from combining dense- and sparse-sensitive components. Simulation studies confirm accurate size control and strong power across a wide range of error distributions and sparsity regimes.

Deploying trustworthy AI systems requires principled uncertainty quantification. Conformal prediction (CP) is a widely used framework for constructing prediction sets with distribution-free coverage guarantees. In many practical settings, including healthcare, finance, and mobile sensing, the calibration data required for CP are distributed across multiple clients, each with its own local data distribution. In this federated setting, data can often be partitioned into, potentially overlapping, groups, which may reflect client-specific strata or cross-cutting attributes such as demographic or semantic categories. We propose group-conditional federated conformal prediction (GC-FCP), a federated extension of conditional conformal calibration for a target mixture over prespecified groups. GC-FCP constructs mergeable, atom-stratified coresets from local calibration scores, enabling compact aggregation at the server when the number of active atoms is moderate. Experiments on synthetic and real-world datasets validate the performance of GC-FCP compared to centralized calibration baselines. The code of our work can be found at https://github.com/HaifengWen/GC-FCP.

Average treatment effects (ATE) and conditional average treatment effects (CATE) are foundational causal estimands, but they target changes in expected outcomes and can miss treatment-induced changes in the shape of outcome distributions. A canonical failure mode occurs when control outcomes are unimodal, treated outcomes become bimodal, and both distributions have the same mean. In such cases mean-based causal estimands are zero even though the geometry and topology of the outcome law change substantially. This paper develops a topological causal framework based on persistent homology. We formalize a persistent-homology ignorability condition, define topological analogues of CATE and ATE, and prove that these estimands are identifiable up to an explicit error bound under approximate topological ignorability. We also clarify a subtle but important point: a marginal persistence-diagram effect is not identified from conditional topological ignorability alone because persistent homology does not in general commute with mixtures over covariates. To preserve the original intuition while ensuring scientific correctness, we retain the marginal effect as a motivating quantity, but place the mathematically sound conditional estimands at the center of the theory. A synthetic experiment with mean-preserving topology change shows that mean-based causal estimands remain near zero while the proposed topological effect increases sharply and remains recoverable after adjustment for confounding.

Sleep quality is influenced by a complex interplay of behavioral, environmental, and psychosocial factors, yet most computational studies focus mainly on predictive risk identification rather than actionable intervention design. Although machine learning models can accurately predict subjective sleep outcomes, they rarely translate predictive insights into practical intervention strategies. To address this gap, we propose a personalized predictive-prescriptive framework that integrates interpretable machine learning with mixed-integer optimization. A supervised classifier trained on survey data predicts sleep quality, while SHAP-based feature attribution quantifies the influence of modifiable factors. These importance measures are incorporated into a mixed-integer optimization model that identifies minimal and feasible behavioral adjustments, while modelling resistance to change through a penalty mechanism. The framework achieves strong predictive performance, with a test F1-score of 0.9544 and an accuracy of 0.9366. Sensitivity and Pareto analyses reveal a clear trade-off between expected improvement and intervention intensity, with diminishing returns as additional changes are introduced. At the individual level, the model generates concise recommendations, often suggesting one or two high-impact behavioral adjustments and sometimes recommending no change when expected gains are minimal. By integrating prediction, explanation, and constrained optimization, this framework demonstrates how data-driven insights can be translated into structured and personalized decision support for sleep improvement.

This study presents a conditional flow matching framework for solving physics-constrained Bayesian inverse problems. In this setting, samples from the joint distribution of inferred variables and measurements are assumed available, while explicit evaluation of the prior and likelihood densities is not required. We derive a simple and self-contained formulation of both the unconditional and conditional flow matching algorithms, tailored specifically to inverse problems. In the conditional setting, a neural network is trained to learn the velocity field of a probability flow ordinary differential equation that transports samples from a chosen source distribution directly to the posterior distribution conditioned on observed measurements. This black-box formulation accommodates nonlinear, high-dimensional, and potentially non-differentiable forward models without restrictive assumptions on the noise model. We further analyze the behavior of the learned velocity field in the regime of finite training data. Under mild architectural assumptions, we show that overtraining can induce degenerate behavior in the generated conditional distributions, including variance collapse and a phenomenon termed selective memorization, wherein generated samples concentrate around training data points associated with similar observations. A simplified theoretical analysis explains this behavior, and numerical experiments confirm it in practice. We demonstrate that standard early-stopping criteria based on monitoring test loss effectively mitigate such degeneracy. The proposed method is evaluated on several physics-based inverse problems. We investigate the impact of different choices of source distributions, including Gaussian and data-informed priors. Across these examples, conditional flow matching accurately captures complex, multimodal posterior distributions while maintaining computational efficiency.

A semiparametric copula-based two-part quantile regression framework is developed for the analysis of semicontinuous outcomes characterized by a point mass at zero and a continuous positive component. The proposed approach models the occurrence and magnitude processes separately and links them through copula-based conditional distributions, allowing for flexible dependence structures and nonlinear covariate effects across quantiles. Large-sample properties of the resulting estimator are established, and extensive simulation studies demonstrate improved finite-sample performance relative to logistic/linear quantile regression, particularly under nonlinear dependence and substantial zero inflation. An application to healthcare data illustrates how the proposed method provides a nuanced characterization of the association between social deprivation and uncompensated and charity care burdens, revealing heterogeneous and nonlinear effects that are not captured by competing approaches.

Scorio.jl is a Julia package for evaluating and ranking systems from repeated responses to shared tasks. It provides a common tensor-based interface for direct score-based, pairwise, psychometric, voting, graph, and listwise methods, so the same benchmark can be analyzed under multiple ranking assumptions. We describe the package design, position it relative to existing Julia tools, and report pilot experiments on synthetic rank recovery, stability under limited trials, and runtime scaling.

We address the brittleness of Bayesian experimental design under model misspecification by formulating the problem as a max–min game between the experimenter and an adversarial nature subject to information-theoretic constraints. We demonstrate that this approach yields a robust objective governed by Sibson's $\alpha$-mutual information (MI), which identifies the $\alpha$-tilted posterior as the robust belief update and establishes the Rényi divergence as the appropriate measure of conditional information gain. To mitigate the bias and variance of nested Monte Carlo estimators needed to estimate Sibson's $\alpha$-MI, we adopt a PAC-Bayes framework to search over stochastic design policies, yielding rigorous high-probability lower bounds on the robust expected information gain that explicitly control finite-sample error.

The Expected Calibration Error (ece), the dominant calibration metric in machine learning, compares predicted probabilities against empirical frequencies of binary outcomes. This is appropriate when labels are binary events. However, many modern settings produce labels that are themselves probabilities rather than binary outcomes: a radiologist's stated confidence, a teacher model's soft output in knowledge distillation, a class posterior derived from a generative model, or an annotator agreement fraction. In these settings, ece commits a category error - it discards the probabilistic information in the label by forcing it into a binary comparison. The result is not a noisy approximation that more data will correct. It is a structural misalignment that persists and converges to the wrong answer with increasing precision as sample size grows. We introduce the Soft Mean Expected Calibration Error (smece), a calibration metric for settings where labels are of probabilistic nature. The modification to the ece formula is one line: replace the empirical hard-label fraction in each prediction bin with the mean probability label of the samples in that bin. smece reduces exactly to ece when labels are binary, making it a strict generalisation.

Real-world learning tasks often encounter uncertainty due to covariate shift and noisy or inconsistent labels. However, existing robust learning methods merge these effects into a single distributional uncertainty set. In this work, we introduce a novel structured credal learning framework that explicitly separates these two sources. Specifically, we derive geometric bounds on the total variation diameter of structured credal sets and demonstrate how this quantity decomposes into contributions from covariate shift and expected label disagreement. This decomposition reveals a gating effect: covariate modulates how much label disagreement contributes to the joint uncertainty, such that seemingly benign covariate shifts can substantially increase the effective uncertainty. We also establish finite-sample concentration bounds in a fixed covariate regime and demonstrate that this quantity can be efficiently estimated. Lastly, we show that robust optimization over these structured credal sets reduces to a tractable discrete min-max problem, avoiding ad-hoc robustness parameters. Overall, our approach provides a principled and practical foundation for robust learning under combined covariate and label mechanism ambiguity.

This paper deals with a copies-based continuously differentiable and strictly decreasing estimator of the drift function for stochastic differential equations defining recurrent diffusion processes. The first part of our paper deals with non-asymptotic $\mathbb L^1$-risk bounds and a bandwidths selection procedure for a universal monotone estimator. These results are tailor-made to our framework, and then applied to the estimation of the drift function of recurrent diffusion processes in the second part of the paper.

Capturing the structured mixing within a population is key to the reliable projection of infectious disease dynamics and hence informed control. Both heterogeneity in the number of contacts and age-structured mixing have been repeatedly demonstrated as fundamental, yet are rarely combined. Networks provide a powerful and intuitive method to realise population structure, and simulate infection dynamics. However the explicit measurement of contact networks is not scalable to larger populations. Here, using data from social contact surveys, we develop a generalisable and robust algorithm utilizing machine learning to generate a surrogate population-scale network that preserves both age-structured mixing and heterogeneity of contacts. We simulate the spread of infection across different populations, considering how the epidemic size varies over basic reproduction number ($R_0$) scenarios - mirroring the process of determining public health impact from early epidemic growth. Our approach shows that both age structure and degree heterogeneity substantially reduce the epidemic size. We also demonstrate that these simulations more accurately capture the heterogeneity in secondary cases observed for COVID-19 when transmission is scaled by contact duration, dampening the effect of highly connected “super-spreaders". By using survey data collected during 2020-2022, these network models also inform about the impacts of control and targeting of public health interventions: quantifying the non-linear reduction in transmission opportunities that occurred during lockdowns, and the ages and contact types most responsible for onward transmission. Our robust methodology therefore allows for the inclusion of the full wealth of data commonly collected by surveys but frequently overlooked to be incorporated into more realistic transmission models of infectious diseases.

We introduce the notion of a bivariate random discrete copula on an equidistant mesh and explore its stochastic properties. A random discrete copula is a discrete random field, hence, its value at a given point on the mesh is a random variable. We determine the distribution of this random variable and calculate its expected value and variance. We also consider bilinear extension of a random discrete copula to a random field over the whole unit square.

We develop a nonparametric two-sample test for distributions supported on the cone of symmetric positive definite matrices. The procedure relies on the Wishart kernel density estimator (KDE) introduced by Belzile et al. (2026), whose support-adaptive kernel alleviates boundary bias by remaining confined to the cone. Our test statistic is the rescaled integrated squared difference between two Wishart KDEs and can be expressed as a two-sample $V$-statistic via an explicit closed-form overlap of Wishart kernels, avoiding numerical integration. Under the null hypothesis of equal densities, we derive the asymptotic distribution in both the common shrinking-bandwidth and fixed-bandwidth regimes. The proposed method provides a kernel-based competitor to the empirical Laplace-transform two-sample test of Lukić (2024). Unlike the orthogonally invariant Hankel-transform test of Lukić and Milošević (2024), our statistic can detect alternatives that differ only through eigenvector structure, for instance, Wishart models with the same shape parameter and the same scale eigenvalues but different orientations. A comparative simulation study examines the empirical Type I error rates and power of the proposed and Laplace-transform tests.

Model averaging, as an appealing ensemble technique, strategically integrates all valuable information from candidate models to construct fast and accurate prediction. Despite of having been widely practiced in many fields such as cross-sectional data, censored data and longitudinal data, its application to spatial data characterized by inherent spatial heterogeneity remains surprisingly limited. To mitigate risk of model misspecification and enhance the flexibility of prediction, we propose a combined estimator constructed by computing the weighted average of estimators derived from a set of spatially varying coefficient candidate models. Herein, the model weights are determined via a Mallows-type criterion, which dynamically calibrates the relative importance of individual candidate models in the ensemble. Theoretically, we establish desirable asymptotic properties under two practical scenarios. First, in the case where all candidate models are misspecified, the proposed model averaging estimator attains asymptotic optimality in the sense that it minimizes the squared error loss function asymptotically. Second, when the candidate model set encompasses at least one quasi-correct model, the weights assigned by the Mallows-type criterion asymptotically concentrate on the quasi-correct models, and the resulting model averaging estimator converges in probability to the true conditional mean. Both simulation studies and a real-world empirical example demonstrate that the proposed method generally outperforms alternative comparative approaches in terms of predictive accuracy and robustness.

We propose a family of association measures for two-way contingency tables whose latent distribution can be assumed to be bivariate normal. When this assumption holds, the power-divergence measuring departure from independence can be approximated in closed form as a function of the latent correlation coefficient. By inverting this relationship, we obtain a family of measures $\rho_{(\lambda)}$, indexed by a scalar parameter $-1 \leq \lambda \leq 1$, that directly approximates the latent correlation. Special cases include the informational measure of correlation proposed by Linfoot (1957) at $\lambda = 0$ and Pearson's contingency coefficient $C$ at $\lambda = 1$. Additionally, we derive asymptotic distributions via the delta method and construct two families of confidence intervals. Simulation studies confirm that the proposed measures approximate the true latent correlation more faithfully than conventional divergence-based measures, and that they successfully distinguish between weak and moderate associations where existing measures tend to give indistinguishable values. Compared with the polychoric correlation coefficient, the proposed measures are computed several thousand times faster and remain numerically stable even when the latent correlation is close to one.

Classical sparse recovery treats all nonzero entries equally, though numerical noise often creates long tails of negligible coefficients. This paper develops an entropy-based notion of effective sparsity to measure the coefficients carrying significant mass. The central quantity, the effective number of nonzeros (ENZ), is obtained by exponentiating the Shannon entropy of the normalized magnitude distribution. We show that ENZ decomposes exactly into the support cardinality multiplied by a distributional efficiency factor, thereby making precise its relation to the $\ell_0$ count and explaining how it discounts uninformative coefficients. Furthermore, the Shannon ENZ is embedded into a parallel Rényi family that recovers several scale-invariant sparsity measures, including the $\ell_1/\ell_2$ ratio, as special cases. We then prove a stability result under a restricted isometry condition, establishing an explicit bound that depends on the tail energy, measurement perturbation, and restricted isometry constant. For computation, a separable unnormalized entropy surrogate is introduced to avoid global coupling. Numerical experiments on sparse signal recovery and gradient-domain image denoising demonstrate that the resulting regularizer is robust, computationally efficient, and competitive with standard sparsity penalties.

Sparse principal component analysis (SPCA) addresses the poor interpretability and variable redundancy often encountered by principal component analysis (PCA) in high-dimensional data. However, SPCA typically imposes uniform penalties on variables and does not account for differences in variable importance, which may lead to unstable performance in highly noisy or structurally complex settings. We propose SP-SPCA, a method that introduces a single equilibrium parameter into the regularization framework to adaptively adjust variable penalties. This modification of the L2 penalty provides flexible control over the trade-off between sparsity and explained variance while maintaining computational efficiency. Simulation studies show that the proposed method consistently outperforms standard sparse principal component methods in identifying sparse loading patterns, filtering noise variables, and preserving cumulative variance, especially in high-dimensional and noisy settings. Empirical applications to crime and financial market data further demonstrate its practical utility. In real data analyses, the method selects fewer but more relevant variables, thereby reducing model complexity while maintaining explanatory power. Overall, the proposed approach offers a robust and efficient alternative for sparse modeling in complex high-dimensional data, with clear advantages in stability, feature selection, and interpretability

In this paper, we introduce flexible observation-driven $\mathbb{Z}$-valued time series models constructed from mixtures of negative and non-negative components. Compared to models based on the standard Skellam distribution or on a difference of two integer-valued variables, our specification offers greater versatility. For example, it easily allows for skewness and bimodality. Furthermore, the observation of one component of the mixture makes interpretation and statistical analysis easier. We establish conditions for stationarity and mixing, and develop a mixed Poisson quasi-maximum likelihood estimator with proven asymptotic properties. A portmanteau test is proposed to diagnose residual serial dependence. The finite-sample performance of the methodology is assessed via simulation, and an empirical application on tick prices demonstrates its practical usefulness.

Understanding how an exposure transmits its effect through high-dimensional intermediaries is a central problem in observational research. We study the problem of finding a composite mediator that maximises the indirect effect of an exposure on an outcome in a linear structural equation model. Although the objective is non-convex in the weight vector, a geometric argument yields a closed-form global solution: the optimal weight bisects the angle between two computable path vectors in a weighted inner product space, recovered via two linear solves. The resulting algorithm, MaxIE, runs at the same cost as ordinary least squares – orders of magnitude lower than numerical optimisation – with a dual formulation for settings where mediators outnumber observations. The same path vectors yield a test for the global null that no composite mediator exists, with t(p-1) in the classical and t(n-2) in the dual regime. Power is characterised analytically as a function of the population path angle; simulations confirm size control and the power characterisation. Applied to a UK Biobank proteomics dataset (n=38,383, p=2,916), the method rejects the global null (p-value = 6.4e-9) and identifies the optimal proteomic composite mediating age's effect on dementia.

We study stochastic multi-armed bandits under simultaneous constraints on space and adaptivity: the learner interacts with the environment in $B$ batches and has only $W$ bits of persistent memory. Prior work shows that each constraint alone is surprisingly mild: near-minimax regret $\widetilde{O}(\sqrt{KT})$ is achievable with $O(\log T)$ bits of memory under fully adaptive interaction, and with a $K$-independent $O(\log\log T)$-type number of batches when memory is unrestricted. We show that this picture breaks down in the simultaneously constrained regime. We prove that any algorithm with a $W$-bit memory constraint must use at least $\Omega(K/W)$ batches to achieve near-minimax regret $\widetilde{O}(\sqrt{KT})$, even under adaptive grids. In particular, logarithmic memory rules out $O(K^{1-\varepsilon})$ batch complexity. Our proof is based on an information bottleneck. We show that near-minimax regret forces the learner to acquire $\Omega(K)$ bits of information about the hidden set of good arms under a suitable hard prior, whereas an algorithm with $B$ batches and $W$ bits of memory allows only $O(BW)$ bits of information. A key ingredient is a localized change-of-measure lemma that yields probability-level arm exploration guarantees, which is of independent interest. We also give an algorithm that, for any bit budget $W$ with $\Omega(\log T) \le W \le O(K\log T)$, uses at most $W$ bits of memory and $\widetilde{O}(K/W)$ batches while achieving regret $\widetilde{O}(\sqrt{KT})$, nearly matching our lower bound up to polylogarithmic factors.

Tropical deforestation and rural poverty are deeply intertwined, yet isolating the causal effect of income on forest loss remains challenging. We use the 2015 global vanilla price boom, triggered by food-industry shifts toward natural flavoring, as an exogenous income shock affecting Madagascar's primary vanilla-producing region. Using a matching-augmented synthetic control design, we estimate that income gains reduced annual deforestation by 1.7 percentage points in 2017, equivalent to approximately 701 hectares of avoided forest loss. Under a monotonicity assumption linking the price boom to farmers' income, the sign of this reduced-form effect is informative about the causal direction of income on deforestation. However, effects were strongly heterogeneous: higher incomes reduced deforestation in drier, more accessible municipalities but increased clearing in wetter, low-elevation areas with high agricultural potential. These divergent patterns suggest that income simultaneously relaxes subsistence pressures driving forest dependence and raises the opportunity cost of conservation where agricultural returns are high. Our findings indicate that commodity-based agroforestry can align poverty alleviation with forest conservation under conditions of low agricultural opportunity cost. Still, policies must anticipate contexts where rising incomes amplify deforestation in agriculturally suitable land. The strategic targeting of livelihood interventions based on local agricultural potential may help reconcile development and conservation objectives in tropical forest frontiers.

Conditional independence is a fundamental concept in many areas of statistical research, including, for example, sufficient dimension reduction, causal inference, and statistical graphical models. In many modern applications, data arise in the form of random functions, making it important to determine whether two random functions are conditionally independent given a third. However, to the best of our knowledge, existing conditional independence tests in the literature apply only to multivariate data, and extensions to the functional setting are not available. To fill this gap, we develop a reproducing-kernel-based test for conditional independence of random functions based on the conjoined conditional covariance operator (CCCO). We rigorously derive the asymptotic distribution of the CCCO estimator using a recently established sharpened convergence rate for the regression operator (Choi et al., 2026). Based on this result, we construct a test statistic using the spectral decomposition of the operator appearing in the asymptotic distribution. The proposed method is illustrated through applications to an activity and biometrics dataset and a macroeconomic dataset.

AI systems increasingly assist decision making by producing cheap factor-level assessments of complex inputs, but these assessments can be biased or incomplete. We study selective human evaluation: given AI signals, which factors should be dispatched to human experts? We formulate this human–AI collaboration problem as a factor-level information-acquisition problem. Under squared loss, the optimal dispatching rule maximizes a contextual reward; under a linear model, this reward admits a closed-form decomposition into two interpretable terms: predictive relevance and residual uncertainty in the human evaluation after conditioning on the AI signal. We instantiate the framework on peer review, decomposing papers into ten aspects and evaluating up to 3,408 ICLR submissions across three LLMs and multiple regression heads. In this retrospective proxy, where human aspect signals are extracted from existing reviews, predictions that query three of the ten aspects under the optimal dispatching rules match the full ten-aspect human benchmark. The finding holds when the human signal comes from a single noisy reviewer, and across review years. These results position principled dispatching as a practical building block for scalable human–AI decision systems. We also discuss safeguards under which such a rule can serve as decision support that leaves the final decision with a human.

Structural assumptions are central to the causal inference literature. In practice, it is often crucial to assess their validity or to test implications that follow from them. In many settings, such tests can be framed as evaluating whether a function-valued parameter equals zero. In this paper, we propose a class of generalized projection tests based on series estimators for function-valued parameters. We establish conditions under which the proposed tests are valid and illustrate their applicability through examples from the data fusion and instrumental variables literature. Our approach accommodates flexible machine learning methods for estimating nuisance parameters. In contrast to many existing approaches, the limiting distributions of the proposed test statistics are straightforward to compute under the null hypothesis. We apply our method to test the equality of conditional COVID-19 risk across vaccine arms in the COVID-19 Variant Immunologic Landscape (COVAIL) trial, and to test an instrumental variable compatibility condition in a study of the effect of family size on female labor supply.

Mental health difficulties among elementary school students represent a growing public health concern in South Korea, yet analytical tools for identifying school-specific vulnerability patterns from item response data remain limited. We propose the hierarchical latent space item response model (HLSIRM), which adds hierarchical respondent effects and an inner-product latent interaction for signed respondent-item associations, yielding a unified interaction map that separates school, individual main effects from school/individual-item interactions. We apply HLSIRM to mental health vulnerability data from 2,210 elementary school students across 35 schools in Incheon, South Korea. Clustering item vectors by directional similarity identifies four empirically derived vulnerability domains. School-level analysis reveals that the absence of counseling experience is the primary vulnerability domain aligned with most school vectors, while stress, depression, and smartphone dependency concentrate in specific schools. Within-school analysis demonstrates how individual student positions in the interaction map translate into targeted intervention strategies that address school-specific needs.

Most machine learning methods assume fixed probability distributions, limiting their applicability in nonstationary real-world scenarios. While continual learning methods address this issue, current approaches often rely on black-box models or require extensive user intervention for interpretability. We propose SyMPLER (Systems Modeling through Piecewise Linear Evolving Regression), an explainable model for time series forecasting in nonstationary environments based on dynamic piecewise-linear approximations. Unlike other locally linear models, SyMPLER uses generalization bounds from Statistical Learning Theory to automatically determine when to add new local models based on prediction errors, eliminating the need for explicit clustering of the data. Experiments show that SyMPLER can achieve comparable performance to both black-box and existing explainable models while maintaining a human-interpretable structure that reveals insights about the system's behavior. In this sense, our approach conciliates accuracy and interpretability, offering a transparent and adaptive solution for forecasting nonstationary time series.

Kernel methods are widely used in causal inference for tasks such as treatment effect estimation, policy evaluation, and policy learning. The bootstrap is a standard tool for uncertainty quantification because of its broad applicability. As increasingly large datasets become available, such as the 2023 U.S. Natality data from the National Vital Statistics System (NVSS), which includes 3,596,017 registered births, the computational demands of these methods increase substantially. Kernel methods are known to scale poorly with sample size, and this limitation is further exacerbated by the repeated re-fitting required by the bootstrap. As a result, bootstrap-based inference for kernel-based estimators can become computationally infeasible in large-scale settings. In this paper, we address these challenges by extending the causal Bag of Little Bootstraps (cBLB) algorithm to kernel methods. Our approach achieves computational scalability by combining subsampling and resampling while preserving first-order uncertainty quantification and asymptotically correct coverage. We evaluate the method across three representative implementations: kernelized augmented outcome-weighted learning, kernel-based minimax weighting, and double machine learning with kernel support vector machines. We show in simulations that our method yields confidence intervals with nominal coverage at a fraction of the computational cost. We further demonstrate its utility in a real-world application by estimating the effect of any amount of smoking on birth weight, as well as the optimal treatment regime, using the NVSS dataset, where the standard bootstrap is prohibitively expensive computationally and effectively infeasible at this scale.

This paper develops a measure-theoretic framework establishing when and how a possibilistic representation of incomplete knowledge contracts into a probabilistic representation of intrinsic stochastic variability. Epistemic uncertainty is encoded by a possibility distribution and its dual necessity measure, defining a credal set bounding all probability measures consistent with current evidence. As evidence accumulates, the credal set contracts. The epistemic collapse condition marks the transition: the Choquet integral converges to the Lebesgue integral over the unique limiting density. We prove this rigorously (Theorem 4.5), with all assumptions explicit and a full treatment of the non-consonant case. We introduce the aggregate epistemic width W, establish its axiomatic properties, provide a canonical normalization, and give a feasible online proxy resolving a circularity in prior formulations. Section 7 develops the dynamics of epistemic contraction: evidence induces compatibility, compatibility performs falsification, posterior possibility is the min-intersection of prior possibility and compatibility, and a credibility-directed flow governs support geometry contraction. This is not belief updating. It is knowledge contraction. Probability theory is the limiting geometry of that process. The UKF and ESPF solve different problems by different mechanisms. The UKF minimizes MSE, asserts truth, and requires a valid generative model. The ESPF minimizes maximum entropy and surfaces what evidence has not ruled out. When the world is Gaussian and the model valid, both reach the same estimate by entirely different routes – convergent optimality, not hierarchical containment. We prove this (Theorem 9.1) and compare both on a 2-day, 877-step orbital tracking scenario. Both achieve 1-meter accuracy. The UKF is accurate but epistemically silent. The ESPF is accurate and epistemically honest.