Papers

We study large-sample properties of higher-order Markov chains on a finite alphabet $\Sigma$ when the order $m_n$ is allowed to grow with the sequence length $n$. By embedding the process into a first-order chain on $\Sigma^{m_n}$ and exploiting return-time decompositions, we establish a central limit theorem for additive functionals $\sum_{t}\! g_n(Y_t^{(n)})$ under natural ergodicity and sparsity conditions. The normalization involves the stationary return time to a suitably chosen state and accommodates triangular arrays with $m_n\!\to\!\infty$ and $m_n/n\!\to\!0$. We further illustrate the assumptions in a binary variable length Markov chain (VLMC), deriving explicit lower bounds on stationary masses that yield a concrete growth regime (e.g., $m_n\log m_n/n \to 0$) ensuring the CLT. These results provide asymptotic foundations for inference in sparse/partitioned higher-order models; including VLMCs and sparse Markov models (SMMs) where the effective dimensionality grows with the sample size.

Sparse pursuit after dictionary learning can yield a precise atom support even when its physical interpretation is not justified by the calibration data, especially for highly coherent dictionaries where alternative calibration-compatible dictionaries may assign different physical meanings to the same selected support. We develop resolution-aware physical-support inference that jointly accounts for uncertainty in the learned dictionary and in the representation of a deployment signal. Our cross-dictionary confidence correspondence retains calibration-compatible dictionaries and deployment-compatible sparse representations, then projects the surviving explanations onto physical-support space. For local coherent-atom classes with separation scale s, once the deployment data resolve the coherent-block explanation and its atom support, the minimax physical resolution from N calibration signals satisfies $\delta_{\mathrm{opt}}(N,s)\asymp\min\{s,\frac{1}{\sqrt{N}s^2}\}$, with relative resolution governed by the orientation-information scale $Ns^6$. Deployment replication improves physical localization only when orientation changes cannot be absorbed by adjusting the active coefficients. For computation, we introduce active endpoint bracketing (AEB), an adaptive finite-bank procedure that evaluates only candidates that can still affect the physical report and otherwise safely coarsens or abstains. Finite-bank experiments, including a four-region synthetic application, show that a point-valued plug-in selector can be physically overprecise, whereas AEB avoids unsupported refinement with fewer candidate evaluations.

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.

In Markov chain Monte Carlo sampling, light-tailed target distributions present something of a poisoned chalice: their light tails offer good confinement, and tend to imply good mixing properties for natural continuous-time dynamics, but the steepness of their tail decay means that they often fall outside of the scope of modern quantitative convergence theory. For usual gradient-based samplers, this reflects a genuine instability issue, whereby Metropolis acceptance rates can degrade badly. In this work, we study the gradient-free random-walk Metropolis sampler, and show that for a wide range of light-tailed targets, the acceptance probability remains stable for reasonable choices of proposal variance, from which effective and favourable mixing time estimates can be deduced. The analysis relies on a simple relationship between the first and second derivatives of the log-density of the target distribution.

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.

Decision tree-based models are widely used in machine learning due to their interpretability and strong empirical performance. However, training decision trees can be computationally expensive, particularly for large and high-dimensional datasets, largely due to the exhaustive search over candidate splits at each node. To improve computational efficiency, we propose Data-Informed Centroid Splitting (DICS), a clustering-based framework that constructs a compact and informative set of candidate splits using data-driven priors. By incorporating class-aware structure, DICS significantly reduces the split search space for classification tasks while preserving predictive performance. We further provide theoretical analysis showing that under the stated assumptions, DICS does not degrade the performance of classification trees compared to exhaustive split search. DICS can be incorporated into classification trees, random forests, and gradient-boosting models. Extensive experiments demonstrate that DICS achieves comparable accuracy while substantially reducing training time across synthetic and benchmark datasets, highlighting the benefit of integrating data-informed priors into split selection for scalable classification tree learning.

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.

Many estimators are ratios of coprime polynomials in a sample covariance matrix, and their accuracy depends on the relative fluctuation of the sample denominator. Under Gaussian sampling in fixed dimension, we call a nonconstant polynomial denominator self-normalizing if the first-order variance of its relative error does not depend on the population covariance. We prove that these denominators are exactly the flag powers, nonzero constant multiples of products of positive integer powers of nested generalized variances. Equivalently, the denominator's sample-to-population ratio has a covariance-independent finite-sample law, which we determine explicitly. Sufficiency is classical; the new converse shows that a first-order variance condition forces an exact sampling law. We show that relative stability, meaning bounded first-order relative variance, characterizes uniform tightness of scaled relative errors over positive-definite covariances. It permits replacing the sample denominator by its population value in the limit theory of the ratio. Self-normalization is its rigid core. We locate these classes in applications, where regression on predecessors in a fixed order yields only constant or self-normalizing denominators, instrumental-variable formulas yield relatively unstable ones, and nonparametric identifiability does not guarantee relative stability.

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.

Classical information criteria such as the Bayesian Information Criterion (BIC) rely on regularity assumptions that break down for singular models, leading to incorrect model selection in settings such as deep learning. The Widely Applicable Bayesian Information Criterion (WBIC) relies on local learning coefficients $\lambda$, which in the analytic case coincides with local Real Log Canonical Thresholds (RLCT) of the Kullback-Leibler divergence of the model, to capture correct marginal likelihood asymptotics. Exact computation of the learning coefficients has been limited to special cases, and only sampling-based estimation methods are generally applicable. We present the first deterministic algorithm that computes local RLCTs exactly for any two-dimensional model whose Kullback-Leibler distance is contact equivalent to a polynomial, derive a bound on its complexity, and demonstrate its effectiveness for a broad class of models, with applications including polynomial neural networks. Beyond providing ground truth to calibrate sampling-based estimators, exact computation reveals algebraic structure in learning coefficients that sampling cannot and out-speeds it in the shallow regime.

We solve the open problem of determining the maximal value of Spearman's rho when Spearman's footrule is prescribed, thereby completing the exact attainable region of these two quantities. To prove this result, we reformulate the underlying copula optimization problem as an optimal transport problem with a linear moment constraint and construct the unique optimal coupling through a matching feasible dual potential and its contact set. Equivalently, this coupling minimizes the variance of $|U-V|$ among all couplings of $U,V\sim\mathcal{U}(0,1)$ with prescribed mean $\mathbb{E}|U-V|$. Our main result admits several applications: First, in the context of finite rankings, we obtain an improved Cauchy–Schwarz inequality between Spearman's footrule distance and the associated quadratic rank difference. Second, in the framework of generalized mixability, we characterize the attainable constant values of $|U'+V'|$, for $U',V'\sim\mathcal{U}(-1/2,1/2)$, and determine the minimal quadratic deviation for a given mean. Third, we derive explicit bounds relating Chatterjee's rank correlation $\xi(X,Y)$, which can detect complex functional dependence of $Y$ on $X$, to the copula correlation ratio–a rank-based fraction of explained variance–by exploiting their conditional i.i.d. representations in terms of Spearman's footrule and Spearman's rho.

We study inference-time control for text generation in discrete diffusion language models, where the goal is to steer sampling toward sequence-level rewards without retraining. Prior work in this domain has focused on particle-based methods such as best-of-$n$ sampling and bootstrap sequential Monte Carlo, which may suffer from overoptimism and weight degeneracy, respectively. We address these limitations using nested sequential Monte Carlo methods. We formulate nested SMC (NSMC) and fully-adapted nested SMC (FA-NSMC) for Feynman–Kac steering, identifying and correcting errors in prior formulations that lead to biased final estimates. We evaluate these methods on toxicity and fluency steering tasks, showing that NSMC and FA-NSMC consistently outperform best-of-$n$ and bootstrap SMC.

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.

Environmental conditions are major drivers of malaria transmission, but epidemiological analyses are often constrained by temporal misalignment between health outcomes reported at coarse time scales and environmental exposures available at finer resolutions. Conventional approaches aggregate environmental data to match health outcomes, potentially obscuring delayed and nonlinear relationships. We propose a Bayesian spatio-temporal framework that addresses this limitation through a latent daily disease process linked to observed monthly malaria counts by temporal disaggregation. The framework integrates distributed lag nonlinear models for climatic effects, spatio-temporal random effects, and intervention covariates within a unified hierarchical model. The methodology was applied to malaria surveillance data from 161 districts in Mozambique between 2017 and 2024, integrating temperature, precipitation, relative humidity, vegetation, elevation, and malaria interventions. Compared with a conventional monthly model, the proposed framework improved predictive accuracy and uncertainty quantification while exploiting the temporal resolution of environmental data. Estimated relationships showed nonlinear associations between climatic variability and malaria incidence, including an optimal temperature range, increasing risk with positive vegetation anomalies, and nonlinear precipitation effects. By avoiding temporal aggregation of environmental exposures, the framework provides a flexible approach for investigating delayed environmental effects from routine surveillance data and can be extended to other environmentally sensitive diseases with mismatched temporal resolutions.

Reputation is widely recognized as a key mechanism for sustaining cooperation. However, most existing game-theoretic models treat reputation primarily as an external factor that modulates payoffs, interaction structures, or strategy update rules. In many social contexts, though, reputation operates primarily as information – it shapes how individuals interpret their own experiences and assess the behavior of others. To bridge this gap, we propose a spatial prisoner's dilemma game grounded in the reinforcement learning paradigm, in which agents equipped with Q-learning integrate both individual and social information via a locally defined reputation metric to guide their decisions. Our results reveal that reputation-modulated learning significantly promotes the emergence of cooperative behavior, and we observe a discontinuous phase transition from full cooperation to full defection as the temptation increases. Cooperation spreads through the nucleation of cooperative clusters, whereas the disintegration of these clusters drives the system into an absorbing state of complete defection. Overall, this study demonstrates that reputation facilitates cooperation not only by providing direct incentives but also by reshaping the social information landscape that agents rely on for learning and adaptation.

Timely, paddock-scale estimates of plant-available water (PAW) can support crop management in water-limited grain systems. We present the Sydney Soil Water-Energy Balance (SWEB) model, a scalable, physically consistent modelling framework that integrates satellite and climate data with soil properties to estimate crop evapotranspiration and root-zone soil moisture (RZSM) at daily, 30 m resolution. SWEB was validated nationally against different SM monitoring networks across Australia, which demonstrated robust performance across diverse grain-growing environments (correlation coefficients generally ranged from 0.70 to 0.85 for most regions). In future applications, mid-season PAW nowcasts could be combined with water-use-efficiency approaches to estimate water-limited yield potential and inform responsive management decisions, such as nitrogen fertiliser top-up recommendations.

Probability estimation over large alphabets under log loss is a well-studied problem, with celebrated methods such as the Good-Turing estimator. We introduce and study a new Bayesian estimator with four notable properties. First, its construction is exceptionally simple: multiply independent uniform draws from the probability simplex coordinate-wise and renormalize. Depth is the only structural parameter, and averaging over depths eliminates the need to tune it. Second, the regret of the resulting mixture, the excess code length it pays relative to a code that knows the source, admits an explicit and efficiently computable expression. Third, despite its simplicity and lack of tuned constants, the estimator is competitive across a diverse set of synthetic and real-text benchmarks with substantially more specialized methods, including Good-Turing. Fourth, the tractability of its regret allows us to identify scaling laws in data, alphabet size, and depth. For Zipf targets with exponent above one, the regret has a simple reading as long as the sample reveals only a small fraction of the alphabet. It closely matches the description length of the set of discovered symbols, at one bit of code per bit of description, plus a further cost per symbol. The data exponent is therefore the rate at which new symbols are discovered.

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.

Skchange is an open-source Python library for detecting structural changes in time series. It implements modern change detection algorithms within a unified and extensible framework. The algorithms are modular and composable, and they include changepoint search methods based on both cost minimisation and statistical tests. Key features include the detection of anomalous segments in addition to changepoints; theoretically well-founded fast and approximate search methods; theoretically well-founded algorithms for high-dimensional data, covering settings where either few or many features change simultaneously; utilities for automatic and data-driven penalty calibration, which balances false alarms against missed detections; and a large collection of built-in costs and statistical tests. The design follows established scikit-learn conventions to streamline both user and contributor experience, and Numba is used extensively to achieve high computational performance. Source code and documentation are available at https://github.com/NorskRegnesentral/skchange.

A minibatch can influence training beyond the update at which it is observed because AdamW stores past gradient information in its optimizer states. We study this delayed effect through paired trajectories that differ only in one gradient update and share the same subsequent training sequence. We formulate AdamW as a finite-horizon input–state–output (ISO) system whose state contains the model parameters and first- and second-moment estimates. Linearizing the joint dynamics yields a signed response operator that maps a localized gradient perturbation to its future loss effects, revealing how optimizer memory shapes their magnitude, timing, and sign. We further derive an exact multistep error decomposition and establish first-order finite-horizon accuracy under local smoothness and controlled activation switching. Experiments validate the response mechanism and optimizer-state effects, while repeated-future analyses reveal substantial prospective structure in delayed influence that can be partially recovered from ISO approximations. Code is available at https://github.com/Kanyooo/Loss_ISO.

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.

Coccidioidomycosis is a fungal lung infection endemic to parts of the Pacific Northwest and southwestern United States, Mexico, Central America, and South America. A 2017 study by Thompson et al. reported that many analyzed Coccidioides isolates had elevated minimum inhibitory concentration values for fluconazole but comparatively low minimum inhibitory concentration values for other triazole drugs. We constructed 172 synthetic joint minimum inhibitory concentration profiles from the published drug-specific marginal frequency tables. Values sampled from each marginal distribution were paired across drugs using a Gaussian copula, and potential cross-drug patterns were examined using k-means clustering, hierarchical clustering, and Gaussian mixture models. On the selected reconstruction, a forced four-cluster partition consistently identified an upper caspofungin minimum-inhibitory-concentration tail. Across the evaluated dependence scenarios, the gap statistic favored a single cluster in 96% to 100% of nested reconstructions, providing no evidence that the reconstructed multivariate data supported a broader multicluster structure. A separate simulation study examined recovery of an upper-severity-score category defined from prespecified quantiles of a composite minimum-inhibitory-concentration score. The study included 4,000 replications across 20 prevalence and measurement-noise conditions. The multiclass adjusted Rand index ranged from moderate to high depending on the method and prevalence, whereas binary partition agreement for the upper-severity-score category approached zero at 1% prevalence even though recall remained near 1.0. Clustering conclusions therefore depended on the assumed cross-drug dependence structure and on the realized number of observations in the target category.