Papers

In function-on-function regression, the coefficient surface $\beta(s,t)$ may exhibit complex support structure—from localized patches to global patterns such as disconnected regions, bands, or rings—where effect similarity does not align with Euclidean proximity. Projection-based methods that rely on fixed basis expansions can obscure such structure, while direct smoothing approaches risk oversmoothing the surface and its boundaries. We propose Functional Attentive Interpretable Regression (FAIR), which represents $\beta(s,t)$ directly through coordinate features and uses self-attention to learn effect-adaptive neighborhoods, enabling information sharing at both local and global scales. A scalar compression network maps these learned representations to the coefficient surface. Sparsity and smoothness penalties applied over these neighborhoods promote localized support with coherent boundaries. We establish a sieve equivalence to tensor-product spline spaces and derive convergence rates. Simulations and applications to oceanographic and hydrological data demonstrate that FAIR recovers support geometry more accurately than existing methods while achieving superior prediction, particularly under sparse sampling.

We study adaptive routing of prompts to large language model (LLM) experts to maximize response quality in an online setting with limited feedback. We formulate it as a bandit problem with $K$ actions that represent experts and $d$ features that encode prompts, over a horizon of $T$ rounds. We propose algorithms that strategically select and observe rewards to minimize regret. In the full-information setting, we achieve a regret of $\tilde{O}(d T / \sqrt{m})$, while in the bandit setting we achieve $\tilde{O}(d T \sqrt{K / m})$, where $m \ll T$ is a budget on feedback. Our experiments show that we efficiently learn high-quality routing strategies across diverse LLMs from limited feedback.

Spatiotemporal areal data are commonly observed in various fields such including epidemiology, social science, economics and so on. To capture both spatial trends and temporal trends, spatiotemporal modeling is often employed, and the conditional autoregressive (CAR) model is one of the most widely used approaches for modeling areal data. This paper proposes a new framework for estimating spatiotemporal trends based on the CAR model. The proposed method provides locally adaptive temporal smoothing while yielding interpretable temporal trends by effectively utilizing information from both spatially neighboring areas and temporally adjacent time points. We also develop a Gibbs sampling algorithm and demonstrate the ability of the proposed method to adapt to to local temporal changes through numerical examples.

Principal component analysis (PCA) can rotate away from its population target when a covariance matrix is estimated from limited data. We introduce diagonal attenuation, which preserves sample cross-covariances while reducing coordinatewise sample variances. The method is revealed exactly by averaging a linear full-output reconstruction loss over random input masks; studying the correction directly extends it beyond the range attainable by masking. We isolate the part of the random coupling between retained and omitted population directions that is contributed by sample-variance errors, and show how attenuation can reduce the resulting rotation. Under balanced marginal variances, we derive an explicit expected-risk theorem, uniform over the attenuation path for all sufficiently large finite samples, and obtain the asymptotically risk-minimizing strength. For general covariances, we characterize when attenuation leaves the population PCA subspace unchanged and give a risk theorem that also accounts for changing eigengaps and the population cost when the target moves. Simulations track this tradeoff from exact preservation back to PCA. Across local image patches, speech spectra, and smartphone acceleration, both mask-derived and direct attenuation improve PCA under two fitting-sample budgets, and one of them has the largest mean gain among seven methods in every data–budget cell. The full path selects strengths beyond the mask-derived boundary on $63\%$–$95\%$ of the subsamples.

The Lehmer transform encodes a positive dataset as a single analytic curve, the ratio of its power sums at consecutive orders read as a function of the order. As the order sweeps the real line the curve generates every location statistic between the sample extremes, and its logarithm is the unit increment of the free energy of an exponentially tilted ensemble; the statistical theory of the curve flows from that identity. The slope of the curve is a Jeffreys divergence, the arithmetic-geometric gap is a relative entropy, and multiplicativity over independent factors makes deconvolution of multiplicative noise a pointwise division. A quantitative rigidity theorem locates the frontier of identifiability at geometric growth of the curve, with resonant log-periodic families of distinct laws sharing one curve beyond it. The empirical curve is an exact re-coordinatization of the order statistic, hence minimal sufficient, and its influence function, exact leading bias and limit theory are developed in full. At heavy tails the curve undergoes a phase transition whose two knees, one unit apart, sit at the tail index and its unit shift, a whole-sample diagnostic complementing threshold-based estimators.

We develop a network-structured Bayesian hierarchical model for sparse association mapping between genomic alterations and quantitative treatment-response phenotypes. The framework combines a Gaussian Markov random field prior that borrows strength across pathway-connected genes, a global-local horseshoe prior inducing sparsity, and a conjugate Gibbs sampler requiring no Metropolis-Hastings steps. Though broadly applicable to high-dimensional settings with known predictor networks, we validate it using cancer cell-line drug-sensitivity data. Applied to GDSC2 ($N=951$ cell lines, $G=219$ driver genes, $D=295$ drugs), the model identifies 126 gene-drug associations (0.195% of 64{,}605 pairs), concentrated in EZH2 (45 drugs, all sensitivity-direction, mean effect $-0.911$ $\ln$IC50) and KMT2D (36 drugs, all sensitivity-direction, mean effect $-0.496$ $\ln$IC50). These markers show external support in an independent PRISM screen (1{,}518 compounds), with KMT2D achieving complete directional replication (36/36) and EZH2 partial replication (8/12). Five-fold cross-validated predictive log-likelihood confirms each prior layer's value: the full model outperforms the no-network ablation by $+3{,}109$ log-units per fold and the no-horseshoe ablation by $+14{,}039$ log-units, consistently across folds. Simulations under three scenarios show the full model achieves the highest precision and lowest false-discovery rate throughout, while the network prior improves sensitivity recovery under network-structured signal. A tissue-stratified extension identifies coherent subgroup refinements, including lung-specific EGFR-inhibitor sensitivity and skin-specific BRAF-Dabrafenib sensitivity. These results show the framework identifies sparse, interpretable, externally supported drug-sensitivity markers while enabling principled investigation of tissue-specific departures from shared effects.

We develop a Dynamic Spatial Panel Bayesian Additive Regression Trees model with Horseshoe shrinkage (DSP-BART-HS) for high-dimensional spatio-temporal panel data. We jointly evaluate the model against a comprehensive suite of structural spatial econometrics, non-parametric machine learning methods, and small-area estimators across nine data-generating scenarios spanning 200 replicates each, including irregular spatial topologies, dense policy effects, and non-linear individual-level interactions. DSP-BART-HS is the best or statistically indistinguishable from the best estimator in every scenario. Conventional region-time-aggregate comparators suffer severe performance degradation – trailing by a factor of three or more – whenever individual-level non-linearity drives outcome variance, a limitation this framework's tree-ensemble design directly addresses. The model also maintains strong predictive accuracy under a zero-training-region spatial holdout via its spatial diffusion mechanism. We demonstrate practical utility across two U.S. county-level panel applications – intergenerational economic mobility and geographic income inequality – under genuine unseen-region, random, and temporal holdouts, with results validated through repeated-split uncertainty quantification and paired significance testing against every comparator. One clear limitation emerges: under temporal extrapolation specifically, a lighter per-region autoregressive specification (MTS-CAR-X) achieves a robust, and consistent advantage. DSP-BART-HS nonetheless establishes strong predictive performance, automated variable selection, and flexible inference for hierarchical spatio-temporal panel data.

This study introduces the three-parameter Kumaraswamy–Teissier distribution (KTD) by applying the Kumaraswamy-G construction to the Teissier distribution. The proposed distribution provides additional shape flexibility for modelling positive-valued observations and accommodates different density and hazard-rate shapes. Several statistical properties, including moments, the moment generating function, quantile function, and order statistics, are derived. Maximum likelihood, maximum product spacing, and Bayesian methods are considered for parameter estimation, and simulation results demonstrate improving estimation accuracy with increasing sample size. A median-based regression model is further developed for the KTD, with its finite-sample performance examined through simulation. The practical utility of the proposed regression model is demonstrated through an application to monthly gridded rainfall data from the Northwest Himalayas, incorporating annual and semi-annual harmonic terms to capture seasonal variation. Its performance is assessed against Kumaraswamy and beta regression using residual-based goodness-of-fit diagnostics and likelihood-based model selection. The results demonstrate effectiveness of the proposed distribution for modelling heterogeneous and skewed positive-valued rainfall data.

The purpose of this paper is to rigorously quantify the statistical and learning-theoretic properties of adversarial training models for classification. Equivalently, we establish the statistical properties of empirical optimal partial transport. Precisely, first we provide two types of central limit theorems (CLT): CLT centered at the expected empirical value, and CLT centered at the population one with smoothing. These results are based on the uniqueness of optimal potential for various equivalent optimal transport formulations, and the empirical process theory argument. For the binary setting, we indeed prove the uniqueness of optimal potential by leveraging the connection between optimal partial transport and the derived multi-marginal optimal transport formula. As byproducts, we also obtain the stability of a saddle point of the adversarial training model, and the sample complexity and concentration probability of the generalization error.

The robustness of methods for characterizing the origin of wave-like propagating signals is often challenged by the heterogeneity of transmitting media and sensor network. Detecting an individual wave under such noisy conditions remains particularly difficult. In this paper, we propose a robust framework to estimate wave origins from spatiotemporal data collected by a sensor array. First, a Butterworth filter is designed to extract relevant signals from each sensor channel. Next, a 3D randomized Hough transform is introduced to identify candidate signals originating from the same wave front. Finally, a wave propagation model is fitted to the identified signals using the least-squares method. By combining the iterative voting mechanism of the randomized Hough transform with least-squares optimization, our proposed method demonstrates superior robustness and computational efficiency in both simulation studies and real-world data analyses.

Modern statistical models are growing increasingly complex in an effort to realistically capture system dynamics. Using standard simulation-based inference, these models may be computationally prohibitive, necessitating the use of model calibration methods. Bayesian score calibration is a computationally efficient framework for model calibration with strong theoretical guarantees. This framework learns an appropriate correction for an approximate model using a small number of simulations from the data-generating process. Currently, only a location-scale transformation has been explored, which may lack the flexibility to correct the complex error introduced by some approximate models. In this paper, we develop two flexible transformations for use in the Bayesian score calibration framework. The first is a polynomial extension, which can appropriately adjust approximate models with location-varying error. The second is a sequential application of Bayesian score calibration, which can accommodate approximate models with posteriors that have low support for the true parameter values. We also discuss an additional diagnostic for use with this framework. We demonstrate the increased flexibility these two approaches provide over Bayesian score calibration in two illustrative simulation studies.

The High Plains Aquifer (HPA) is a critical water resource in the Central United States, yet its depletion remains a major concern. While the Gravity Recovery and Climate Experiment (GRACE) satellite mission provides large-scale estimates of liquid water equivalent thickness (LWET), its coarse spatial resolution (approx. 24 km) limits local inference. In contrast, well observations from the National Ground-Water Monitoring Network (NGWMN) offer valuable but spatially sparse measurements of depth-to-groundwater. In this paper, we develop a downscaling framework for the satellite data that integrates the two sources and covariates using a Bayesian hierarchical framework. Our model uses a latent Gaussian Markov Random Field (GMRF) that describes the groundwater storage at a high spatial resolution. To address computational issues, we use a basis representation approach specified via the Moran basis. We find that fine-scale covariates like irrigation intensity and precipitation help refine spatial predictions. We thus provide, to our knowledge, the first statistically-rigorous approach for downscaling groundwater information based on GRACE satellite data and NGWMN groundwater measurements. Our approach yields high-resolution estimates of groundwater variations across the HPA from 2002–2022. The resulting fine-scale inference provides valuable insights into groundwater dynamics, highlighting the effects of land use and local extraction patterns.

We give a necessary and sufficient condition for the existence of power-one sequential tests in an i.i.d. composite testing problem. A level-\(\alpha\) test with power one against every alternative exists if and only if the alternatives are separated from the null by a countable family of finite-block events. We provide other equivalent conditions using randomized fixed-sample tests, bounded finite-block scores, e-processes, reduced-filtration test supermartingales, and a countable cover whose finite-block weak-$*$ closed convex hulls are positively separated in total variation. As a bonus, the constructive proof yields tests have pointwise expected sample size \(O_Q(\log(1/\alpha))\). Exactly the same conditions also characterize i.i.d.\ change detectability under optional-horizon average-run-length control: for every \(\eta>0\), they are equivalent to an alarm family \((T_\gamma)_{\gamma\ge1}\) satisfying \(\Prob_{P^\infty}(T_\gamma\le\sigma)\le \E_{P^\infty}\sigma/\gamma\) for every null law and every stopping time \(\sigma\). In fact, when these conditions hold, we can construct a single e-detector such that every null-law average run length lies between \(\gamma\) and \((1+\eta)\gamma+1\), and having robust Lorden delay \(O_Q(\log\gamma)\).

Reconstructing continuous terrain manifolds from massive, unstructured airborne LiDAR point clouds remains challenging in complex Wildland-Urban Interface (WUI) environments, where deep neural networks require costly point-wise annotations and nonparametric surface reconstruction methods often lack structural interpretability. This paper introduces the Gaussian Linear Functional Manifold (GLFM), a physics-informed statistical framework that represents continuous surface topography using deterministic linear functional bases while modeling microscale diffuse laser backscatter as an isotropic Gaussian process. To avoid the quadratic computational cost of exact constrained maximum likelihood estimation, we develop an algebraic singular value decomposition (SVD) rank-reduction algorithm that enables linear-time parameter estimation and closed-form quadric classification. Evaluated on 35.2 km^2 of real-world aerial LiDAR data, GLFM automatically filters ground points and extracts morphological features, achieving an adjusted Rand index (ARI) of 0.9933 against field-verified ground truth and outperforming four leading baselines while maintaining an out-of-core memory footprint. The framework provides a rigorous, interpretable, and scalable foundation for large-scale point cloud analytics.

When data are grouped, hierarchical or multilevel models are commonly used to account for group-level variation with group-specific parameters. Leave-one-group-out cross-validation (LOGO-CV) is a suitable tool for evaluating predictive performance for new groups, providing an estimator of the expected log predictive density (elpd). Brute-force LOGO-CV requires one model refit per held-out group, often using computationally expensive inference algorithms such as MCMC. This is costly, particularly for large numbers of groups or complex model structures. Commonly used importance sampling approximations, intended to reduce this cost, tend to fail because the group-specific parameters of the held-out group must be integrated out. We identify two key challenges in LOGO-CV elpd estimation: approximating the LOGO posterior and computing the grouped marginal likelihood. We compare 11 strategies, including 5 newly proposed, to address them. Among others, we combine Pareto-smoothed importance sampling or adaptive importance sampling with integration techniques such as Laplace approximation, adaptive Gauss-Hermite quadrature, and bridge sampling. We evaluate these strategies in both simulation experiments and real-world case studies, which show that marginalising over the group-specific parameters substantially improves the reliability of the importance sampling approaches.

We study variance-preserving diffusion of the response in mixed linear regression (MLR) with unknown mixing weights. Our analysis separates the statistical guarantees of score matching from the loss geometry and optimization signal at a fixed diffusion noise level. The KL divergence links the denoising score matching objective integrated over the diffusion path with the likelihood and a terminal discrepancy. Under mild regularity conditions and terminal schedule, the resulting estimator converges up to the ground truth parameters of MLR, and its scaled error converges to the Gaussian limit of the maximum-likelihood estimator. At a fixed scale of the diffusion noise level, we derive a decomposition linking the score matching loss to cross-entropy and Expectation-Maximization (EM) operators. This decomposition yields an EM-related low-noise gradient expansion with additional correction terms of latent variance. In the high-noise limit, we further characterize gradient descent on this limiting loss under isotropic covariance. Along fixed high signal-to-noise ratio rays, the score matching imbalance gradient and the latent-variance term tend to zero pointwise. Numerical experiments illustrate our theoretical findings and statistical guarantees.

Single-cell RNA sequencing studies routinely use clustering to define putative cell types and cell states, yet the observed separation may arise from sampling variability rather than genuine biological heterogeneity. This paper studies formal significance testing of such clustering structure in high-dimensional data. Existing SigClust methods assess clustering significance through Monte Carlo simulation under a Gaussian single-cluster null, but this assumption can be unreliable for normalized gene expression data and other non-Gaussian settings. We propose SigClust-LCP, a nonparametric extension that models a single cluster by a log-concave distribution. To make this approach computationally feasible in moderate to high dimensions, we develop a score-matching estimator for log-concave projection inspired by recent generative modeling ideas. We establish theoretical guarantees for the estimator and for its use in clustering significance testing. Simulations show that SigClust-LCP controls Type-I error more reliably than existing methods across a range of unimodal and mixture distributions while retaining competitive power. In a single-cell RNA sequencing analysis of Hydra cells, the method avoids spurious subclusters within annotated cell populations and supports biologically meaningful separation across lineages and body-axis regions.

Edge selection in Gaussian graphical models is fundamentally a variable selection problem where pairwise relationships determine construct validity and variable importance in psychological networks. In psychology, network estimation relies predominantly on \(\ell_1\) regularization where uniform shrinkage systematically underestimates edge and centrality parameters. Alternative penalties overcome this bias but rely on fixed hyperparameters that do not adapt to the signal in the data. We develop a family of data-adaptive regularization penalties grounded in extreme value theory. Across 290 empirical psychological datasets, we show that absolute partial correlations are well-described by the Weibull distribution. Using this empirical regularity, we derive Weibull, Gumbel, and Exponential penalties that approximate \(\ell_0\) penalization and calibrate their hyperparameters to each dataset's noise floor. We formally prove the asymptotic properties of their static forms and conduct a large-scale simulation spanning two network topologies and various sample sizes (\(N\) = 100–10,000), demonstrating that their adaptive forms maintain high specificity while accumulating sensitivity as sample size increases with low parameter bias and high rank-order centrality congruence relative to field standards. Empirically, method choice alone determined centrality rankings at sample sizes typical in psychology. Of the three adaptive penalties, Weibull is recommended given the interpretability of its parameters.

Community detection is fundamental to understanding the modular organization in functional brain networks, yet noise in neuroimaging-derived networks and auxiliary node-level covariates pose critical challenges. Existing methods typically either assume networks are noise-free or ignore covariate information. We propose a Bayesian framework for recovering a shared latent community structure from multiple noisy network realizations and auxiliary covariates. The model combines a degree-corrected stochastic block model for the latent network, a block-structured noise model linking noisy observations to latent edges, and a covariate cluster model for node-level attributes. This specification allows anatomical or functional attributes of regions of interest to contribute information when network signals are weak or sparse. We develop an efficient Markov chain Monte Carlo algorithm for posterior sampling and select the number of communities using the widely applicable information criterion, avoiding prior specification of this quantity. Simulation studies demonstrate improved community recovery relative to existing methods across varying noise levels, covariate signal strengths, and numbers of noisy networks, with larger gains when network noise is moderate to high or only a small number of noisy networks is available. Applications to functional brain networks from the Alzheimer's Disease Neuroimaging Initiative and the Human Connectome Project identify biologically interpretable structures and capture disease-related reorganization and individual-level variation.

Estimating a low-dimensional subspace shared across noisy data matrices is a fundamental problem in multi-view matrix estimation. We study this problem under the two-view JIVE model, where each data matrix contains shared and view-specific low-rank components. We demonstrate that standard plug-in subspace intersection, including AJIVE, suffers from a second-order bias caused by direction-dependent leakage of the empirical singular vectors. We propose bias-corrected subspace intersection (BCSI), which removes this bias before estimating the shared subspace. We establish finite-sample risk bounds for BCSI that accommodate unequal view dimensions, signal strengths, and view-specific ranks and require no condition-number assumptions on the signal matrices. When the shared and view-specific ranks are comparable, these bounds match our minimax lower bounds up to universal constants. The resulting minimax rate contains a new second-order term, arising from quadratic leakage perturbations relative to the shrinking spectral gap when the view-specific subspaces are nearly aligned. This term is absent from previous JIVE minimax lower bounds. Numerical experiments demonstrate the advantage of BCSI over AJIVE when the leakage bias is pronounced. Along the way, we establish a nonasymptotic concentration result for the bias-corrected leakage Gram matrix of a rectangular spiked matrix, which may be of independent interest.

Every team sport that lets a team replace players rations the replacements, and the ration settles who plays and for how long. Across eight codes, three in both sexes, we measure how playing time is allocated and find one equation behind it, complete in the one-way codes, its terms separating what the rulebook fixes from what a competition chooses. Under scarcity every league behaves alike: loaded starters are kept on at the same rate on four continents. Under freedom each expresses a preference, and the size of a league's departure is priced near one-for-one by what its own withdrawal minute prices (lambda = 0.87, 95% interval 0.54 to 1.21, twelve leagues), a law confirmed in four out-of-sample predictions and refused in one. The ordering of leagues by appetite persists across a rule change, and club wealth does not price it. Rules are the geometry of a competition; culture is its material.

We study finite-sample valid tests of the one-sided mean hypothesis $H_0:\mu\leq 1$ against $H_1:\mu>1$ for nonnegative random variables. To do so, we develop a leave-one-out dual certificate framework, where certain pointwise inequalities imply p-value validity under the conditional mean null $\mathbb{E}[X_i\mid\mathbf{X}_{-i}]\leq 1$, and which also gives conditions that allow combining dual certificates for p-values to show that their pointwise minimum is also a valid p-value. The framework proves finite-sample validity of Wang and Zhao's nonparametric likelihood-ratio statistic $T_{\mathrm{nplr}}$, yields a new p-value $T_{\mathrm{bin}+}$ extending the Clopper–Pearson binomial test to general nonnegative random variables, and shows that the pointwise minimum $\min\{T_{\mathrm{nplr}},T_{\mathrm{bin}+}\}$ is itself a valid and more powerful p-value. We establish sharp optimality results for such testing problems in two regimes: both $T_{\mathrm{nplr}}$ and $T_{\mathrm{bin}+}$ attain a universal detectability boundary for the null $H_0$ without moment or tail assumptions, and $T_{\mathrm{bin}+}$ attains a nonparametric power lower bound under $n^{-1/2}$-local alternatives to $H_0$. Efficient algorithms and numerical experiments demonstrate substantial finite-sample power gains over existing valid methods.

Consider $n$ independent random vectors sampled from uniform distribution on $(p-1)$-dimensional unit sphere. This paper investigates the limiting joint distribution for the minimum and the maximum values of their pairwise angles. It proves that the minimum and the maximum angles are asymptotically independent when both $n$ and $p$ tend to infinity, which solves an open problem raised in Cai, Fan and Jiang (2013) [Journal of Machine Learning Research 14, 1837-1864]. Cai, Fan and Jiang (2013) obtained the limiting marginal distributions for both the minimum and the maximum angles under assumption $\lim_{n\to\infty}{\ln n}/p=\beta$ according to whether $\beta=0$, $\beta\in (0,\infty)$, or $\beta=\infty$. This paper presents unified limits for both joint distributions and marginal distributions regardless of the relative divergence rate of $n$ and $p$. The paper also derives the limiting distributions for some statistics based on the minimum and the maximum angles,

Bayesian pseudo-posteriors based on moment conditions, such as Bayesian empirical likelihood (EL) and Bayesian exponentially tilted empirical likelihood (ETEL), provide a robust route to Bayesian inference when the model is specified only through moment restrictions, but their computation is often prohibitive. In this work, we address two barriers to Bayesian pseudo-inference under moment restrictions. First, scalable sampling is challenging for tall data because the pseudo-likelihoods are not log-additive across observations, so standard likelihood-subsampling methods do not apply. Second, in simulation-based and latent-variable problems, the moment function itself may be defined through an intractable expectation, making full-data pseudo-posterior inference infeasible. We develop a new family of subsampled pseudo-posteriors that replaces the full-data pseudo-posterior with an aggregate of mini-batch pseudo-posteriors. We show that naive mini-batching induces a shifted-mixture distortion, yielding aggregates that are correctly centered but overly diffuse. To remove this distortion, we introduce moment-function-level control variates that align mini-batch moment equations around a reference estimator and recover the full-data posterior shape. For Bayesian ETEL, we establish finite-sample total variation bounds to the full-data pseudo-posterior, allowing discontinuous and intractable moment functions. Numerical experiments show that the method applies broadly across moment-condition-based Bayesian pseudo-inference, closely approximates full-data pseudo-posteriors, and substantially reduces computational cost.

Late Gadolinium Enhancement (LGE) on cardiac magnetic resonance is a key marker of myocardial scar, but its limited accessibility motivates routine ECG-based screening. We evaluated whether $\beta$-variational autoencoder (VAE)-derived ECG representations can discriminate LGE+ from LGE- cardiomyopathic patients in a local cohort of 300 subjects. We compared 32-dimensional features from the foundation ECGx.AI model with those from a shallower $\beta$-VAE trained on normal PTB-XL ECGs, evaluating downstream classification and Dynamic Time Warping (DTW)-based reconstruction errors. ECGx.AI reached an area under ROC of 0.686 with Random Forest, while the proposed $\beta$-VAE reached 0.577 with sensitivity of 0.775 with Gradient Boosting. Notably, DTW-reconstruction errors significantly differed between classes in 10 out of 12 leads according to Mann-Whitney U test and help in classification, leading to an area under ROC of 0.643 with Logistic Regression, supporting their potential as markers of scar-related ECG alterations.

Suppose that the eventual use of data is not known when the data are reduced or collected. This note considers two simple boundary cases. In a finite statistical experiment, a statistic preserves the Bayes risk for every finite later decision problem if and only if it is sufficient. Hence, when the minimal sufficient statistic is one-to-one, exact preservation of all later decision problems permits no nontrivial reduction. We then consider adaptive sampling from $m$ independent Gaussian streams when an external query specifies the coordinate to be classified only after sampling stops. Under coordinatewise error control, the optimal symmetric average sample size is exactly $m$ times the one-coordinate optimum. A change-of-measure argument gives the corresponding pointwise lower bound in terms of binary relative entropy.

We consider a rectangular random matrix formed by adding a rank-one term to a matrix with independent entries. The direction on the left side of that term is estimated by the leading left singular vector, and the error is multiplied by the square of the size of the added term. For entries with mean zero and variance one, we identify the exact tail condition for the following statement to hold for every deterministic sequence of directions: the largest error over all sizes of the added term converges to the same fixed value determined by the limiting ratio of rows to columns. This condition (weaker than the existence of fourth moments) requires that the tail probability, multiplied by the fourth power of the threshold, to tend to zero. If it fails, convergence to this value already fails when both directions are coordinate vectors, even at a size fixed before the matrix is drawn. For regularly varying tails of order between two and four, the largest error tends to infinity.

Long COVID is a condition usually defined by persisting symptoms following infection by the SARS-CoV-2 virus beyond the acute phase of infection. The condition has a significant impact on healthcare systems, the economy, and the individuals living with it. Due to the diverse and extensive symptomatology of long COVID, symptom co-occurrence tracking can be used to capture patient experiences and improve understanding, diagnosis, and management. Here, we leverage the UK Office for National Statistics (ONS) COVID-19 Infection Survey (CIS). The CIS was run between April 2020 and March 2023. On February 3, 2021, the ONS launched a new CIS question evaluating self-reported symptom persistence of 23 long COVID symptoms post self-reported COVID-19 infection. We use Jaccard symptom-by symptom distance matrices, derived from the binary survey responses of the presence of each symptom. Three methods are then used to visualise symptom co-occurrence: heatmaps, non-metric multidimensional scaling, and agglomerative hierarchical clustering with complete linkage. We split our analysis into two parts, first looking at all long COVID survey responses (n = 207,319) and then looking at responses stratified by time-since-onset of long COVID up to 24 months (n = 30,224 at zero months-since-onset). We find higher symptom co-occurrence in prolonged long COVID. We also find clusters of neurological/systemic symptoms, gastrointestinal symptoms, and respiratory symptoms, with separability in symptom co-occurrence by organ system becoming less pronounced as time-since-onset of long COVID increases. Shortness of breath, weakness/tiredness, and muscle ache present as core symptoms long COVID. We demonstrate that the symptom experience of long COVID evolves from early stages to late stages with higher symptom burden and multi-systemic presentation. We also find three possible phenotypes of early long COVID.

Forecasting time series accurately is critical for applications with complex data ranging from energy systems to healthcare and finance. Among current state of the art models, generative latent variable models are increasingly implemented; yet principled generalisation guarantees for modern latent variable models remain limited. In particular, while Variational AutoEncoders are widely used for sequential data, their theoretical analysis is largely restricted to i.i.d. settings. In this work, we develop a PAC-Bayesian framework for latent variables models applied to time series. Building on reconstruction-based bounds, we extend PAC-Bayesian guarantees to Markovian latent structures, capturing temporal dependencies through a sequential generative process. These guarantees do not grow with the length of the trajectory. Our bounds depend on assumptions which are common in the literature; we provide an example framework where they would be verified to show that they are not as restrictive as they may seem.

Dynamical symbolic regression methods identify governing differential equations from noisy data, balancing interpretability and predictive accuracy. However, standard methods often produce expressions that violate known physical laws. To address this, we propose FluxDisco, a physics-informed framework tailored for flux-based, stoichiometric ODE systems. By leveraging a known stoichiometry, we reduce the expression search space and ensure physical adherence. Our framework adapts the Monte Carlo Graph Search algorithm for the unique challenges associated with joint flux discovery of stoichiometric systems. We evaluate our method across a range of physical and biological systems, demonstrating its ability to accurately recover governing dynamics through interpretable equations.