Papers

Members of collective institutions may leave public traces while their individual choices remain concealed. This paper separates a corpus-conditional public position from the behavioral rule linking that position to participation and secret choice. I measure the first with a dynamic ordinal state-space model and establish a likelihood-exclusion result for the second. If behavioral-link parameters enter only the distribution of an entirely unobserved outcome and are a priori independent of measurement parameters, public signals leave their posterior equal to their prior. Declared monotone mappings are therefore reported as sensitivity envelopes, not estimates or identified bounds. Cabinet-sized simulations compare dynamic measurement with a static ordinal model and transparent summaries, exposing gains from temporal pooling and failures under weak measurement or omitted dimensionality. The application reconstructs 41 pre-decision official-source records preceding a concealed Slovenian cabinet decision. Only six of 21 ministers have attributable signals. The model locates a small visible group but leaves the remainder prior-dominated. Event-dependence adjustments, coding perturbations, rolling prediction, and the subsequently disclosed record support the same conclusion. Uncertainty should track the public information environment rather than be converted into unsupported behavioral precision.

Sequential target trial emulation evaluates eligibility at multiple baseline times to emulate a sequence of randomized trials using observational data. Estimating per-protocol effects in this setting is challenging because treatment deviations and loss to follow-up induce selection among individuals who remain observed and adherent over time. Conventional inverse-probability methods address this selection using cumulative weights constructed from estimated adherence and censoring probabilities, but these weights can be highly variable, leading to unstable and imprecise effect estimates. We propose a different approach based on marginal density ratios (MDRs). The MDR directly compares the state distribution among individuals who would remain event-free under a target treatment strategy with the corresponding distribution among observed-adherent individuals. We use longitudinal g-computation to generate the target risk sets and a probabilistic classifier to estimate density ratios for reweighting the observed outcomes. Building on this approach, we also develop a doubly robust extension. Favorable performance across the simulation study suggests that MDR weighting is a promising alternative to cumulative longitudinal weights when its identification assumptions are plausible.

This paper introduces a novel penalized spatial function-on-function quantile regression framework for analyzing spatially indexed functional data, bridging a critical gap between spatial functional models and quantile regression. Our work makes three key contributions. First, we propose the first spatial function-on-function quantile regression model that jointly accounts for spatial correlation across curves through a functional spatial autoregressive structure while allowing inference on arbitrary conditional quantiles of the functional response. Unlike traditional mean-based alternatives, this approach successfully captures state-dependent volatility and distributional dynamics beyond the conditional mean. Second, we develop a two-stage instrumental-variable estimation strategy to address endogeneity induced by the functional spatial lag. By utilizing tensor-product B-spline expansions with tensor-product roughness penalties, our method ensures optimal smoothness without the destructive information loss inherent in principal component truncation. Third, for fixed spline dimensions, we establish $\sqrt n$-asymptotic normality of the spline coefficient estimators and the induced finite-rank Gaussian-process limits for the reconstructed coefficient surfaces. Extensive Monte Carlo experiments and a high-resolution analysis of Italian PM$_{2.5}$ air quality data demonstrate that spatial function-on-function quantile regression significantly outperforms non-spatial and mean-based competitors, providing a robust and informative tool for environmental risk management and complex functional data analysis. Our method has been implemented in the SpatialFoFReg R package.

For continuous treatments such as drug dose or ventilator intensity, a key clinically actionable question is whether a modest, patient-specific adjustment to the current dose would help or harm, rather than whether to treat at all. Standard estimands such as average or conditional dose-response functions require positivity across a wide range of doses, an assumption that routinely fails in observational clinical data where protocols tie dosing to patient characteristics. We develop a framework for characterizing heterogeneity in the effects of small shifts (“nudges”) of a continuous treatment. We study two estimands: the conditional nudge effect, the expected outcome change if an individual at dose $a$ with covariates $\bx$ had their dose shifted by $\delta$, and the conditional modified treatment policy (CMTP) effect, which averages the nudge over the observed dose distribution given covariates. Both are identified under weak, shift-specific local positivity and exchangeability conditions. Recasting the $\delta$-shift as a two-arm comparison through a duplicated-data construction, we develop weighting and A-learning estimators based on squared-error and negative log-likelihood losses, introduce augmented versions that reduce variance without changing the target, and establish asymptotic normality of proposed estimators. Simulations support the theory, and an analysis of mechanical ventilation data from MIMIC-III identifies patient profiles predicted to benefit from a modest reduction in mechanical power.

Tests of conditional mean independence can lose power when departures are confined to a bounded part of a multivariate predictor space and the relevant spatial scale is unknown. We propose a Multiscale Ball Conditional Mean Independence (MBCMI) test that aggregates support-weighted local mean contrasts in an outcome variable across balls centered on each data point in a predictor set. Fixed-grid theory identifies the population target, establishes consistency for grid-visible alternatives, and derives a Pitman local-power limit governed by the ball-smoothed mean departure. For serial data, feasible recursive-sign-bootstrap validity for stable finite-order autoregressions with conditionally sign-symmetric innovations is established. Application-aligned serial null experiments reject 4.25% of the time. MBCI is demonstrated to be strongest for local and radial signals. Predictor-law experiments show that these conclusions are not an artefact of independent Gaussian covariates. In monthly U.S. finance data, cross-fitted residual MBCMI tests remove every full-sample rejection, suggesting contemporaneous conditional-mean dependence rather than evidence of distinctive nonlinear structure.

Survival models that incorporate a cure fraction provide a flexible framework for jointly modeling the cure and the survival distributions. However, when the data comprise a high proportion of censored observations or highly unbalanced binary covariates, maximum likelihood estimation may become unstable, leading to parameter estimates that diverge to infinity. This phenomenon, commonly referred to in the literature as monotone likelihood, compromises statistical inference by precluding the existence of finite maximum likelihood estimates. Specifically, the likelihood function increases monotonically along certain directions in the parameter space, so no finite maximizer exists. To the best of our knowledge, the monotone likelihood problem has received little or no attention in the context involving the promotion time model. This paper addresses this gap by proposing a modified score function based on Firth's bias-reduction method, which adjusts the estimation procedure to ensure finite and stable parameter estimates. The performance of the proposed approach is evaluated through extensive Monte Carlo simulation studies. An application to a real dataset further demonstrates its practical advantages, showing that the mitosis factor, an established prognostic marker, becomes statistically significant under the proposed methodology.

Many scientific problems are relational: the quantity of interest is a connection between two objects, while information about similarity is available for the objects themselves. We develop a covariance framework for unordered relationships that transfers object-level geometry to the relations they form while preserving endpoint identity and invariance to ordering. Building on symmetric pairwise-kernel representations, we develop theory for the loop-free domains used in undirected networks. We establish spectral interlacing and trace-loss results after self-pairs are removed, connect the relational spectrum to regularization and risk, derive an exact inferential error for spectral truncation, and quantify how perturbations of the underlying geometry propagate to pair covariance and estimation. Simulations show when structured borrowing improves estimation and how geometric misspecification can erode that benefit. We apply the framework to autism neuroimaging using resting-state functional-connectivity data from the Autism Brain Imaging Data Exchange (ABIDE). With a 116-region parcellation and 6,670 unique connections, the application shows that a large connectome can have a much smaller effective covariance dimension. It also demonstrates that high explained covariance alone is insufficient for choosing a low-rank representation when inferential accuracy is the goal. The framework provides a principled foundation for covariance and regularization when the statistical units are unordered relationships.

A forecasting benchmark reports which method won. We show that the answer is set by the evaluator's choices before any model is fitted. We benchmark 24 forecasting methods and one textbook reference, including six 2025-era time series foundation models, on a production marketplace panel of 1,887 business customers over 67 months. We hold the data, the horizon and the period fixed, and vary only the evaluation design. Three choices each reverse or dissolve a headline conclusion. Changing the unit of analysis from the market total to the individual customer moves our production baseline from second of nineteen, beaten by nothing, to twenty-third of twenty-five. Nineteen of its twenty-four challengers beat it there. Changing how much error is pooled decides whether a Diebold-Mariano test finds anything at all. Scoring prediction intervals rather than point forecasts reorders the field almost completely, with a rank correlation of 0.02 on intermittent demand. We then measure what the deployed system gets from this. Its selection rule captures 55% of the distance between doing nothing and choosing with hindsight. The reversal is not a quirk of our data. We ran the released protocol, unchanged, on the public M5 retail panel. The same baseline shape places first at the market total and last per series, beaten by everything, and a replayed selection rule closes 64.7% of the same floor-to-ceiling distance there. Adding five zero-shot foundation models to that roster changes who wins at the total, not the shape. The bands' blind spot travels too: conformal bands under-cover most on the spikiest items. Splitting our own panel into ever smaller groups turns the contrast into a curve: the baseline's rank worsens at every level of disaggregation. We release the evaluation protocol and report an error of our own that inverted a result before we caught it.

We study causal inference in interrupted time series designs where a treatment affects every unit simultaneously, so that the contemporaneous controls used by difference-in-differences and synthetic control are unavailable and the counterfactual must be extrapolated from a unit's own pre-treatment history. We establish identification within the potential outcomes framework and estimate the counterfactual by Gaussian process regression. Rather than committing to a single best-fitting trend, the estimator retains the functions consistent with the pre-treatment series and widens its intervals where extrapolation magnifies their divergence. Connecting it to reproducing kernel Hilbert space theory, we derive a bias decomposition that isolates the component extrapolation inflates and a worst-case bound on that component, justifying the Gaussian process estimator's posterior variance as extrapolation-aware uncertainty quantification. In closed form, the band equals the worst-case divergence the model class permits among functions consistent with the pre-treatment data. The method is illustrated with calibrated simulations and an analysis of handgun purchases after the Supreme Court's Heller decision, a universal treatment whose practical effect concentrates in a single jurisdiction. An R package, gpss, implements the approach.

In many applications, from government to ecology, integrating data from diverse and noisy sources is critical for downstream inference. However, a unique identifier to link records cleanly from the same entity may not exist. Entity resolution (also referred to as de-duplication or record linkage) merges such databases to identify duplicates, allowing for more complete data for inference. A multitude of methods from statistics and computer science in recent years assume a single, immutable true value for each variable used in linkage. We argue this restrictive assumption is often violated in practice, leading researchers to discard useful data and biasing downstream inference. For example, a respondent's education status may truly change between two different surveys, yet existing methods would treat at least one observation as a distorted version of the truth, even though both are correct. In this paper, we propose a novel entity resolution model that comprehensively accommodates "multiple truths" by introducing a mixture of exponential family distributions that further handles multiple data types. We provide options to fit the model with Markov chain Monte Carlo routines and variational inference for massive datasets. We demonstrate the method's value via simulation and linking a longitudinal survey of Italian household wealth.

Neural survival models are increasingly asked to support counterfactual claims—how much a treatment would change survival in a population—rather than only prognostic risk scores. Answering such questions from observational data requires valid inference for treatment-specific survival contrasts under confounding and covariate-dependent censoring, targets for which standard deep survival estimators are biased and provide no honest uncertainty. We propose Targeted Deep Survival Contrasts (TDSC), which extends Targeted Deep Architectures (TDA)—targeted maximum likelihood estimation embedded in a network's weight space—to the full vector of treatment-specific survival curves over a time grid, and hence to the benefit curve and the restricted mean survival time (RMST) difference. A single universal targeting path, one ridge projection of the stacked efficient influence functions onto closed-form last-layer gradients per iteration, simultaneously solves the projected estimating equations for all coordinates; a one-step residual top-up converts the plug-in into a doubly robust estimator of the unrestricted target; and a multiplier bootstrap yields simultaneous confidence bands for the benefit curve. We prove joint asymptotic linearity, band validity, and double robustness of the top-up for a cross-fitted variant requiring no Donsker conditions. Across seven Monte Carlo banks with confounded treatment, sign-varying effect heterogeneity, and dependent censoring, the TDSC plug-in attains nominal pointwise and simultaneous coverage with 35% lower MSE than a per-timepoint one-step (AIPCW) built from the same nuisance fits. Under a badly wrong outcome model the plug-in tracks its working parameter and its intervals fail (44% coverage), while the top-up restores nominal inference for the unrestricted causal target (94-95%)—and in-sample diagnostics separate the two regimes.

Mixed-type data containing both numerical and categorical variables arise in many scientific and real-world applications. Existing representation learning and generative modeling approaches typically focus either on reconstruction accuracy or unconditional data generation, but often fail to recover the full conditional distribution of the data while preserving interpretable structural relationships between heterogeneous variable types. In this work, we introduce Conditional-Independence-Regularized Distributional Autoencoders, a framework for learning low-dimensional representations of mixed-type data through conditional distribution matching and structural regularization. Our method combines an energy-score-based objective for numerical variables, a likelihood-based objective for categorical variables, and an auxiliary conditional independence regularization term encouraging the learned representation to capture the dependence between numerical and categorical components. We provide theoretical analysis showing that the optimal representation balances unexplained numerical variability, conditional entropy of categorical variables, and residual conditional dependence. Empirically, the proposed method achieves strong performance on both synthetic and real-world datasets, substantially improving categorical distribution recovery, achieving competitive overall conditional distribution recovery, and preserving mixed-type dependence structure. The code has been made available at GitHub.

The Hosmer-Lemeshow calibration test groups patients by predicted risk for a valid reference and loses power that more groups cannot recover. Later tests weight each record's residual alone, which makes them fragile: on an otherwise correct model, one record in a thousand with a corrupted covariate raises the false-alarm rate of Stukel's score test from 5% to 12%, and ten to 63%. Pooling on equal-size groups bounds a wrong record's influence, dividing its residual by its groupmates' variance; without pooling, the same directions are as fragile as Stukel's test after a refit. EDGE, the test proposed here, projects the grouped residuals onto a small basis of calibration shapes. Its degrees of freedom do not depend on the number of groups, so the partition becomes a setting, fine-grained for power and coarse when records may be wrong, and its reference needs no resampling. In a prespecified simulation EDGE was comparable in power to Stukel's test on clean data and 0.064 more powerful on average than the ten-group Hosmer-Lemeshow test. With one and ten exaggerated covariates in a thousand its false-alarm rates were 0.056 and 0.097, and with ten groups below 0.10 up to about ten exaggerated or five reversed. In external validation, at ten groups, its average power was that of Cox's recalibration test and the GiViTI belt, and its false-alarm rate stayed below 0.10 with ten reversed records in a thousand, where theirs did not. In a 70,000-patient cohort its verdict did not change with the partition.

Most data-driven policy learning methods maximize average outcomes, overlooking the possibility that a policy beneficial on average may still harm a substantial fraction of individuals. Motivated by the ethical principle of "first do no harm", we study how to design a change from a baseline policy that improves overall welfare while keeping the worst-case probability or expectation of individual harm below a specified limit. We establish sufficient conditions under which an optimal policy transition has a lexical leapfrogging structure: groups defined by covariates and current treatment are ranked by a priority score, and any treatment change moves them directly to the conditionally optimal treatment. We derive this score under several models for the dependence among potential outcomes. We demonstrate this harm-aware policy optimization approach in a reanalysis of the I-SPY2 breast cancer platform trial and show how the consideration of counterfactual harm may lead to different conclusions about which treatment-subgroup pairs may warrant deprioritization in further clinical evaluation.

Kernel density estimation converts finite samples into probability densities, but its performance depends critically on bandwidth selection. Classical selectors prescribe the sample-to-bandwidth rule analytically or asymptotically, or solve a new optimization for each sample. An amortized framework is proposed that instead learns this mapping across a distribution of density-estimation tasks by optimizing the logarithmic score. A truncated-and-renormalized bounded-support formulation enables stable learning across heterogeneous tasks, while affine standardization allows a selector trained on a single reference interval to transfer across bounded intervals. Experiments under Gaussian sampling, a multi-family benchmark, and randomized Gaussian-mixture training show that the amortized selector consistently and substantially outperforms Silverman's rule, the Sheather–Jones selector, and least-squares cross-validation, with especially large gains in small and heterogeneous samples. Finite Gaussian mixtures provide a generic training mechanism supported by their $L^1$ approximation property. Selectors trained in this way generalize strongly across different density structures, allowing the same trained selector to be applied directly to finite samples from unknown densities without specifying or fitting a distributional family. This combination of broad applicability and strong empirical performance makes the framework attractive for a wide range of applications in which finite samples or ensembles must be converted into continuous probability densities.

We propose computationally efficient tests for equality of mean vectors of two or more high-dimensional populations. Central to our approach is an equivalence between equality of means and a zero population logistic regression parameter. We establish this equivalence for independently distributed observations without imposing common distributional assumptions across populations. Our procedure uses logistic Lasso to screen informative variables and an unpenalized logistic refit for inference in the reduced dimension, yielding asymptotically correct size and consistency. For a specified two-sample Gaussian submodel and sparse discriminative class, the test also attains the minimax separation rate. The framework extends to multiple populations through multi-class logistic regression. Simulations demonstrate accurate size control, strong power, and favorable computational scaling compared with existing tests under unbalanced designs and variance heterogeneity. Applications to gene-expression data with more than twenty-two thousand variables illustrate the practical scalability of the proposed procedures.

Spatial statistics has grown from kriging for spatial prediction into a broad framework for learning from complex dependent data. This article traces that development from random fields and spectral methods to Bayesian hierarchical models and scalable computation. It then connects these foundations to Spatial AI, where graph learning and neural networks are being adapted to spatially dependent data. The article introduces the main ideas behind kriging and nonstationarity and explains how data fusion and uncertainty quantification extend spatial inference to more complex settings. The central contribution is a unified account of how these developments lead naturally to new forms of Spatial AI. Rather than treating spatial statistics and machine learning as separate traditions, we show how both learn from dependence while preserving interpretable structure. We also examine how spatial geometry and physical knowledge can guide flexible representation learning and support scientifically meaningful prediction.

This paper develops a general transfer learning framework for nonparametric regression with data consisting of multiple groups. Under the assumption that groups share a common structure along with group-specific deviations in additive form, the proposed method employs a two-stage offset learning procedure: the first stage pools data from all groups to estimate an overall mean function, and the second stage estimates offsets for each group, yielding final group-level estimators through additive combination. Upper bounds on the $\mathcal L_2$ error are established for the proposed framework, covering a broad class of nonparametric estimators under mild complexity and noise conditions. When instantiated with deep ReLU networks, explicit convergence rates are derived under hierarchical composition models, demonstrating the ability to overcome the curse of dimensionality. Conditions that enable positive transfer with faster rates are considered, including learning with simpler functions and data augmentation through pooling samples across groups. Various simulations and real-data experiments further validate the effectiveness of the proposed method.

The SARS-CoV-2 pandemic highlighted the ongoing risk infectious diseases pose to society and the value of reliable information on the likely future burden. When forecasting an epidemic at fine spatial resolution, traditionally used mechanistic compartmental model struggle to capture highly complex granular transmission dynamics, resulting in inaccurate and overconfident forecasts. However, detailed Agent-Based Models (ABMs), are challenging to calibrate and are too computationally expensive to use in real-time. Amortized simulation-based inference promises to overcome this difficulty by exploiting the power of machine learning (ML) to perform approximate forecasting at near-real-time using arbitrarily complex models of epidemics. In this work we introduce Generative Neural Inference for Epidemics (GENIE), a spatio-temporal ML-based framework for high-resolution forecasting of the burden of respiratory pathogens. GENIE is designed to reflect two key characteristics of outbreaks: (i) shared biological mechanisms across locations and (ii) location-specific characteristics affecting transmission dynamics. This results in the model architecture having two modules: (i) a Local Infection Encoder - which learns to represent disease dynamics shared across all locations and (ii) a Local Profile Encoder - which learns location-specific representations. Using simulations from a high-resolution spatio-temporal ABM, GENIE is trained to generate samples from an approximate posterior predictive distribution of future epidemic trajectories. Benchmarked against established statistical and ML models, GENIE demonstrates superior performance across a range of measures including the timing and magnitude of peak hospitalisations.

Autism spectrum disorder (ASD) is associated with heterogeneous alterations across distributed brain systems, creating challenges for whole-connectome inference. The difficulty arises not only from the large number of connections, but also from dependence among effects indexed by anatomically and functionally related region pairs. We introduce a Bayesian Edge-Space regression framework that treats each participant's connectome as a network-valued response and models the adjusted ASD effect over unordered brain-region pairs. The main methodological contribution is a positive-semidefinite covariance construction defined directly on connections. Anatomical and diagnosis-blind functional similarities are lifted from regions to edge space through a symmetrized endpoint-matching operation that preserves endpoint identity and is invariant to endpoint ordering. An additive Bayesian hierarchy estimates anatomical, functional, and interaction contributions together with multisite adjustments and connection-specific effects. Theoretical results establish covariance validity and continuous nesting of the structured components. Low-rank kernel representations and an exact sufficient-statistic reduction enable whole-connectome computation without preliminary edgewise estimation. Simulations show improved recovery of the effect surface, particularly under weak signals. In the Autism Brain Imaging Data Exchange, the framework identifies widespread reductions together with localized increases in ASD-associated connectivity. This pattern supports heterogeneous reorganization across distributed neural systems rather than uniform hyper- or hypoconnectivity. Under the fitted parameterization, the functional component has the largest structural scale, indicating organization beyond anatomical proximity alone.

Practitioners inferring causality from observational data usually rely on a single method and treat its output as causal truth. Recent tools select an optimal method for a dataset, and recent ensembles aggregate multiple causal-discovery algorithms into one graph, but little work pools evidence across different mathematical traditions, including non-causal ones. We present Multi-Method Causal Evidence Synthesis (MCES), a framework that ranks which candidate drivers in an observational system are most likely relevant to a set of outcomes, and with what strength of evidence. MCES runs eleven methods across eight mathematical traditions on observational panel data and pools their outputs into a Convergent Evidence Score (CES), a linear opinion pool. CES quantifies convergence of evidence across analytical lenses: the degree to which methods with different assumptions point to the same driver-outcome relationship. It does not claim causal identification in the interventionist sense; it supports hypothesis prioritization, not a transferable probability of causation. MCES first applies Structural-Behavioral Decomposition to remove definitional (algebraic) relationships, then runs all methods, normalizes outputs to [0,1], and pools them. We distinguish MCES from method selection, structural ensembles, prediction ensembles, and literature synthesis. Using synthetic data with embedded ground truth, the Sachs protein-signaling benchmark, six Bayesian-network structure benchmarks, and two further synthetic domains, we show MCES ranks true edges near the top (Precision@5 = 1.0, Precision@10 = 0.96 on the primary scenario), with a low empirical rate of null pairs reaching Moderate-or-higher convergence. Our central point is not that the pool beats every individual method, but that no single method is uniformly best across the evaluated scenarios, so MCES offers a method-agnostic default.

Propensity score methods for causal inference are increasingly being used in cohort and experimental designs, but their development and uptake in outcome-dependent sampling schemes, such as case-control studies, remains limited. Case-control studies involve the sampling of individuals with and without an outcome of interest with the goal of estimating the effects of past exposures. When the design is observational, statistical adjustment for confounding bias is necessary. In case-control studies, propensity score models can be fit using control data under the assumption that the controls are representative of the source population with respect to their exposure distribution conditional on covariates ("control exchangeability"). In this paper, we first demonstrate that relative effects, such as causal risk ratios, are estimable under three different case-control design variants using control-fitted propensity scores. We appropriate two existing estimators for these designs: inverse probability of treatment weighting and an efficient and doubly robust estimator. We also introduce a novel two-step propensity score caliper-matching procedure for case-control designs. We introduce novel diagnostic tools to verify two necessary types of overlap. We then contrast our estimators using simulated data and apply them to examine the association between regular aspirin use and ovarian cancer risk.

In fixed-confidence best-arm identification, proofs often use a union bound across the competing arms. From a multiple-testing point of view this can look puzzling: if the best arm is unique, only one hypothesis of the form “arm $i$ is best” can be true. Why then should there be a Bonferroni-type factor of $K-1$? The answer is that there are two natural ways to orient the hypotheses. In one orientation, best-arm identification is literally a strong familywise-error-rate (FWER) problem with $K-1$ true nulls. In the opposite orientation, exactly one null is true, but a pairwise implementation can falsely reject that one null through any of $K-1$ comparisons. Thus the multiplicity has not disappeared; it just pops up in different places. This note makes the equivalence explicit in the terminology of both communities.

This document describes the application of a first order linearised nonlinear repeated measurements approach to the analysis of battery cell ageing profiles generated under controlled conditions in a laboratory. The primary advantage of the model is it reflects the obvious structure in the data. Consequently, it is a two-component of variance model: variation within ageing profiles (measurement noise) and variation among ageing profiles (test-to-test or cell-to-cell) variation. Novel regularised iterative generalised least squares parameter identification schemes, with optimal hyper-parameter re-estimation, are used to identify the hierarchical nonlinear model. The training data comprised $SoH$ profiles for 10 cells aged at various constant discharge and charge current cycles at a fixed chamber environmental temperature of 25 [$^\circ$C]. Each cell $SoH$ profile is modelled using a simple power law expression, whereas the variation in ageing parameters is modelled using a single knot cubic B-spline. $SoH$ is accurately predicted to $\pm 0.191\%$ for $SOH \in [0,20]$.

We study a function-on-function linear regression model in which the response at time $t$ depends on both the past trajectory of a predictor and its concurrent value. The model combines an $L^2$-historical effect with a point-evaluation effect, and these two coefficient functions are not automatically identifiable. We characterize the resulting non-identifiability and show that the concurrent and historical effects are separately identifiable whenever the covariance eigenfunctions of the covariance operator of the predictor are not pointwise square-summable. This mild and novel condition prevents the concurrent point evaluation from being represented by an $L^2$-historical effect. Building on an orthogonalized representation of the predictor process, we propose a smoothing-spline estimator for both coefficient functions and establish consistency rates. The rates reveal an interesting trade-off between path regularity and eigenvalue decay: smoother predictor trajectories lead to faster convergence of the historical-effect estimator, whereas rougher trajectories lead to faster convergence of the concurrent-effect estimator. Simulation studies and two real-data applications demonstrate the practical importance of disentangling concurrent and historical effects.

We develop a partial identification learning framework for individualized treatment rules (ITRs) with categorical treatments, outcomes, and instrumental variables. Rather than relying on strong causal assumptions required for point identification, our framework leverages causal bounds to characterize the optimal treatment decision. Existing methods for ITR optimization under partial identification are largely restricted to binary treatment settings and the bounds derived by Balke and Pearl under the canonical instrumental variable design. We extend this framework to accommodate a broader class of causal structures as well as scenarios with categorical treatment, outcome, and instrumental variables. We introduce a generalized minimax loss criterion for treatment selection from among more than two options, which minimizes the maximum possible difference between the chosen and the optimal treatment based on partial identification bounds. To construct the ITR, we use a symmetric embedding strategy that maps discrete treatments to the vertices of a regular simplex, avoiding the geometric inconsistencies of standard one-vs-rest approaches. We derive a differentiable, weighted surrogate risk function and show that optimizing it solves the original problem. Furthermore, we provide finite sample convergence rates via an oracle inequality under general regularity conditions, which we show are satisfied by a kernel based implementation. Numerical experiments demonstrate that the framework yields ITRs significantly closer to the oracle ITR compared to existing alternatives in settings with unmeasured confounding.

Predicting combinatorial effects from limited-range observations is a fundamental challenge in many scientific domains, including drug discovery and hyperparameter optimization. We study combinatorial extrapolation, where training data consists of axis-aligned samples with only one active covariate, while test-time inputs involve multiple simultaneously active covariates. We introduce DExtrI, a method for extrapolating interaction effects beyond the support of the training data. We provide theoretical guarantees characterizing when such extrapolation is possible. Empirical results on synthetic and real-world datasets demonstrate that DExtrI successfully generalizes to unseen combinations of covariates. Our approach enables applications such as predicting previously untested drug combinations and improving the efficiency of hyperparameter optimization.

Reliability set estimation identifies input regions where a response probability exceeds a target level, bridging estimation and safety-critical decisions. Practitioners typically start with a working model, an imperfect approximation of the true response surface. Relying on this imperfect model may incur decision risk, potentially certifying unsafe regions as safe. We develop a unified framework that turns such a working model into a trustworthy decision rule. First, a modeling-then-calibration procedure decouples estimation from decision. Since the true set is unobservable, we introduce an asymmetric, observable surrogate loss and use a separate calibration set to select a bias-correcting threshold, reducing decision risk and achieving $O_P(1/n)$ volume convergence. Second, we leverage conformal risk control with the surrogate loss to control false inclusion risk, which is the most safety-critical error, at a pre-specified level regardless of working model quality. Together, these calibration procedures show that a separate calibration set is necessary for risk control. Third, an adaptive design concentrates observations on the reliability set and its boundary, improving model quality where errors most affect decisions while controlling budget elsewhere. Numerical studies show not only more accurate set estimates but also calibrated finite-sample risk control that classical plug-in methods lack.

Instrumental variable (IV) methods are powerful for causal effect estimation with unmeasured confounding, but in practice researchers often face a set of candidate IVs whose validity is difficult to determine from observational data. This paper studies the problem of testing the validity of IV sets under Causal Additive Models with Non-Constant Effects (CAM-NCE). To address this problem, we propose a testable condition, termed the Cross Auxiliary-based independence Test (CAT) condition, for assessing IV set validity from observational data. We show that, under the completeness condition, if the CAT condition is violated, the corresponding set cannot be a valid IV set. Furthermore, under a cross distributional non-degeneracy condition, we establish that the CAT condition becomes both necessary and sufficient for characterizing valid IV sets under CAM-NCE. We then extend the CAT condition to settings with covariates and develop a practical finite-sample algorithm for testing the validity of candidate IV sets. Extensive experiments on synthetic data and three real-world datasets demonstrate the effectiveness and practical utility of the proposed method.

We study heterogeneous treatment-effect (HTE) estimation in observational survival studies commonly associated with both censored outcomes and unmeasured confounding. We integrate causal survival forests (CSF) with negative controls (NC) from proximal causal inference and introduce Negative Control Causal Survival Forests (NC-CSF), a flexible nonparametric HTE learner for survival analysis. Our approach uses a loss that incorporates proxy variables and Neyman orthogonalization to train the random forest, thereby mitigating bias from unobserved confounding and gaining robustness to nuisance estimation. Through extensive simulations spanning varying levels of confounding, proxy relevance, and censoring mechanisms, we demonstrate that NC-CSF substantially reduces bias and estimation error relative to existing baselines. We further demonstrate the practical utility of our method on various clinical datasets, where it confirms several existing findings and also reveals new interpretable patterns of treatment-effect heterogeneity. To facilitate practical use, we provide an end-to-end Python implementation of NC-CSF that carefully handles implementation details such as nuisance estimation and clipping.