Papers

We study tabular finite-horizon reinforcement learning problems with multiple steps of lookahead information. Before acting, the learner observes $\ell$ steps of future transition and reward realizations: the exact state the agent would reach and the rewards it would collect under any possible course of action. While it has been shown that such information can drastically boost the value, finding the optimal policy is NP-hard, and it is common to apply one of two tractable heuristics: processing the lookahead in chunks of predefined sizes ('fixed batching policies'), and model predictive control. We first illustrate the problems with these two approaches and propose utilizing the lookahead in adaptive (state-dependent) batches; we refer to such policies as adaptive batching policies (ABPs). We derive the optimal Bellman equations for these strategies and design an optimistic regret-minimizing algorithm that enables learning the optimal ABP when interacting with unknown environments. Our regret bounds are order-optimal up to a potential factor of the lookahead horizon $\ell$, which can usually be considered a small constant.

Dimension reduction is a fundamental tool for analyzing high-dimensional data in supervised learning. Traditional methods for estimating intrinsic order often prioritize model-specific structural assumptions over predictive utility. This paper introduces predictive order determination (POD), a model-agnostic framework that determines the minimal predictively sufficient dimension by directly evaluating out-of-sample predictiveness. POD quantifies uncertainty via error bounds for over- and underestimation and achieves consistency under mild conditions. By unifying dimension reduction with predictive performance, POD applies flexibly across diverse reduction tasks and supervised learners. Simulations and real-data analyses show that POD delivers accurate, uncertainty-aware order estimates, making it a versatile component for prediction-centric pipelines.

We consider general parameter to solution maps $\theta \mapsto \mathcal G(\theta)$ of non-linear partial differential equations and describe an approach based on a Banach space version of the implicit function theorem to verify the gradient stability condition of Nickl&Wang (JEMS 2024) for the underlying non-linear inverse problem, providing also injectivity estimates and corresponding statistical identifiability results. We illustrate our methods in two examples involving a non-linear reaction diffusion system as well as a McKean–Vlasov interacting particle model, both with periodic boundary conditions. We apply our results to prove the polynomial time convergence of a Langevin-type algorithm sampling the posterior measure of the interaction potential arising from a discrete aggregate measurement of the interacting particle system.

The asset pricing literature emphasizes factor models that minimize pricing errors but overlooks unselected candidate factors that could enhance the performance of test assets. This paper proposes a framework for factor model selection and testing by (i) selecting the optimal model that spans the joint efficient frontier of test assets and all candidate factors, and (ii) testing pricing performance on both test assets and unselected candidate factors. Our framework updates a baseline model (e.g., CAPM) sequentially by adding or removing factors based on asset pricing tests. Ensuring model selection consistency, our framework utilizes the asset pricing duality: minimizing cross-sectionally unexplained pricing errors aligns with maximizing the Sharpe ratio of the selected factor model. Empirical evidence shows that workhorse factor models fail asset pricing tests, whereas our proposed 8-factor model is not rejected and exhibits robust out-of-sample performance.

A comprehensive asymptotic and bootstrap theory is established for checkerboard-based estimation of the copula and its lower and upper tail copula counterparts under unknown marginal distributions. The proposed estimator of the tail copula extends a local bilinear interpolation of the empirical copula to the tail region, providing a flexible nonparametric approach for modeling extremal dependence. Almost sure uniform consistency is established under mild conditions on the checkerboard grid. Weak convergence of the checkerboard copula process is derived, showing that smoothing preserves the first-order asymptotic limit of the empirical copula process, including the effect of marginal estimation. These results are further extended to lower and upper tail copula processes, yielding asymptotic normality for tail dependence measures. Since the limiting processes depend on unknown characteristics of the underlying true copula, a multiplier bootstrap procedure adapted to the checkerboard structure is proposed and shown to be asymptotically valid. Simulation studies and statistical applications validate our theoretical findings under a range of dependence structures. Although the limiting processes match with that observed for the empirical copula, the finite sample performance shows a noticeable improvement under checkerboard smoothing.

Causal discovery aims to recover “what causes what”, but classical constraint-based methods (e.g., PC, FCI) suffer from error propagation, and recent LLM-based causal oracles often behave as opaque, confidence-free black boxes. This paper introduces Tree-Query, a tree-structured, multi-expert LLM framework that reduces pairwise causal discovery to a short sequence of queries about backdoor paths, (in)dependence, latent confounding, and causal direction, yielding interpretable judgments with robustness-aware confidence scores. Theoretical guarantees are provided for asymptotic identifiability of four pairwise relations. On data-free benchmarks derived from Mooij et al. and UCI causal graphs, Tree-Query improves structural metrics over direct LLM baselines, and a diet–weight case study illustrates confounder screening and stable, high-confidence causal conclusions. Tree-Query thus offers a principled way to obtain data-free causal priors from LLMs that can complement downstream data-driven causal discovery. Code is available at https://anonymous.4open.science/r/Repo-9B3E-4F96.

Manifold fitting aims to reconstruct a low-dimensional manifold from high-dimensional data, whose framework is established by Fefferman et al. \cite{fefferman2020reconstruction,fefferman2021reconstruction}. This paper studies the recovery of a compact $C^3$ submanifold $\mathcal{M} \subset \mathbb{R}^D$ with dimension $d<D$ and positive reach $\tau$ from observations $Y = X + \xi$, where $X$ is uniformly distributed on $\mathcal{M}$ and $\xi \sim \mathcal{N}(0, \sigma^2 I_D)$ denotes isotropic Gaussian noise. To project any points $z$ in a tubular neighborhood $\Gamma$ of $\mathcal{M}$ onto $\mathcal{M}$, we construct a sample-based estimator $F:\Gamma\to\mathbb{R}^D$ by a normalized local kernel with the theoretically derived bandwidth $r = c_D\sigma$. Under a sample size of $O(\sigma^{-3d-5})$, we establish with high probability the uniform asymptotic expansion \[ F(z) = \pi(z) + \frac{d}{2} H_{\pi(z)} \sigma^2 + O(\sigma^3), \qquad z \in \Gamma, \] where $\pi(z)$ is the projection of $z$ onto $\mathcal{M}$ and $H_{\pi(z)}$ is the mean curvature vector of $\mathcal{M}$ at $\pi(z)$. The resulting manifold $F(\Gamma)$ has reach bounded below by $c \tau$ for $c>0$ and achieves a state-of-the-art Hausdorff distance of $O(\sigma^2)$ to $\mathcal{M}$. Numerical experiments confirm the quadratic decay of the reconstruction error and demonstrate the computational efficiency of the estimator $F$. Our work provides a curvature-driven framework for denoising and reconstructing manifolds with second-order accuracy.

The choice of the tuning parameter in the Lasso is central to its statistical performance in high-dimensional linear regression. In this work, we study tuning regimes under which the Lasso exhibits suboptimal prediction performance, in the sense that a simple refinement improves upon it both on high-probability events and in mean squared prediction error. Our analysis shows that the relevant stochastic scale is governed by Gaussian maxima on the selected or localized support, which may be more informative than the universal rate in Lasso theory. We further illustrate how structural factors in the design matrix can influence the suboptimality phenomenon and discuss extensions to other estimators and more general noise structures.

Multivariate linear regression models often face the problem of heteroscedasticity caused by multiple explanatory variables. The weighted least squares estimation with univariate-dependent weights has limitations in constructing weight functions. Therefore, this paper proposes a multivariate dependent weighted least squares estimation method. By constructing a linear combination of explanatory variables and maximizing their Spearman rank correlation coefficient with the absolute residual value, combined with maximum likelihood method to depict heteroscedasticity, it can comprehensively reflect the trend of variance changes in the random error and improve the accuracy of the model. This paper demonstrates that the optimal linear combination exponent estimator for heteroscedastic volatility obtained by our algorithm possesses consistency and asymptotic normality. In the simulation experiment, three scenarios of heteroscedasticity were designed, and the comparison showed that the proposed method was superior to the univariate-dependent weighting method in parameter estimation and model prediction. In the real data applications, the proposed method was applied to two real-world datasets about consumer spending in China and housing prices in Boston. From the perspectives of MAE, RSE, cross-validation, and fitting performance, its accuracy and stability were verified in terms of model prediction, interval estimation, and generalization ability. Additionally, the proposed method demonstrated relative advantages in fitting data with large fluctuations. This study provides an effective new approach for dealing with heteroscedasticity in multivariate linear regression.

In many social, business, economic, and physical systems the true data-generating process is rarely known, so a series forecastability cannot be assumed; it must be assessed from the observed history. This paper evaluates a horizon-specific, pre-modelling measure for that assessment: auto-mutual information (AMI), a training-only measure of past-future dependence at each forecast horizon; higher AMI indicates more recoverable temporal structure. It is evaluated on the M4 Monthly dataset (47,992 of 48,000 series, 18-month horizon) with seasonal naive, ETS, and N-BEATS as probes and MASE as the error measure. The series-level association with realised skill is modest but systematic (mean Spearman p of 0.11 to 0.13 for ETS and N-BEATS), accumulating into a pronounced descriptive gradient: median MASE is 29% (ETS) to 37% (N-BEATS) lower in the top within-horizon AMI decile than in the bottom. AMI outperforms absolute autocorrelation as a horizon-specific diagnostic by a small, consistent margin; paired bootstrap intervals exclude zero for all three probes, and synthetic benchmarks with analytically exact AMI locate the advantage on nonlinear dependence. Decile assignments are sample-relative and require recalibration on a new portfolio. The contribution is a pre-modelling diagnostic, not a forecasting model.

Lymphovascular invasion (LVI) is an important prognostic marker for head and neck squamous cell carcinoma (HNSC), but the true effect of LVI on survival may be distorted by endogeneity arising from unmeasured confounding. Conventional one-stage conditional models and instrument-based two-stage estimators are prone to bias under endogeneity, and sufficiently strong instruments are often unavailable in practice. To address these challenges, we propose a semiparametric recursive copula framework that jointly specifies marginal models for both LVI, treated as an endogenous exposure, and a binary 2-year survival outcome, and links them through a flexible copula to account for latent confounding and accommodate censoring without requiring strong instruments. In two simulation studies, we systematically varied sample sizes, censoring rates from 0% to 60%, and endogeneity strengths, and assessed robustness under moderate model misspecification. The proposed copula framework exhibited reduced bias and improved interval coverage compared with both one-stage and two-stage approaches while maintaining robustness to moderate misspecification. We applied the method to HNSC cases with associated clinical and microRNA data from The Cancer Genome Atlas (n = 215), and found that LVI significantly reduced 2-year survival probability by approximately 47%, with a 95% confidence interval of -0.61 to -0.29 on the probability scale. The estimated positive dependence parameter indicates that the attenuation is driven by residual dependence between unobserved components of LVI and survival. Overall, the proposed copula framework yields more credible effect estimates for survival outcomes in the absence of strong instruments, mitigating biases due to endogeneity and censoring and strengthening quantitative evidence for HNSC research.

This paper presents the exact mathematical derivation of the mean and variance properties for the Exponentially Weighted Moving Average (EWMA) statistic applied to binomial proportion monitoring in Multiple Stream Processes (MSPs). We develop a Cumulative Standardized Binomial EWMA (CSB-EWMA) formulation that provides adaptive control limits based on exact time-varying variance calculations, overcoming the limitations of asymptotic approximations during early-phase monitoring. The derivations are rigorously validated through Monte Carlo simulations, demonstrating remarkable agreement between theoretical predictions and empirical results. This work establishes a theoretical foundation for distribution-free monitoring of binary outcomes across parallel data streams, with applications in statistical process control across diverse domains including manufacturing, healthcare, and cybersecurity.

Large language model (LLM) embeddings are increasingly used to estimate dimensional structure in psychological item pools prior to data collection, yet current applications treat embeddings as static, cross-sectional representations. This approach implicitly assumes uniform contribution across all embedding coordinates and overlooks the possibility that optimal structural information may be concentrated in specific regions of the embedding space. This study reframes embeddings as searchable landscapes and adapts Dynamic Exploratory Graph Analysis (DynEGA) to systematically traverse embedding coordinates, treating the dimension index as a pseudo-temporal ordering analogous to intensive longitudinal trajectories. A large-scale Monte Carlo simulation embedded items representing five dimensions of grandiose narcissism using OpenAI's text-embedding-3-small model, generating network estimations across systematically varied item pool sizes (3-40 items per dimension) and embedding depths (3-1,298 dimensions). Results reveal that Total Entropy Fit Index (TEFI) and Normalized Mutual Information (NMI) leads to competing optimization trajectories across the embedding landscape. TEFI achieves minima at deep embedding ranges (900–1,200 dimensions) where entropy-based organization is maximal but structural accuracy degrades, whereas NMI peaks at shallow depths where dimensional recovery is strongest but entropy-based fit remains suboptimal. Single-metric optimization produces structurally incoherent solutions, whereas a weighted composite criterion identifies embedding dimensions depth regions that jointly balance accuracy and organization. Optimal embedding depth scales systematically with item pool size. These findings establish embedding landscapes as non-uniform semantic spaces requiring principled optimization rather than default full-vector usage.

Physics-Informed Neural Networks (PINNs) have emerged as a powerful tool for solving differential equations and modeling physical systems by embedding physical laws into the learning process. However, rigorously quantifying how well a PINN captures the complete dynamical behavior of the system, beyond simple trajectory prediction, remains a challenge. This paper proposes a novel experimental framework to address this by employing Fisher information for differentiable dynamical systems, denoted $g_F^C$. This Fisher information, distinct from its statistical counterpart, measures inherent uncertainties in deterministic systems, such as sensitivity to initial conditions, and is related to the phase space curvature and the net stretching action of the state space evolution. We hypothesize that if a PINN accurately learns the underlying dynamics of a physical system, then the Fisher information landscape derived from the PINN's learned equations of motion will closely match that of the original analytical model. This match would signify that the PINN has achieved comprehensive fidelity capturing not only the state evolution but also crucial geometric and stability properties. We outline an experimental methodology using the dynamical model of a car to compute and compare $g_F^C$ for both the analytical model and a trained PINN. The comparison, based on the Jacobians of the respective system dynamics, provides a quantitative measure of the PINN's fidelity in representing the system's intricate dynamical characteristics.

A probabilistic framework for irreversible kinetics that unifies forward-in-time evolution and inverse inference, while quantifying epistemic uncertainty over admissible histories, is proposed. The forward-in-time evolution and inverse inference formulations differ only through observations and how they constrain admissible histories. All histories are ranked using a Gibbs-type probability measure $\exp(-\mathcal{J}/\Theta)$, where $\mathcal{J}$ encodes constitutive physics and observations. $\Theta$ controls epistemic uncertainty over the unknown histories, and the measure is interpreted as a Bayesian posterior over histories. Maximizing this posterior is equivalent to simultaneous minimization of $\mathcal{J}$ over the admissible history space. The framework is then specialized to generalized standard materials (GSM), for which $\mathcal{J}$ is constructed from incremental energy–dissipation functionals. This specialization reveals an important difference between the history resulting from simultaneous minimization over entire histories generally differs from the one generated by sequential GSM updates. Specifically, the causal GSM history incurs a higher history-level cost than the one obtained by simultaneous minimization, indicating that enforcing causality carries an additional cost at the history level. This difference is shown through seven representative examples: viscoelasticity, viscoplasticity, rate-independent plasticity, gradient damage, conserved and non-conserved phase transformations, and coupled thermoelectric evolution. Finally, the finite-$\Theta$ formulation is demonstrated on an inverse problem with a non-convex free energy, where incomplete initial-state information is used to infer unobserved intermediate states and quantify uncertainty over admissible histories. As $\Theta$ decreases, the posterior concentrates towards minimum-$\mathcal{J}$ histories.

This paper investigates two fundamental descriptors of data, i.e., density distribution versus mass distribution, in the context of clustering. Density distribution has been the de facto descriptor of data distribution since the introduction of statistics. We show that density distribution has its fundamental limitation – high-density bias, irrespective of the algorithms used to perform clustering. Existing density-based clustering algorithms have employed different algorithmic means to counter the effect of the high-density bias with some success, but the fundamental limitation of using density distribution remains an obstacle to discovering clusters of arbitrary shapes, sizes and densities. Using the mass distribution as a better foundation, we propose a new algorithm which maximizes the total mass of all clusters, called mass-maximization clustering (MMC). The algorithm can be easily changed to maximize the total density of all clusters in order to examine the fundamental limitation of using density distribution versus mass distribution. The key advantage of the MMC over the density-maximization clustering is that the maximization is conducted without a bias towards dense clusters.

The Nested Dirichlet Distribution (NDD) provides a flexible alternative to the Dirichlet distribution for modeling compositional data, relaxing constraints on component variances and correlations through a hierarchical tree structure. While theoretically appealing, the NDD is underused in practice due to two main limitations: the need to predefine the tree structure and the lack of diagnostics for evaluating model fit. This paper addresses both issues. First, we introduce a data-driven, greedy tree-finding algorithm that identifies plausible NDD tree structures from observed data. Second, we propose novel diagnostic tools, including pseudo-residuals based on a saddlepoint approximation to the marginal distributions and a likelihood displacement measure to detect influential observations. These tools provide accurate and computationally tractable assessments of model fit, even when marginal distributions are analytically intractable. We demonstrate our approach through simulation studies and apply it to data from a Morris water maze experiment, where the goal is to detect differences in spatial learning strategies among cognitively impaired and unimpaired mice. Our methods yield interpretable structures and improved model evaluation in a realistic compositional setting. An accompanying R package is provided to support reproducibility and application to new datasets.

Generalized Linear Model (or GLM) extends the ordinary linear regression by linking the mean of the response variable to covariates through appropriate link functions. GLM is widely used in the analysis of datasets arising from diverse fields including medical sciences, clinical trials, population surveys and risk analysis. In this paper, we investigate the Gaussian and Bootstrap approximations of GLM under two separate high dimensional regimes: (I) when the dimension $d$ grows slower than $n$ and (II) when $d$ grows exponentially with $n$. Under regime (I), we essentially show that the Gaussian approximation holds over the collection of Borel convex sets when $d = o\big(n^{2/5}\big)$ and over the collection of Euclidean balls when $d = o\big(n^{1/2}\big)$. We further devise two high dimensional Bootstrap methods which are valid over the collections of Borel convex sets and Euclidean balls under the same dimension growth rates. Then we move to regime (II) where we invoke sparsity to GLM through Lasso. We show that the high dimensional Gaussian approximation fails under regime (II). However, the Bootstrap approximations over convex sets and Euclidean balls are valid for the relevant part of the GLM estimator provided $\log d = o\big(n^{2\tau/3}\big)$ and the number of non-zero regression parameters is $o\big(n^{1/3- 4\tau/3}\big)$, when the Lasso penalty $\lambda_n \sim n^{1/2 + \tau}$, for some $\tau \in (0, 1/4)$. Simulation studies confirm the strong finite-sample performance of our proposed Bootstrap methods under both regime (I) and (II). We also implement our methods on real datasets.

This chapter develops a unified framework for studying misspecified learning situations in which agents optimize and update beliefs within an incorrect model of their environment. We review the statistical foundations of learning from misspecified models and extend these insights to environments with endogenous, action-dependent data, including both single agent and strategic settings.

We establish concentration rates for estimation of treatment effects in experiments that incorporate prior sources of information – such as past pilots, related studies, or expert assessments – whose external validity is uncertain. Each source is modeled as a Gaussian prior with its own mean and precision, and sources are combined using Bayesian model averaging (BMA), allowing data from the new experiment to update posterior weights. To capture empirically relevant settings in which prior studies may be as informative as the current experiment, we introduce a nonstandard asymptotic framework in which prior precisions grow with the experiment's sample size. In this regime, posterior weights are governed by an external-validity index that depends jointly on a source's bias and information content: biased sources are exponentially downweighted, while unbiased sources dominate. When at least one source is unbiased, our procedure concentrates on the unbiased set and achieves faster convergence than relying on new data alone. When all sources are biased, including a deliberately conservative (diffuse) prior guarantees robustness and recovers the standard convergence rate.

For linear models that may have asymmetric errors, we study variable selection by cross-validation. The data are split into training and validation sets, with the number of observations in the validation set much larger than in the training set. For the model coefficients, the expectile or adaptive LASSO expectile estimators are calculated on the training set. These estimators will be used to calculate the cross-validation mean score (CVS) on the validation set. We show that the model that minimizes CVS is consistent in two cases: when the number of explanatory variables is fixed or when it depends on the number of observations. Monte Carlo simulations confirm the theoretical results and demonstrate the superiority of our estimation method compared to two others in the literature. The usefulness of the CV expectile model selection technique is illustrated by applying it to real data sets.

Estimators of parameters of truncated distributions, namely the truncated normal distribution, have been widely studied for a known truncation region. There is also literature for estimating the unknown bounds for known parent distributions. In this work, we develop a novel algorithm under the expectation-solution (ES) framework, which is an iterative method of solving nonlinear estimating equations, to estimate both the bounds and the location and scale parameters of the parent normal distribution utilizing the theory of best linear unbiased estimates from location-scale families of distribution and unbiased minimum variance estimation of truncation regions. The conditions for the algorithm to converge to the solution of the estimating equations for a fixed sample size are discussed, and the asymptotic properties of the estimators are characterized using results on M- and Z-estimation from empirical process theory. The proposed method is then compared to methods utilizing the known truncation bounds via Monte Carlo simulation.

We consider sampling from a Gibbs distribution by evolving a finite number of particles using a particular score estimator rather than Brownian motion. To accelerate the particles, we consider a second-order score-based ODE, similar to Nesterov acceleration. In contrast to traditional kernel density score estimation, we use the recently proposed regularized Wasserstein proximal method, yielding the Accelerated Regularized Wasserstein Proximal method (ARWP). We provide a detailed analysis of continuous- and discrete-time non-asymptotic and asymptotic mixing rates for Gaussian initial and target distributions, using techniques from Euclidean acceleration and accelerated information gradients. Compared with the kinetic Langevin sampling algorithm, the proposed algorithm exhibits a higher contraction rate in the asymptotic time regime. Numerical experiments are conducted across various low-dimensional experiments, including multi-modal Gaussian mixtures and ill-conditioned Rosenbrock distributions. ARWP exhibits structured and convergent particles, accelerated discrete-time mixing, and faster tail exploration than the non-accelerated regularized Wasserstein proximal method and kinetic Langevin methods. Additionally, ARWP particles exhibit better generalization properties for some non-log-concave Bayesian neural network tasks.

Acute respiratory infections (ARI) are a major cause of pediatric hospitalization in Chile, producing marked winter increases in demand that challenge hospital planning. This study presents an alert-based forecasting model to predict the timing and magnitude of ARI hospitalization peaks in Santiago. The approach integrates a seasonal SIR model with a historical mobile predictor, activated by a derivative-based alert system that detects early epidemic growth. Daily hospitalization data from DEIS were smoothed using a 15-day moving average and Savitzky-Golay filtering, and parameters were estimated using a penalized loss function to reduce sensitivity to noise. Retrospective evaluation and real-world implementation in major Santiago pediatric hospitals during 2023 and 2024 show that peak date can be anticipated about one month before the event and predicted with high accuracy two weeks in advance. Peak magnitude becomes informative roughly ten days before the peak and stabilizes one week prior. The model provides a practical and interpretable tool for hospital preparedness.

Batch effects represent a major confounder in genomic diagnostics. In copy number variant (CNV) detection from NGS, many algorithms compare read depth between test samples and a reference sample, assuming they are process-matched. When this assumption is violated, with causes ranging from reagent lot changes to multi-site processing, the reference becomes inappropriate, introducing false CNV calls or masking true pathogenic variants. Detecting such heterogeneity before downstream analysis is critical for reliable clinical interpretation. Existing batch effect detection methods either cluster samples based on raw features, risking conflation of biological signal with technical variation, or require known batch labels that are frequently unavailable. We introduce a method that addresses both limitations by clustering samples according to their Bayesian model evidence. The central insight is that evidence quantifies compatibility between data and model assumptions, technical artifacts violate assumptions and reduce evidence, whereas biological variation, including CNV status, is anticipated by the model and yields high evidence. This asymmetry provides a discriminative signal that separates batch effects from biology. We formalize heterogeneity detection as a likelihood ratio test for mixture structure in evidence space, using parametric bootstrap calibration to ensure conservative false positive rates. We validate our approach on synthetic data demonstrating proper Type I error control, three clinical targeted sequencing panels (liquid biopsy, BRCA, and thalassemia) exhibiting distinct batch effect mechanisms, and mouse electrophysiology recordings demonstrating cross-modality generalization. Our method achieves superior clustering accuracy compared to standard correlation-based and dimensionality-reduction approaches while maintaining the conservativeness required for clinical usage.

Structure-based and ligand-based computational drug design have traditionally relied on disjoint data sources and modeling assumptions, limiting their joint use at scale. In this work, we introduce Contrastive Geometric Learning for Unified Computational Drug Design (ConGLUDe), a single contrastive geometric model that unifies structure- and ligand-based training. ConGLUDe couples a geometric protein encoder that produces whole-protein representations and implicit embeddings of predicted binding sites with a fast ligand encoder, removing the need for predefined pockets. By aligning ligands with both global protein representations and multiple candidate binding sites through contrastive learning, ConGLUDe supports ligand-conditioned pocket prediction in addition to virtual screening and target fishing, while being trained jointly on protein-ligand complexes and large-scale bioactivity data. Across diverse benchmarks, ConGLUDe achieves competitive zero-shot virtual screening performance, substantially outperforms existing methods on a challenging target fishing task, and demonstrates state-of-the-art ligand-conditioned pocket selection. These results highlight the advantages of unified structure-ligand training and position ConGLUDe as a step toward general-purpose foundation models for drug discovery.

The graphical Lasso (GLASSO) is a widely used algorithm for learning high-dimensional undirected Gaussian graphical models (GGM). Given i.i.d. observations from a multivariate normal distribution, GLASSO estimates the precision matrix by maximizing the log-likelihood with an \ell_1-penalty on the off-diagonal entries. However, selecting an optimal regularization parameter \lambda in this unsupervised setting remains a significant challenge. A well-known issue is that existing methods, such as out-of-sample likelihood maximization, select a single global \lambda and do not account for heterogeneity in variable scaling or partial variances. Standardizing the data to unit variances, although a common workaround, has been shown to negatively affect graph recovery. Addressing the problem of nodewise adaptive tuning in graph estimation is crucial for applications like computational neuroscience, where brain networks are constructed from highly heterogeneous, region-specific fMRI data. In this work, we develop Locally Adaptive Regularization for Graph Estimation (LARGE), an approach to adaptively learn nodewise tuning parameters to improve graph estimation and selection. In each block coordinate descent step of GLASSO, we augment the nodewise Lasso regression to jointly estimate the regression coefficients and error variance, which in turn guides the adaptive learning of nodewise penalties. In simulations, LARGE consistently outperforms benchmark methods in graph recovery, demonstrates greater stability across replications, and achieves the best estimation accuracy in the most difficult simulation settings. We demonstrate the practical utility of our method by estimating brain functional connectivity from a real fMRI data set.

Blind image deconvolution refers to the problem of simultaneously estimating the blur kernel and the true image from a set of observations when both the blur kernel and the true image are unknown. Sometimes, additional image and/or blur information is available and the term semi-blind deconvolution (SBD) is used. We consider a recently introduced Bayesian conjugate hierarchical model for SBD, formulated on an extended cyclic lattice to allow a computationally scalable Gibbs sampler. In this article, we extend this model to the general SBD problem, rewrite the previously proposed Gibbs sampler so that operations are performed in the Fourier domain whenever possible, and introduce a new marginal Hamiltonian Monte Carlo (HMC) blur update, obtained by analytically integrating the blur-image joint conditional over the image. The cyclic formulation combined with non-trivial linear algebra manipulations allows a Fourier-based, scalable HMC update, otherwise complicated by the rigid constraints of the SBD problem. Having determined the padding size in the cyclic embedding through a numerical experiment, we compare the mixing and exploration behaviour of the Gibbs and HMC blur updates on simulated data and on a real geophysical seismic imaging problem where we invert a grid with $300\times50$ nodes, corresponding to a posterior with approximately $80,000$ parameters.

All existing match classification models in the tournament design literature suffer from two major limitations: a contestant is considered indifferent only if uncertain future results do never affect its prize, and competitive matches are not distinguished with respect to the incentives of the contestants. We propose a probabilistic framework to address both issues. For each match, our approach relies on simulating all other matches played simultaneously or later to compute the qualifying probabilities for the three main outcomes (win, draw, loss), thereby classifying each match into six categories. The suggested model is applied to the last round of the previous group stage and the new incomplete round-robin league, introduced in the 2024/25 season of UEFA club competitions. The incomplete round-robin tournament is found to contain fewer unimportant matches with two indifferent teams, and substantially more matches where both teams should play offensively. However, the robustly higher proportion of potentially collusive matches can threaten with serious scandals.

While Kolmogorov's probability axioms are widely recognized, it is less well known that in an often-overlooked 1930 note, Kolmogorov proposed an axiomatic framework for a unifying concept of the mean – referred to as regular means. This framework yields a well-defined functional form encompassing the arithmetic, geometric, and harmonic means, among others. In this article, we uncover an elegant connection between two key results of Kolmogorov by showing that the class of regular means can be derived directly from the Kolmogorov superposition theorem. This connection is conceptually appealing and illustrates that the superposition theorem deserves wider recognition in Statistics – not only because of its link to regular means as shown here, but also due to its influence on the development of neural models and its potential connections with other statistical frameworks. In addition, we establish a stability property of regular means, showing that they vary smoothly under small perturbations of the generator. Finally, we provide insights into a recent universal central limit theorem that applies to the broad class of regular means.