Papers

Group testing is an established, highly cost-effective strategy for population-level disease surveillance that identifies positive individuals by pooling biological specimens. Originally introduced during World War II for large-scale screening and heavily utilized in modern high-throughput public health infrastructure, traditional group testing methods are restricted to purely associational analyses. Consequently, they lack the capacity to infer the direct causal effect of an intervention when individual-level data are subject to baseline confounding. In this work, we bridge this fundamental gap by introducing a causal inference framework tailored specifically for group testing designs. We integrate the principles of inverse probability weighting (IPW) directly into a pooled pseudo-likelihood formulation to construct an unbiased pseudo-score function. Under standard regularity conditions, we prove the consistency and asymptotic normality of our proposed plug-in estimator. Extensive numerical simulations demonstrate that our framework successfully purges severe selection bias, accurately recovering the true average treatment effect where traditional unweighted pooling models fail. Finally, we illustrate the practical utility of our method as both an estimation and a diagnostic tool using real-world observational surveillance data from the CDC's U.S. Influenza Vaccine Effectiveness Network.

Estimating causal effects in observational studies requires adjustment for confounding, a task that becomes challenging when the exposure is a function observed over a continuous domain rather than a scalar variable. We develop a functional propensity score weighting framework that achieves covariate balance by removing dependence between time-varying treatments and observed confounders, thereby enabling estimation of marginal causal effects in settings with functional treatments, covariates, and outcomes. We propose a dual formulation of the weight estimation problem that yields a smooth unconstrained optimization and improves computational scalability. The proposed framework extends naturally to settings with time-varying covariates and to longitudinal outcomes via a function-on-function marginal structural model, allowing estimation of causal effect surfaces. The proposed method improves covariate balance, estimation accuracy, and computational efficiency compared to the existing approach and retains these properties when extended to functional covariates and outcomes. We apply the method to data from the UK Biobank to estimate the causal effect of body mass index trajectories on the risk of Type 2 Diabetes and on subsequent glycated hemoglobin trajectories, a functional measure of metabolic status.

In early 2022, FIA mandated the change to the technical regulations for Formula 1, requiring to design cars around ground effect aerodynamics to mitigate the performance loss incurred by driving in the turbulent "Dirty Air" of another car. The reduction of the penalty was subsequently claimed, but never formally evaluated on a per lap basis. We gathered 100486 racing laps for the years 2021-2025 using the FastF1 API, built a compound-specific physics correction for Dirty Air to account for fuel and tyre wear, and evaluated the change introduced by the 2022 regulation using both OLS regression with clustered standard errors and Causal Forest Double/Debiased Machine Learning. We repeated the analysis using season as a categorical variable, applying a generalized circuit filter to account for a changing calendar. Both methods produced similar results, demonstrating no statistically significant change to the Dirty Air penalty when combining 2022-2025 data together (OLS interaction term beta = -0.0025, p = 0.803; Causal Forest mean effects of 0.019s and 0.018s per second of following distance in 2021 and 2022-2025). We tested the hypothesis, that the penalty reduction may have been concentrated in 2022 and partially eroded through 2023-2025. We found no season for which the change was different from the one observed in 2021 in the OLS analysis, while several seasons were significantly different from zero in the Causal Forest analysis, in a non-monotonic pattern, not following the theorized erosion timeline. We conclude there was no statistically significant change to the Dirty Air penalty under the new regulation, both in pooled and season-specific analysis. By evaluating the real-world racing results, we demonstrate that even if an aerodynamic advantage exists, it did not translate into a measurable improvement over following distance, where other factors can swamp such an effect.

Matrix decomposition SEM (MDSEM) is a data-matrix-based alternative to conventional covariance-based SEM, but its theoretical relationship to covariance-based SEM and the statistical properties of its estimator have remained unclear. We first reformulate MDSEM using a single loss function that integrates the measurement and structural models. We then prove that minimizing this loss over the model parameters is equivalent to minimizing the squared Bures-Wasserstein (BW) distance between the observed and model-implied covariance matrices, and use this equivalence to establish the estimator's theoretical properties. Specifically, the equivalence identifies the proposed estimator as both an MDSEM estimator and a covariance-based SEM estimator within the minimum discrepancy estimation framework, from which consistency, asymptotic normality, and standard errors are derived. Simulations show that its finite-sample performance is comparable to that of conventional estimators, including maximum likelihood, and that confidence-interval coverage is close to the nominal level. The estimator is also more numerically stable than conventional SEM estimators in small samples and under model misspecification. Thus, the BW formulation provides a theoretical foundation for MDSEM and a practically useful discrepancy function for covariance-based SEM.

The conditional forecast-revision scale $\It=\{\Var(\E[X_{t+1}\mid\F_t]\mid\F_{t-1})\}^{1/2}$ measures the history-specific size of the forecast update induced by observing $X_t$. Because it is a conditional second moment built from two unknown conditional means, it is not directly observed. We study which estimator of $\It$ should be used under different structural assumptions and computational budgets. The comparison includes a block bootstrap, a conditional-variance model, a fitted state-space model, two $O(1)$ streaming smoothers, and the forget gate of an already-trained recurrent network. An error decomposition separates one-step-prediction error from conditional-second-moment tracking error. We show that externally tuned lag-only smoothers can be inconsistent when $\It$ changes at the sampling scale, although they attain the usual $T^{-2/3}$ mean-squared-error rate ($T^{-1/3}$ for $\It$) under slow variation; a correctly specified state-space estimator escapes this limit by using the current state. In volatility-driven designs, a cheap conditional-variance model is more accurate and over one hundred times cheaper as a point estimator than the implemented block bootstrap, whose value lies in the sampling distribution it provides rather than in point tracking. In state-driven designs, only the structurally matched filter recovers the fast variation. Read directly, a trained network's forget gate does not track $\It$ — though a supervised linear probe on the full gate vector does, so $\It$ is linearly decodable but not available for free. These results yield a practical rule: identify the conditional-second-moment structure, match the estimator to it, and then choose the least costly adequate method.

We study contextual dynamic pricing with arbitrary covariate sequences and bounded, possibly nonbinary purchase quantities. Demand follows a semiparametric surplus-index model with an unknown linear valuation parameter and an unknown Hölder-smooth response. We impose neither concavity nor strong unimodality on revenue and allow nonunique optimal prices. We develop a pilot-corrected layered decision-partitioning policy that combines directional pilot estimation, local polynomial learning, predictable data assignment, and global action elimination. Pilot correction removes the first-order effect of valuation-parameter error, while permanent labels enable concentration under adaptive sampling. The policy attains the minimax smoothness-dependent horizon rate up to logarithmic factors; a matching lower bound already holds for a constant-context binary-demand subclass.

Much causal inference research is focused on methods for optimizing dynamic treatment regimes (Murphy, 2003; Robins, 2004; Schulte et al., 2015), which are rules for deciding which treatments should be assigned and when based on evolving history. There is a certain optimism underlying this endeavor that with enough tinkering we might realize consequential improvements. Another strand of research, previously confined to the point exposure setting, considers bounds on how well any individualized treatment rule could possibly do. Here, we extend to the time-varying setting sharp bounds on the performance of an oracle strategy that selects the best treatment regime for each subject based on their unobserved potential outcomes or `response type'. For binary outcomes, the lower bound (assuming higher is better) is simply the expected outcome attained by the optimal treatment regime based on observed history. For continuous outcomes, the lower bound may strictly exceed the maximal observed covariate based value. In the continuous setting, we also consider bounds on the CDF of oracle continuous potential outcomes.

We introduce a new density-based goodness of fit test for ergodic Markov processes. Our test compares the data against the class of models specified in the null hypothesis, and rejects if no model in the class yields a stationary density that matches with the data. No alternative needs to be specified in order to implement the test. Although our test compares densities, estimation of smoothing parameters is not required, and the test has nontrivial power against $1/\sqrt{n}$ local alternatives. The test provides new perspectives on some existing problems in econometric and financial modeling.

Causal inference has traditionally centered on scalar outcomes: whether a patient recovers, how much a worker earns, or how many visits a website receives. Modern studies increasingly ask causal questions about outcomes with richer form, such as clinical notes, open-ended survey responses, and images. A hospital may want to know how an AI documentation tool changes the notes physicians write, or how a nurse training program alters what patients say in survey responses. For such outcomes, the usual average treatment effect is ill-defined: one cannot meaningfully subtract one text or image from another. To this end, we propose a causal query for unstructured outcomes. The key idea is to learn what features of the outcome are most causally affected by the treatment, which we call the maximally contrasting feature (MCF). To estimate the MCF, we learn a feature-scoring function that maps each outcome to a scalar and exposes the sharpest contrast between treated and control potential outcomes. We develop identification conditions and estimation algorithms for this query, and extend it to heterogeneous effects by allowing the feature-scoring function to depend on observed covariates. We also handle settings where both the treatment and the outcome are unstructured. Empirical studies on text and images show that the algorithm recovers salient aspects of an outcome changed by a treatment.

This document presents a proof of the estimation of a lipschitz parameter by constructing a consistent lower confidence bound through hypothesis test inversion. We prove that as the number of design points grows to infinity, the test correctly identifies any underestimated Lipschitz constant with asymptotic probability 1. The convergence proofs rely on a Uniform Law of Large Numbers and analyze discrepancy metrics under both bounded and unbounded replication sampling.

Breast core needle biopsy (CNB) is central to breast cancer diagnosis yet remains challenging because limited tissue sampling, lesion heterogeneity, and subtle morphologic overlap can obscure subtype distinctions. We developed CorePath, a breast-specialized multimodal pathology foundation model fine-tuned from PRISM using 7901 paired CNB whole-slide images and diagnostic reports from two centers. Evaluated across six CNB cohorts and two public breast pathology benchmarks without task-specific retraining, CorePath consistently outperformed PRISM across cancer detection, invasion assessment, and histological subtyping. It achieved weighted area under the receiver operating characteristic curves (AUCs) of 0.9526-0.9735 for five-class CNB histological subtyping across private centers. On public benchmarks, CorePath outperformed leading pathology foundation models, achieving the highest weighted AUCs of 0.7780 for BCNB invasive carcinoma subtyping, 0.8178 for BRACS lesion stratification, and 0.8252 for BRACS fine-grained classification. In report generation, CorePath reduced the overall non-breast hallucinations from 30.1% to 2.8%, demonstrating improved domain fidelity after breast-specific adaptation. CorePath-CRG further combined conformal filtering of subtype and binary cancer status predictions with Learn-Then-Test-based threshold calibration to support selective narrative release, diagnostic fallback, and deferral. CorePath-CRG achieved zero non-breast hallucinations among released outputs and showed the strongest overall performance in pathologist-validated LLM-based Evaluation Scores and quantitative report-generation metrics across most centers. These results demonstrate that domain-specialized foundation models with statistical risk control offer a promising approach for accurate breast CNB diagnosis and reliable report generation.

Statistical reasoning is multidimensional, yet evaluations of large language models (LLMs) typically emphasize response accuracy while overlooking how models construct and communicate statistical explanations. This study demonstrates the value of a multidimensional evaluation by combining response accuracy, response behavior, structural topic modeling, and lexical similarity analysis. The framework is applied to explanations generated by 15 current-generation LLMs responding to 90 questions drawn from four statistics examinations spanning high school, undergraduate, and graduate levels. Accuracy varied substantially across models, ranging from 55% to 78%. In contrast, structural topic modeling revealed a common conceptual organization of statistical reasoning across all models, while lexical similarity analysis identified modest but consistent vendor-specific differences in explanatory style. Models developed by the same vendor (e.g. Anthropic, OpenAI) produced explanations that were slightly more similar than models from different vendors. These findings demonstrate that statistical reasoning in contemporary LLMs cannot be characterized by accuracy alone and illustrate how complementary analyses of response behavior and model-generated explanations provide a more comprehensive evaluation of statistical reasoning in generative AI.

There has been significant interest in using machine learning algorithms to predict kidney transplant outcomes, such as the number of years until a graft inevitably fails. These prediction algorithms could possibly be used for pre-transplant donor-recipient matching to identify more compatible donors and recipients and thus improve post-transplant outcomes. In this study, we explore the use of survival prediction models trained on deceased donor kidney transplant data from the Scientific Registry of Transplant Recipients (SRTR). We propose a novel paired recipient-based evaluation framework that compares graft outcomes between two recipients who received kidneys from the same deceased donor, allowing us to evaluate the counterfactual benefit of changing the recipient for a certain donor. We find that five different survival prediction models, ranging in complexity from linear to deep learning-based models, all result in ~60% paired recipient-based accuracy. We further translate this accuracy into an interpretable quantity of post-transplant years gained. We also highlight major limitations of the commonly used concordance index (C-index) metric for evaluating survival prediction accuracy in this setting and demonstrate that our proposed paired recipient-based accuracy metric is more clinically relevant and better reflects real-world allocation settings.

Unit excitation (UE) is a common assumption in stochastic saddle avoidance: the stochastic error must have a uniformly positive component along every direction, in expectation. This condition gives a direct way to rule out convergence to strict saddles, but it also oversimplifies the actual noise structure, and does not match many stochastic optimization regimes. In overparameterized or interpolation models, the noise may vanish near stationarity. In finite-sum problems, the stochastic gradient noise may lie in a low-dimensional, data-dependent subspace. In these (common) scenarios, UE is naturally not satisfied. In this paper, we prove an abstract almost sure avoidance theorem for stochastic recursions without UE. The theorem replaces UE-type requirements by verifiable pathwise conditions. In applications, these conditions follow, e.g., from local smoothness and finite-moment assumptions under standard i.i.d. sampling, or from the finite-sum structure under without-replacement sampling. Since the stochastically sampled maps generally do not share a fixed point, the celebrated center-stable manifold argument used in deterministic analyses is not directly applicable. Instead, we use a path-dependent change of variables together with a pathwise Lyapunov–Perron-based proof strategy. As applications, we obtain strict saddle avoidance for stochastic mirror descent (including SGD) and for random reshuffling. For nonsmooth composite objectives, we prove avoidance results for a proximal-type stochastic gradient method. Combining these insights with suitable iterate convergence guarantees, this allows establishing convergence to local minimizers of the original objective function.

The standard check for contamination in LLM backtests is simple: compare scores before and after the training cutoff. We show this check is uninformative. Four flagship models fail it on questions they cannot have memorized: every scored question resolved after their cutoffs. The reason is structural. Models legitimately know more about times near their cutoff, so recency mimics leakage, and we prove no passive backtest can separate the two from genuine skill. Measurement, not just detection, requires information from outside the backtest. We supply it in two forms. A known cutoff identifies leakage at the boundary; a matched clean control identifies it globally and yields a leakage-adjusted score. We also derive where leakage hides: it concentrates on outcomes that surprised the crowd and were well covered in training, and partial memorization is disproportionately rewarded. We validate the estimators against ground truth by planting leakage in twin models, where they recover the injected dose and return null on clean questions. Deployed on frontier models, they detect one cutoff-localized signature and, at the audit's power floor, clear five models whose apparent advantages were recency alone. Backtests need not be discarded; they need one defensible reference.

Recursive nonlinear impulse responses require an estimated innovation law whenever the impact shock is normalized by innovation ranks and future innovations are integrated out. The closest semiparametric recursive construction in the literature estimates the relevant innovation quantile functions smoothly and discusses a direct empirical-residual implementation without developing its complete first-order inference theory. We tackle this gap in a finite-dimensional nonlinear structural autoregression with unrestricted continuous marginal innovation distributions and a fixed normal-rank shock. Our estimator replaces each innovation quantile function with the empirical quantile of generated structural residuals and iterates the same structural transition. For any fixed collection of responses, we establish a joint \sqrt{T} asymptotic linear representation with four components: direct transition estimation, the effect of transition estimation on residual order statistics, ordinary innovation-quantile estimation, and the shifted impact quantile. After projection through the recursion, the quantile terms admit a residual-rank-and-spacing representation, yielding feasible inference without innovation-density estimation or quantile smoothing. We then characterize the propagated bias from smoothing, establish validity of a full recursive residual bootstrap, and derive the additional covariance contribution from a finite number of simulated paths, providing bandwidth-free inference for the empirical-residual version of the same normal-rank response used in the smooth recursive construction.

Weighted distributional tests for covariate balance are currently limited to two-group comparisons. We extend the Kolmogorov-Smirnov, Anderson-Darling, and Cramer-von Mises tests to an arbitrary number of weighted groups k >= 2, using existing k-sample generalizations and a shared permutation-inference procedure; each statistic reduces exactly to its two-group counterpart at k = 2. An accompanying post-hoc pairwise procedure with four multiple-comparison adjustments localizes which groups differ following an omnibus rejection. In a four-scenario simulation study at k = 3, Type I error remained close to nominal, and the comparative advantages established for two groups were preserved: Kolmogorov-Smirnov was most powerful against a centrally located discrepancy, Anderson-Darling against a tail-located discrepancy, and Anderson-Darling and Cramer-von Mises performed comparably against a diffuse discrepancy. Omnibus power was nonetheless uniformly lower than in the matching two-group setting - not because the underlying discrepancy is diluted, but because adding groups enlarges the null distribution itself, so the post-hoc procedure, whose pairwise statistics carry no such penalty, is often the more sensitive tool whenever a specific group's imbalance is suspected. The methods are implemented in the Stata commands kstest, adtest, and cvmtest.

Causal inference increasingly extends beyond classical causal effects defined by deterministic treatment assignments, such as the average treatment effect, to stochastic intervention effects that can weaken positivity requirements and offer greater policy relevance. Nonparametric Bayesian models are attractive for estimating these effects due to their flexibility and inherent uncertainty propagation, but this posterior uncertainty need not be well calibrated for the causal effect of interest. We develop a simple post-processing correction that can be applied to posterior samples without changing the prior or fitting algorithm. We prove that, for a broad class of stochastic interventions, the corrected posterior yields asymptotically efficient inference and credible intervals with asymptotically valid frequentist coverage; formally, it satisfies a semiparametric Bernstein-von Mises theorem. The theory covers interventions specified independently of the observed treatment process, as well as interventions that modify it, including incremental propensity score interventions and a new power-tilt intervention. A central contribution is new theory for SoftBART, including conditions under which this flexible tree-based Bayesian model supports calibrated Bayesian inference for stochastic intervention effects. In simulations, the correction reduces bias and improves coverage relative to the uncorrected Bayesian analysis while remaining competitive with frequentist alternatives. We illustrate the method by estimating how expected LDL cholesterol would change under hypothetical increases or decreases in the odds of receiving statin therapy.

The Transient Climate Response to cumulative CO2 Emissions (TCRE) is a key metric for linking greenhouse gas emissions to global temperature change and informing climate policy. However, extant estimates of the TCRE often depend on subjective model selection or assumed sensitivity ranges, with limited validation against observed data. We develop a fully statistical data-driven approach using a Bayesian Model Averaging (BMA) approach to estimate the TCRE. This uses 37 climate models from the Coupled Model Intercomparison Project phase 6 (CMIP6), weighted according to their consistency with observed temperature data. Compared to the Intergovernmental Panel on Climate Change (IPCC)'s Sixth Assessment Report (AR6) TCRE estimate, our BMA approach yields a very likely range (90% interval) that overlaps substantially with that from the AR6, but with a higher mean and a lower standard deviation. The resulting projections of global temperature change to 2100 show somewhat higher warming and less uncertainty than some current methods. The use of statistical modeling methods makes it easier to validate the approach and to partition the uncertainty according to its sources. Out-of-sample predictive validation shows the method to be well calibrated. Variance decomposition shows model parameter uncertainty to be a main source of projection variance.

Spectral clustering for community detection is analysed in multivariate time series models whose dependence structure is determined by an unobserved stochastic blockmodel. We establish that spectral clustering of the sample covariance matrix achieves exact recovery of the underlying communities. The recovery rates depend explicitly on the network size, sample length, block separation, and degree of data dependence. This demonstrates that exact community recovery under a stochastic blockmodel is possible even when the adjacency matrix is unobserved. Our theory provides extensions of both classical and fine-grained matrix perturbation theory to the setting of dependent data, which may be of independent interest.

We introduce Survival-IDR (S-IDR), a nonparametric estimator of conditional survival distributions under order restrictions, extending Isotonic Distributional Regression (IDR; Henzi et al., 2021) to right-censored outcomes. S-IDR has no tuning parameters and accommodates continuous, discrete, and partially ordered covariates. We first study the direct Kaplan-Meier adaptation of IDR: it is uniformly consistent at the minimax rate, but only when the conditional outcomes are hazard-rate ordered. We trace this restriction to the Kaplan-Meier estimator's failure to satisfy the Cauchy mean value property on non-i.i.d. samples, and use the diagnosis to construct S-IDR. The S-IDR estimator is uniformly consistent under only stochastic dominance of the conditional outcomes, attains the minimax rate when the smoothness of the conditional CDFs is known, and admits a known cross-threshold PAVA acceleration. We further embed S-IDR in a distributional single-index framework on a benchmark suite, and apply it in a case study that validates the MELD score used for liver-transplant wait list management. Accompanying R, Python and Rust packages are available at https://github.com/AlexanderHenzi/isodistrreg.

Prediction-based methods, including Large Language Models (LLMs) and other machine learning techniques, are often used to construct measures of political phenomena that are difficult to quantify directly, such as policy positions in manifestos or emotions expressed on social media. In many applications, these prediction-generated measures are used as explanatory variables in regression models, even though they are measured with error. This leads to biased estimates. In this paper, we propose a simple solution to these biases: instrumental variables constructed from multiple measures created on independent splits of the original data. This approach is theoretically valid, easy to implement, and does not require new data. Through simulations, we show that this approach recovers estimates close to the true values, even in relatively small samples, while the standard approach can produce substantial bias in practice. We illustrate the method by revisiting two applications: whether gendered speech affects legislative outcomes in the German Parliament, and whether political risk influences poverty alleviation programs in China.

Understanding the dynamics of suicidal ideation and behaviour in youth and the factors associated with transitions from thoughts to behaviours is critical for early identification, monitoring, and prevention. Using longitudinal self-report data from the Adolescent Brain Cognitive Development (ABCD) Study (n = 11,864) spanning ages 9 to 13 years, we developed a time-inhomogeneous discrete-time Markov chain framework to model transitions across eight states defined by suicidal ideation and behaviour and the co-reported presence or absence of non-suicidal self-injury (NSSI). The framework enables inference of year-to-year and multi-year transition probabilities, quantification of transition stability and uncertainty, and statistical comparison of transition likelihoods. We identified structured but developmentally changing transition patterns, including a generally high probability of recovery to a no-report state following reports of suicidal ideation or behaviour. Co-reported lifetime NSSI marked a distinct trajectory profile characterized by both greater risk and lower predictability: children with NSSI were more likely to transition to or persist in suicidal behaviour, were less likely to recover to a no-report state, and exhibited greater uncertainty in their transition likelihoods compared to those reporting suicidal ideation and/or behaviour alone. These findings suggest that NSSI marks not only elevated risk but also greater trajectory instability during pre- to early adolescence. By estimating probabilities of escalation, remission, persistence, and fluctuation in longitudinal cohort data, the framework provides a systematic, interpretable, and scalable approach to characterising suicidal trajectory dynamics in large, sparse mental health datasets, with potential to inform future research on monitoring, early prevention, and time-varying risk in youth mental health.

We develop a class of general diffusion-based stochastic particle optimisation methods for loss functions with intractable gradients. Specifically, we consider problems in which the loss gradient is an integral with respect to a parameter-dependent distribution, a structure that includes training generative models, fine-tuning, and learning latent-variable models. We introduce mean-field dynamics and its interacting-particle approximations, which contain several existing algorithms as special cases and provide a route to constructing new methods. Under well-posedness and joint contractivity assumptions, we prove exponential convergence and show that the continuous-time particle system admits a non-asymptotic error bound. We illustrate our framework by developing higher-order Langevin and momentum optimisers and evaluating them on maximum marginal-likelihood estimation and energy-based-model training.

Observation-driven filters typically use likelihood-score updates, corresponding to the logarithmic scoring rule. We generalise these updates to negative parameter derivatives of differentiable proper scoring rules, under a declared working family and predictable scaling. The rule determines the conditional risk projection and tail response, scaling converts its derivative into the update, and the autoregressive component determines the composite dynamic centre. Locally, risk curvature and scaling govern mean reversion, while the variance of the scaled innovation governs update noise. Under correct specification, unscaled curvature and score variance coincide for the log score by the information identity, but generally differ for other proper rules. For static parameters, we establish consistency and asymptotic normality under explicit stability and fixed-tuning conditions. In high-frequency scale models, centred updates converge to diffusions, whereas non-centred updates follow deterministic mean flows. For time-varying rule-specific projections, the local tracking error admits an Ornstein-Uhlenbeck approximation up to a stopping time, allowing correlated update and target shocks. Simulations and an international-equity application illustrate how criterion choice affects robustness, adaptation, variance-forecast loss, value-at-risk calibration and probability-integral-transform diagnostics. Predictive density and updating criterion are distinct design choices whose relative performance depends on the target and disturbance.

Reinforcement learning is a subfield of machine learning that studies how an agent interacts with an environment in order to extract as large a reward as possible. A standard approach to study such interaction is through Markov Decision Processes (MDPs) and the task of choosing an optimal policy — a function that tells the agent which action to take. In this work, we study two types of MDPs — finite-horizon and infinite-horizon discounted — and propose new quantum algorithms for computing approximate optimal policies. Our quantum algorithms are based on a new combination of standard value iteration and quantum subroutines like quantum mean estimation and quantum maximum finding, overall enhanced with techniques from sample-optimal classical algorithms. Our resulting query complexities improve upon previous works, thus approaching already established quantum lower bounds.

Score-based diffusion models are typically formulated using continuous-time stochastic differential equations and measure-theoretic stochastic calculus. In this paper, we develop a hyperfinite formulation of score-based generative modeling within the framework of Nonstandard Analysis. Starting from an internal diffusion process on a hyperfinite grid, we derive the associated infinitesimal generator and establish its correspondence with the classical Fokker–Planck equation. We then obtain a hyperfinite backward-mean identity that yields the reverse-time drift and provides a constructive derivation of the reverse-time SDE. Building on these results, we show that minimization of an internal score-matching objective recovers the score function required by the reverse-time dynamics, thereby connecting score estimation with generative sampling directly at the hyperfinite level. Under suitable assumptions, we further derive a hyperfinite Girsanov formula and establish a relationship between likelihood optimization and Fisher-divergence objectives. Finally, we analyze the second-order consistency of the hyperfinite dynamics and show that the leading correction term depends explicitly on the fourth moment of the increment distribution, with the Gaussian value $\kappa=3$ eliminating the leading dispersion contribution. Taken together, these results provide a unified hyperfinite framework for diffusion-based generative modeling–while laying foundations for further extensions–that links discrete grid dynamics, reverse-time diffusion, score matching, and likelihood-based formulations within a common nonstandard setting.

In this note we describe a method for comparing inferred dynamics in evolutionary accumulation models (EvAMs). These models involve the acquisition of multiple, potentially codependent, binary features over time – for example, mutations in cancer development, or phenotypes in evolutionary biology. As the set of methods for inferring EvAM dynamics expands, approaches for comparing inference across algorithms, datasets, and covariates are required. In particular, a comparison method supporting reversible, stochastic dynamics, interactions between feature sets, and potentially non-independent samples (as well as simpler cases) has yet to be established. It is possible for EvAM with similar relative feature orderings to produce completely different sets of observed states due to “frameshift”-like differences; methods distinguishing state and transition similarity are therefore also desirable. Here we suggest a method focussed on ordering matrices, describing the probability that a feature is acquired under different conditions on other features, and is thus generally comparable across methods and datasets. We demonstrate how the approach captures both statistical robustness (given EvAM uncertainty) and scientifically meaningful differences in inferred dynamics. The method is applied to synthetic and real-world data on the evolution of chromosomal aberrations in different tumour types and of drug-resistant bacteria in different countries.

We study distributed testing of $\mathrm{Ber}(\alpha)$ versus $\mathrm{Ber}(\beta)$ in the broadcast, or shared-blackboard, model. For protocols with constant advantage, we characterise up to universal constant factors the information complexity under either hypothesis for every pair $\beta<\alpha$. The characterisation shows that the two information costs can be quite different and identifies three parameter regimes, with optimal protocols based respectively on clean samples, a noisy binary symmetric channel, and an asymmetric $Z$-channel. The lower bounds rely on a novel mixed Hellinger–Jensen–Shannon inequality that may be of independent interest. We also characterise the constant-advantage information complexity of testing arbitrary discrete distributions via an optimisation problem over channels, and show that binary-output channels suffice. We obtain bounds for bounded likelihood-ratio distributions, and give general upper bounds in terms of $\chi^2$ divergence. As applications, we recover the broadcast-model set-disjointness lower bound, and derive stronger lower bounds in the multi-pass streaming setting for some problems considered in prior work.

Multimodal supervised learning seeks to leverage multiple heterogeneous data sources to improve predictive performance. A central challenge is determining the fusion granularity across modalities: over-integration may amplify noise while under-integration fails to exploit cross-modal dependence. Existing approaches rely on pre-specified fusion architectures, from early to late fusion, that may not adapt to the underlying dependence structure among modalities. We propose DAIF, a data adaptive intermediate fusion framework that combines random matrix theory and non-parametric dependence measures to learn fusion structure directly from data. We operate under a Bayesian multimodal factor model where the prior on the latent factors determines the cross-modal dependence. Our method clusters modalities based on estimated intermodal dependence, then performs clusterwise empirical Bayes estimation of the priors. These estimated priors are used to construct denoisers within an approximate message passing (AMP) framework, yielding denoised low-dimensional features that borrow strength across related modalities while preserving modality-specific signal. The resulting embeddings are used for downstream supervised prediction. We evaluate the framework through simulations under varying dependence structures and signal regimes, comparing against several benchmark methods, and demonstrate its practical utility on two multimodal datasets, namely a trimodal TEA-seq dataset (Swanson et al., 2021) and TCGA-BRCA dataset (Goldman et al., 2020). In the first example, we predict the expression level of a T-cell differentiation marker protein and in the second case we analyze patient survival prediction based on multimodal information. Our method competes with or outperforms the state-of-the-art techniques in both prediction problems, demonstrating its versatility across diverse supervised learning tasks.