Papers

We introduce Teleodynamic Learning, a new paradigm for machine learning in which learning is not the minimization of a fixed objective, but the emergence and stabilization of functional organization under constraint. Inspired by living systems, this framework treats intelligence as the coupled evolution of three quantities: what a system can represent, how it adapts its parameters, and which changes its internal resources can sustain. We formalize learning as a constrained dynamical process with two interacting timescales: inner dynamics for continuous parameter adaptation and outer dynamics for discrete structural change, linked by an endogenous resource variable that both shapes and is shaped by the trajectory. This perspective reveals three phenomena that standard optimization does not naturally capture: self-stabilization without externally imposed stopping rules, phase-structured learning dynamics that move from under-structuring through teleodynamic growth to over-structuring, and convergence guarantees grounded in information geometry rather than convexity. We instantiate the framework in the Distinction Engine (DE11), a teleodynamic learner grounded in Spencer-Brown's Laws of Form, information geometry, and tropical optimization. On standard benchmarks, DE11 achieves 93.3 percent test accuracy on IRIS, 92.6 percent on WINE, and 94.7 percent on Breast Cancer, while producing interpretable logical rules that arise endogenously from the learning dynamics rather than being imposed by hand. More broadly, Teleodynamic Learning unifies regularization, architecture search, and resource-bounded inference within a single principle: learning as the co-evolution of structure, parameters, and resources under constraint. This opens a thermodynamically grounded route to adaptive, interpretable, and self-organizing AI.

We consider the robustness of score-based generative modeling to errors in the estimate of the score function. In particular, we show that Langevin dynamics is not robust to the $L^2$ errors (more generally $L^p$ errors) in the estimate of the score function. It is well-established that with small $L^2$ errors in the estimate of the score function, diffusion models can sample faithfully from the target distribution under fairly mild regularity assumptions in a polynomial time horizon. In contrast, our work shows that even for simple distributions in high dimensions, Langevin dynamics run for any polynomial time horizon will produce a distribution far from the target distribution in Total Variation (TV) distance, even when the $L^2$ error (more generally $L^p$) of the estimate of the score function is arbitrarily small. Considering such an error in the estimate of the score function is unavoidable in practice when learning the score function from data, our results provide further justification for diffusion models over Langevin dynamics and serve to caution against the use of Langevin dynamics with estimated scores.

Process capability indices such as $C_{pk}$ are widely used in manufacturing quality control to support supplier qualification and product release decisions based on fixed acceptance thresholds (e.g., $C_{pk} \geq 1.33$). In practice, these decisions rely on sample-based estimates computed from moderate sample sizes ($n \approx$ 20-50), yet the stochastic nature of the estimator is often overlooked when interpreting threshold compliance. This study establishes a local asymptotic characterization of decision behavior when the true process capability lies near a fixed threshold. Under standard regularity conditions, if the true capability equals the threshold, the acceptance probability converges to 0.5 as sample size increases, implying that a fixed $C_{pk}$ gate embeds an inherent boundary decision risk even under ideal distributional assumptions. When the true capability deviates from the threshold by $O(n^{-1/2})$, the decision probability converges to a non-degenerate limit governed by a scaled signal-to-noise ratio. Monte Carlo simulations and an empirical study on 880 manufacturing dimensions demonstrate substantial resampling-based decision instability near the commonly used 1.33 criterion. These findings provide a probabilistic interpretation of threshold-based capability decisions and quantitative guidance for assessing boundary-induced release risk in engineering practice.

Real-world data in health, economics, and environmental sciences are often collected across heterogeneous domains (such as hospitals, regions, or time periods). In such settings, distributional shifts can make standard PCA unreliable, in that, for example, the leading principal components may explain substantially less variance in unseen domains than in the training domains. Existing approaches (such as FairPCA) have proposed to consider worst-case (rather than average) performance across multiple domains. This work develops a unified framework, called wcPCA, applies it to other objectives (resulting in the novel estimators such as norm-minPCA and norm-maxregret, which are better suited for applications with heterogeneous total variance) and analyzes their relationship. We prove that for all objectives, the estimators are worst-case optimal not only over the observed source domains but also over all target domains whose covariance lies in the convex hull of the (possibly normalized) source covariances. We establish consistency and asymptotic worst-case guarantees of empirical estimators. We extend our methodology to matrix completion, another problem that makes use of low-rank approximations, and prove approximate worst-case optimality for inductive matrix completion. Simulations and two real-world applications on ecosystem-atmosphere fluxes demonstrate marked improvements in worst-case performance, with only minor losses in average performance.

The two-point correlation function (2PCF) is a cornerstone of precision cosmology, yet its estimation from imaging surveys is vulnerable to contamination and incompleteness arising from imperfect target selection and pipeline-level inclusion decisions. In practice, the scientific target is a physically defined population, while the working catalog is constructed from noisy measurements and selection cuts, leading to mismatches between true and observed inclusion. These errors are often spatially structured, correlating with survey depth, observing conditions, and foregrounds, and can imprint spurious large-scale power or suppress the true clustering signal. High-resolution spectroscopic samples provide gold-standard inclusion in the target population but are typically available for only a small subset of objects. We introduce a prediction-powered Landy–Szalay (PP–LS) estimator that combines noisy inclusion labels across the full catalog with exact labels on a small spectroscopic subset while preserving the standard random-catalog normalization for survey geometry and selection. PP–LS debiases pair counts using residual-based, design-weighted corrections computed only on the labeled subset, requiring no probability calibration, known misclassification rates, or explicit modeling of contamination. Under simple random sampling of the labeled subset, we establish recovery of the oracle (true-label) Landy–Szalay pair counts and thus consistency for the target 2PCF. In simulations with clustered and spatially structured contaminants, PP–LS removes the bias of naive catalog-level estimators while achieving substantially lower variance than spectroscopic-only clustering. The resulting estimator is statistically principled, computationally lightweight, and integrates directly with standard pair-counting pipelines, enabling robust clustering inference in next-generation surveys.

Standard local polynomial estimators of a nonparametric regression function employ a weighted least squares loss function that is tailored to the setting of homoscedastic Gaussian errors. We introduce the outrigger local polynomial estimator, which is designed to achieve distributional adaptivity across different conditional error distributions. It modifies a standard local polynomial estimator by employing an estimate of the conditional score function of the errors and an 'outrigger' that draws on the data in a broader local window to stabilise the influence of the conditional score estimate. Subject to smoothness and moment conditions, and only requiring consistency of the conditional score estimate, we first establish that even under the least favourable settings for the outrigger estimator, the asymptotic ratio of the worst-case local risks of the two estimators is at most $1$, with equality if and only if the conditional error distribution is Gaussian. Moreover, we prove that the outrigger estimator is minimax optimal over Hölder classes up to a multiplicative factor $A_{\beta,d}$, depending only on the smoothness $\beta \in (0,\infty)$ of the regression function and the dimension~$d$ of the covariates. When $\beta \in (0,1]$, we find that $A_{\beta,d} \leq 1.69$, with $\lim_{\beta \searrow 0} A_{\beta,d} = 1$. A further attraction of our proposal is that we do not require structural assumptions such as independence of errors and covariates, or symmetry of the conditional error distribution. Numerical results on simulated and real data validate our theoretical findings; our methodology is implemented in R and available at https://github.com/elliot-young/outrigger.

Real-world contextual bandit problems with complex reward models are often tackled with iteratively trained models, such as boosting trees. However, it is difficult to directly apply simple and effective exploration strategies–such as Thompson Sampling or UCB–on top of those black-box estimators. Existing approaches rely on sophisticated assumptions or intractable procedures that are hard to verify and implement in practice. In this work, we explore the use of an exploration-free (pure-greedy) action selection strategy, that exploits the randomness inherent in model fitting process as an intrinsic source of exploration. More specifically, we note that the stochasticity in cross-validation based regularization process can naturally induce Thompson Sampling-like exploration. We show that this regularization-induced exploration is theoretically equivalent to Thompson Sampling in the two-armed bandit case and empirically leads to reliable exploration in large-scale business environments compared to benchmark methods such as epsilon-greedy and other state-of-the-art approaches. Overall, our work reveals how regularized estimator training itself can induce effective exploration, offering both theoretical insight and practical guidance for contextual bandit design.

Scientific experimentation is largely driven by statistical hypothesis testing to determine significant differences in interventions. Traditionally, experimenters allocate samples uniformly between each intervention. However, such an approach may lead to suboptimal outcomes - multi-armed bandits (MABs) addresses this problem by allocating samples adaptively to maximize outcomes. Yet, two challenges have hindered the use of MABs in scientific domains. First, common hypothesis tests (e.g., $t$-tests) become invalid under adaptive sampling without correction, leading to inflated type~I and type~II errors. This is an understudied problem, and prior solutions suffer from issues such as low statistical power which prevent adoption in many practical settings. Second, practitioners must explicitly balance cumulative reward with statistical efficiency, yet no general methodology exists to quantify this trade-off across algorithms. In this paper, we study assumption modification and critical region correction approaches for hypothesis testing that enable common tests to be applied to adaptively collected data. We provide heuristic justification for its power efficiency and show in simulation that it achieves higher power than existing approaches. Further, we derive a theoretically and practically motivated objective function for adaptive experiment evaluation, which we integrate into a unified experimental framework. Our framework asks experimenters to specify an experiment extension cost for their problem, and based on that enables our proposed optimization procedure to select the bandit algorithm that best balances reward and power in their setting. We show that our approach enables practitioners to improve outcomes with only slightly more steps than uniform randomization, while retaining statistical validity.

We revisit Schnieper's model, which decomposes incurred but not reported (IBNR) reserves into two components: reserves for newly reported claims (true IBNR) and reserves for changes over time in the estimated cost of already reported claims (IBNER). We propose a continuous-time stochastic model for the aggregate claims process, driven by a random Poisson measure for the arrival of newly reported claims and by Brownian motion for the cost fluctuations of reported claims. This framework is consistent with the key assumptions of Schnieper's original approach. Within this setting, we develop a bootstrap method to estimate the full predictive distribution of claims reserves. Our approach naturally accounts for asymmetry, ensures non-negativity, and respects intrinsic bounds on reserves, without requiring additional assumptions. We illustrate the method through a case study and compare it with alternative stochastic techniques based on Schnieper's model.

Evaluating and interpreting latent representations, such as variational autoencoders (VAEs), remains a significant challenge for diverse data types, especially when ground-truth generative factors are unknown. To address this, we unify several state-of-the-art disentangled VAE approaches for latent space disentanglement into one framework – bfVAE. To assess the effectiveness of a disentangled VAE model and enhance latent space interpretability, we propose Feature Variance Heterogeneity via Latent Traversal (FVH-LT) and Dirty Block Sparse Regression in Latent Space (DBSR-LS). To ensure robust interpretability of learned latent space, we develop a greedy alignment strategy (GAS) that mitigates label switching and aligns latent dimensions across runs to set the foundation of result aggregation. We also introduce a convenient scalar latent space separation index (LSSI) based on the GAS-aligned outputs of FVH-LT and DBSR-LS to summarize the overall latent structural separation without knowledge of the ground-truth generative factors. We compare bfVAE to five VAE models and validate the effectiveness FVH-LT, DBSR-LS, and LSSI in on seven tabular and image datasets. Under our examined experimental settings, bfVAE provides a more flexible disentanglement framework achieves more favorable overall trade-off between disentanglement and reconstruction than the benchmark VAE models; FVH-LT and DBSR-LS reliably uncover semantically meaningful and domain-relevant latent structures and generally yield consistent results; and LSSI makes an effective quantitative summary of latent structural separation.

Research and Development is the largest budget position in the pharmaceutical industry, with clinical trials being a critical, yet costly and time-consuming component to inform decisions. Beyond drug efficacy, the probability of success and efficiency of research and development are highly dependent on the approaches used for designing, analyzing, and interpreting clinical trials. Deep understanding of statistical methodology and quantitative approaches is therefore essential. Consequently, dedicated methodology groups have emerged in mid-size and large pharmaceutical companies and CROs. Their remit is to lead the conception and implementation of innovative quantitative methodologies in order to improve drug development, often by addressing complexities or offering more efficient designs. To achieve this, they collaborate internally and externally (e.g., with academics, regulators) to identify common challenges and tear down silos in order to invest in methods with the highest impact on efficiency and value to the portfolio. Given the immense financial stakes of drug development – where delays carry massive implications – these groups represent a critical strategic investment. However, to realize this business impact, statistical innovations must be rigorously validated and seamlessly integrated. This manuscript explores the setup, remit, and value of dedicated methodology groups, alongside the critical organizational considerations and success factors required to maximize their impact on the speed, efficiency, and probability of success.

Machine learning forecast systems are moving beyond point predictions to full predictive distributions for future outcomes y conditional on complex inputs x. However, these distributions are often locally miscalibrated, especially for high-stakes tail events where accurate uncertainty quantification is most needed to establish trust in models. Local miscalibration occurs because training data often lack examples of low-frequency events. The goal of this paper is to describe a simple, yet flexible framework that, at deployment, produces interpretable diagnostics and a robust correction mechanism of predictive distributions when train examples are limited. With this goal in mind, we introduce a semiparametric version of the Local Amortized Diagnostic and Reshaping (LADaR) framework that posits a covariate-dependent parametric model for a diagnostic transport map regressed nonparametrically on inputs to describe how to correct tail probabilities across the feature space to match calibration data. These maps provide the user with local, real-time diagnostics and a reshaped predictive distribution that can be related back to physical processes in the input space. We apply these semiparametric diagnostic transport maps to short-term tropical cyclone intensity forecasting to detect evolutionary modes linked to local miscalibration in the National Hurricane Center's forecasts and improve predictions for severe weather hazards.

We present FlowSN, a statistical framework using simulation-based inference (SBI) with normalising flows to account for selection effects in observational astronomy. Failure to account for selection effects can lead to biased inference on global parameters. An example is Malmquist bias, where detection limits result in a sample skewed towards brighter objects. In Type Ia supernova (SN Ia) cosmology, these selection effects can systematically shift the inferred posterior distributions of cosmological parameters, necessitating the development of robust statistical frameworks to account for the biases. SBI enables us to implicitly learn probability distributions that are analytically intractable to calculate. In this work, we introduce a novel approach that employs a normalising flow to learn the non-analytic selected SN likelihood for a given survey from forward simulations, independent of the assumed cosmological model. The resulting likelihood approximation is incorporated into a hierarchical Bayesian framework and posterior sampling is performed using Hamiltonian Monte Carlo to obtain constraints on cosmological parameters conditioned on the observed data. The modular learnt likelihood approximation can be reused without retraining to evaluate different cosmological models, providing a key advantage over other SBI approaches. We demonstrate the performance of this methodology by training and testing the SBI technique using realistic LSST-like SNANA simulations for the first time. Our FlowSN approach yields accurate posterior estimates on cosmological parameters, including the dark energy equation of state $w_0$, that are an order of magnitude less biased than those obtained with conventional techniques and also exhibit improved frequentist calibration.

We formally define algorithmic capture of combinatorial tasks as the ability of a transformer to extrapolate to arbitrary task sizes with controllable error and logarithmic sample adaptation, providing a sharp scaling criterion for distinguishing logic internalization from statistical interpolation. Empirically, across scaling ranges spanning up to 2.5 orders of magnitude, we observe evidence of capture and non-capture. By analyzing infinite-width transformers in both the lazy and rich regimes, we derive upper bounds on the inference-time computational complexity of the combinatorial tasks these networks can capture. We show that, despite their universal expressivity, transformers possess an inductive bias that disfavors higher-complexity algorithmic procedures within the efficient polynomial-time heuristic scheme class, consistent with successful capture on simpler combinatorial tasks such as induction heads, sort, and string matching.

This paper considers nonparametric regression from strongly mixing observations. The proposed approach is based on deep neural networks with minimum error entropy (MEE) principle. We study two estimators: the non-penalized deep neural network (NPDNN) and the sparse-penalized deep neural network (SPDNN) predictors. Upper bounds of the expected excess risk are established for both estimators over the classes of Hölder and composition Hölder functions. For the models with Gaussian error, the rates of the upper bound obtained match (up to a logarithmic factor) with the lower bounds established in \cite{schmidt2020nonparametric}, showing that both the MEE-based NPDNN and SPDNN estimators from strongly mixing data can achieve the minimax optimal convergence rate.

This note extends conformal e-prediction to cover the case where there is observed confounding between the random object $X$ and its label $Y$. We consider both the case where the observed data is IID and a case where some dependence between observations is permitted.

This work addresses two fundamental limitations in neural network approximation theory. We demonstrate that a three-dimensional network architecture enables a significantly more efficient representation of sawtooth functions, which serves as the cornerstone in the approximation of analytic and $L^p$ functions. First, we establish substantially improved exponential approximation rates for several important classes of analytic functions and offer a parameter-efficient network design. Second, for the first time, we derive a quantitative and non-asymptotic approximation of high orders for general $L^p$ functions. Our techniques advance the theoretical understanding of the neural network approximation in fundamental function spaces and offer a theoretically grounded pathway for designing more parameter-efficient networks.

Predicting drug-target affinity is fundamental to virtual screening and lead optimization. However, existing deep models often suffer from representation collapse in stringent cold-start regimes, where the scarcity of labels and domain shifts prevent the learning of transferable pharmacophores and binding motifs. In this paper, we propose Co-Diffusion, a novel affinity-aware framework that redefines DTA prediction as a constrained latent denoising process to enhance generalization. Co-Diffusion employs a two-stage paradigm: Stage I establishes an affinity-steered latent manifold by aligning drug and target embeddings under an explicit supervised objective, ensuring that the latent space reflects the intrinsic binding landscape. Stage II introduces modality-specific latent diffusion as a stochastic perturb-and-denoise regularizer, forcing the model to recover consistent affinity semantics from noisy structural representations. This approach effectively mitigates the reconstruction-regression conflict common in generative DTA models. Theoretically, we show that Co-Diffusion maximizes a variational lower bound on the joint likelihood of drug structures, protein sequences, and binding strength. Extensive experiments across multiple benchmarks demonstrate that Co-Diffusion significantly outperforms state-of-the-art baselines, particularly yielding superior zero-shot generalization on unseen molecular scaffolds and novel protein families-paving a robust path for in silico drug prioritization in unexplored chemical spaces.

This paper proposes a partition-based functional ridge regression framework to address multicollinearity, overfitting, and interpretability in high-dimensional functional linear models. The coefficient function vector \( \boldsymbol{\beta}(s) \) is decomposed into two components, \( \boldsymbol{\beta}_1(s) \) and \( \boldsymbol{\beta}_2(s) \), representing dominant and weaker functional effects. This partition enables differential ridge penalization across functional blocks, so that important signals are preserved while less informative components are more strongly shrunk. The resulting approach improves numerical stability and enhances interpretability without relying on explicit variable selection. We develop three estimators: the Functional Ridge Estimator (FRE), the Functional Ridge Full Model (FRFM), and the Functional Ridge Sub-Model (FRSM). Under standard regularity conditions, we establish consistency and asymptotic normality for all estimators. Simulation results reveal a clear bias–variance trade-off where FRSM performs best in small samples through strong variance reduction, whereas FRFM achieves superior accuracy in moderate to large samples by retaining informative functional structure through adaptive penalization. An empirical application to Canadian weather data further demonstrates improved predictive performance, reduced variance inflation, and clearer identification of influential functional effects. Overall, partition-based ridge regularization provides a practical and theoretically grounded method for high-dimensional functional regression.

Prior-data fitted networks (PFNs) have emerged as powerful foundation models for tabular causal inference, yet their extension to time series remains limited by the absence of synthetic data generators that provide interventional targets. Existing time series benchmarks generate observational data with ground-truth causal graphs but lack the interventional data required for training causal foundation models. To address this, we propose CausalTimePrior, a principled framework for generating synthetic temporal structural causal models (TSCMs) with paired observational and interventional time series. Our prior supports configurable causal graph structures, nonlinear autoregressive mechanisms, regime-switching dynamics, and multiple intervention types (hard, soft, time-varying). We demonstrate that PFNs trained on CausalTimePrior can perform in-context causal effect estimation on held-out TSCMs, establishing a pathway toward foundation models for time series causal inference.

Agent-based models (ABMs) are widely used to estimate causal treatment effects via paired counterfactual simulation. A standard variance reduction technique is common random numbers (CRNs), which couples replicates across intervention scenarios by sharing the same random inputs. In practice, CRNs are implemented by reusing the same base seed, but this relies on a critical assumption: that the same draw index corresponds to the same modeled event across scenarios. Stateful pseudorandom number generators (PRNGs) violate this assumption whenever interventions alter the simulation's execution path, because any change in control flow shifts the draw index used for all downstream events. We argue that this execution-path-dependent draw indexing is not only a variance-reduction nuisance, but represents a fundamental mismatch between the scientific causal structure ABMs are intended to encode and the program-level causal structure induced by stateful PRNG implementations. Formalizing this through the lens of structural causal models (SCMs), we show that standard PRNG practices yield causally incoherent paired counterfactual comparisons even when the mechanistic specification is otherwise sound. We show that a remedy is to combine counter-based random number generators (e.g., Philox/Threefry) with event identifiers. This decouples random number generation from simulation execution order by making random draws explicit functions of the particular modeled event that called them, restoring the stable event-indexed exogenous structure assumed by SCMs.

Standard thresholding techniques for correlation matrices often destroy positive semidefiniteness. We investigate the construction of positive definite functions that vanish on specific sets $K \subseteq [-1,1)$, ensuring that the thresholded matrix remains a valid correlation matrix. We establish existence results, define a criterion for faithfulness based on the linear coefficient of the normalized Gegenbauer expansion in analogy with Delsarte's method in coding theory, and provide bounds for thresholding at single points and pairs of points. We prove that for correlation matrices of rank $n$, any soft-thresholding operator that preserves positive semidefiniteness necessarily induces a geometric collapse of the feature space, as quantified by an $\mathcal{O}(1/n)$ bound on the faithfulness constant. Such demonstrates that geometrically unbiased soft-thresholding limits the recoverable signal.

Multilevel network meta-regression (ML-NMR) enables population-adjusted indirect treatment comparisons by combining individual patient data (IPD) with aggregate data. When individual-level covariates are unavailable, ML-NMR marginalizes over the covariate distribution, but this strategy cannot exploit subgroup-level summary results that are often available and potentially highly informative. We propose using Bayesian Synthetic Likelihood (BSL) to leverage this ancillary summary information and present an implementation strategy for Hamiltonian Monte Carlo (HMC), a gradient-based Markov chain Monte Carlo (MCMC) algorithm. At each MCMC iteration, the BSL method imputes missing covariates by sampling from the model-implied conditional distribution, computes synthetic subgroup summaries from the imputed data, and matches these synthetic summaries to observed summaries via a multivariate normal synthetic likelihood. Fitting this model with HMC presents multiple challenges: first, gradients cannot be computed exactly but must be estimated stochastically; and second, the model's likelihood may be non-differentiable at certain points, a pathology that can deeply frustrate the performance of HMC. We address these challenges with pre-drawn random numbers, continuous relaxation of the likelihood, and Pareto-smoothed importance sampling. This work (1) introduces a novel application of BSL to missing data problems where summary statistics from the complete dataset are available despite substantial missingness in the individual-level data, (2) demonstrates how BSL strategies can be implemented within Stan's HMC framework, and (3) shows, using a network of plaque psoriasis trials, that BSL-enhanced ML-NMR can substantially improve upon standard ML-NMR by leveraging informative ancillary information.

This paper proposes a novel framework to assess individual player contributions in football, explicitly accounting for the cooperative nature of shot-ending offensive actions. By incorporating team interaction into player evaluation, it also supports economically sustainable decision-making, with practical implications for performance analysis and player scouting. Extending the expected Goals (xG) paradigm, we propose the expected Goal Action (xGA), an action-based metric designed to assess the quality of actions through passing networks. Furthermore, we adapt cooperative game theory and introduce the Player's Restricted Shapley Value (PRSV) statistic, a contribution metric based on restricted coalition structures derived from observed passing interactions, where xGA is adopted to compute the cohesion function. Unlike traditional Shapley approaches, the PRSV one restricts coalitions to tactically admissible player subsets, offering action-specific, interpretable measures of marginal contribution in a cooperative context. We apply the framework to 8,421 shot-actions from the Italian League Serie A season 2022/23, and the case studies of AC Milan and SSC Napoli reveal heterogeneity in contributions within teams. Combining the PRSV statistic with an individual performance metric highlights the discrepancies between a player's cooperative engagement and goal-conversion ability.

Building local surrogates to accelerate stationary point searches on potential energy surfaces spans decades of effort. Done correctly, surrogates can reduce the number of expensive electronic structure evaluations by roughly an order of magnitude while preserving the accuracy of the underlying theory, with the gain depending on oracle cost, search distance, and the availability of analytical forces. We present a unified Bayesian optimization view of minimization, single-point saddle searches, and double-ended path searches: all three share one six-step surrogate loop and differ only in the inner optimization target and the acquisition criterion. The framework uses Gaussian process regression with derivative observations, inverse-distance kernels, and active learning, and we develop optional extensions for production use, including farthest-point sampling with the Earth Mover's Distance, MAP regularization, an adaptive trust radius, and random Fourier features for scaling. Accompanying pedagogical Rust code demonstrates that all three applications use the same Bayesian optimization loop, bridging the gap between theoretical formulation and practical execution.

Deep learning models are being used for the analysis of parametric statistical models based on simulation-only frameworks. Bayesian models using normalizing flows simulate data from a prior distribution and are composed of two deep neural networks: a summary network that learns a sufficient statistic for the parameter and a normalizing flow that conditional on the summary network can approximate the posterior distribution. Here, we explore frequentist models that are based on a single summary network. During training, input of the network is a simulated data set based on a parameter and the loss function minimizes the mean-square error between learned summary and parameter. The network thereby solves the inverse problem of parameter estimation. We propose a branched network structure that contains collapsing layers that reduce a data set to summary statistics that are further mapped through fully connected layers to approximate the parameter estimate. We motivate our choice of network structure by theoretical considerations. In simulations we demonstrate three desirable properties of parameter estimates: finite sample exactness, robustness to data contamination, and algorithm approximation. These properties are achieved offering the the network varying sample size, contaminated data, and data needing algorithmic reconstruction during the training phase. In our simulations an EM-algorithm for genetic data is automatically approximated by the network. Simulation only approaches seem to offer practical advantages in complex modeling tasks where the simpler data simulation part is left to the researcher and the more complex problem of solving the inverse problem is left to the neural network. Challenging future work includes offering pre-trained models that can be used in a wide variety of applications.

Platform trials allow treatment arms to enter and exit over time while maintaining a shared control arm, yielding concurrent and non-concurrent controls (NCC). Pooling NCC is often motivated as a strategy to improve statistical efficiency, but it is unclear which estimand is targeted, what assumptions justify identification and estimation, and when precision gains are achievable; these questions are further complicated by time-to-event/survival data. Motivated by the Adaptive COVID-19 Treatment Trial (ACTT) platform trial with time to recovery as the primary endpoint, we develop an estimand-first causal survival framework targeting the treatment-specific counterfactual survival curve in the concurrent population and the corresponding functionals including the concurrent restricted mean survival time (RMST). We give nonparametric identification results and formalize conditions that justify pooling using NCC. We study covariate-adjusted outcome-regression (OR) and doubly robust (DR) estimators for the concurrent RMST, comparing concurrent-only versions to pooled-control versions. Pooling improves precision for OR estimators only when the pooling assumption holds and parametric hazard models are correctly specified; otherwise, pooling can induce bias. Moreover, in certain settings, pooling NCC yields no efficiency gain for the DR estimator. Overall, the most robust route to improve precision is to target concurrent causal survival estimands and use a covariate-adjusted DR estimation that uses only concurrent controls. An ACTT application corroborates these results.

Test-time scaling evaluates reasoning LLMs by sampling multiple outputs per prompt, but ranking models in this regime remains underexplored. We formalize dense benchmark ranking under test-time scaling and introduce Scorio, a library that implements statistical ranking methods such as paired-comparison models, item response theory (IRT) models, voting rules, and graph- and spectral-based methods. Across $20$ reasoning models on four Olympiad-style math benchmarks (AIME'24, AIME'25, HMMT'25, and BrUMO'25; up to $N=80$ trials), most full-trial rankings agree closely with the Bayesian gold standard $\mathrm{Bayes}_{\mathcal{U}}@80$ (mean Kendall's $\tau_b = 0.93$–$0.95$), and $19$–$34$ methods recover exactly the same ordering. In the single-trial regime, the best methods reach $\tau_b \approx 0.86$. Using greedy decoding as an empirical prior ($\mathrm{Bayes}_{\mathbf{R}_0}@N$) reduces variance at $N=1$ by $16$–$52\%$, but can bias rankings when greedy and stochastic sampling disagree. These results identify reliable ranking methods for both high- and low-budget test-time scaling. We release Scorio as an open-source library at https://github.com/mohsenhariri/scorio.

Machine learning methods for identifying molecular structures from tandem mass spectra (MS/MS) have advanced rapidly, yet current approaches still exhibit significant error rates. In high-stakes applications such as clinical metabolomics and environmental screening, incorrect annotations can have serious consequences, making it essential to determine when a prediction can be trusted. In this work, we introduce a selective prediction framework for molecular structure retrieval from MS/MS spectra, separating low-risk predictions automatically from lower-confidence predictions. We formulate the problem within the risk-coverage tradeoff framework and systematically evaluate uncertainty quantification strategies at three levels: input-level distance in the learned representation, fingerprint-level uncertainty over predicted molecular fingerprint bits, and retrieval-level uncertainty over candidate rankings. We compare scoring functions including first-order confidence measures, aleatoric and epistemic uncertainty estimates from second-order distributions, as well as distance-based measures in the latent space. All experiments are conducted on the MassSpecGym benchmark. Our analysis reveals that while fingerprint-level uncertainty scores are poor proxies for retrieval success, retrieval-level total uncertainty provides the overall strongest rejection criterion, and first-order confidence measures are computationally inexpensive, strong baselines. We demonstrate that by applying distribution-free risk control via generalisation bounds, practitioners can specify a tolerable error rate and obtain a subset of annotations satisfying that constraint with high probability.

In this paper, we revisit the notion of partial copula, originally introduced to test conditional independence, highlighting its capability to represent the dependence between two random variables after removing their dependence with a covariate. Building upon results previously presented in the literature, we show that partial copulas can be seen as a nonlinear analogue of partial correlation. Then, we prove several results showing how dependence properties of the conditional copulas constrain the form of the partial copula. Finally, a simulation study is conducted to illustrate the results and to show the potential of the partial copula as a way to describe covariate-adjusted statistical dependence. This highlights the potential of the method to be used in causal inference problems and to recover the true sign of a causal effect.