Papers

Missing data is pervasive in many scientific domains such as public health, environmental science, and the social sciences. Recoverability from missing data is typically studied using fully specified variable-level missingness models despite that, in many applications, only coarse structural information is available, for instance when variables are grouped into clusters due to limited knowledge or interpretability reasons. In this paper, we investigate recoverability from such abstract representations. We introduce two classes of cluster-based missingness graphs: the m-C-DMG, which retains variable-specific missingness indicators, and the cm-C-DMG, which aggregates missingness mechanisms at the cluster level. We formalize the notion of compatibility between these abstract graphs and underlying variable-level missingness models, and study how this abstraction affects the recoverability of probabilistic and causal queries. In particular, we give graphical conditions of recovering the joint distribution as well as graphical conditions of recovering a macro causal effect. Overall, our results clarify when cluster-level missingness information is sufficient for valid inference, and when finer-grained modeling is necessary.

Communication is a major bottleneck in distributed learning, especially in large-scale settings and in federated learning environments with slow links. Three standard ways to reduce this cost are communication compression, local training, and communication-computation overlap. Methods that combine these ingredients are used in practice and have been found to be effective for large-scale training, but there is little theory for methods that combine all three. We study a heterogeneous-compute setting in which different workers may take different numbers of local steps, and we propose LOSCAR-SGD, a Local SGD method that communicates only a sparse subset of model coordinates and continues optimizing while communication is in flight. A key ingredient is a delay-corrected merge rule that incorporates delayed synchronized information without discarding the progress made during the overlap phase. We give convergence guarantees for smooth non-convex objectives and show how sparsity, overlap, and worker heterogeneity affect the rate. To the best of our knowledge, this is the first theory for this combination of ingredients. Experiments further show that communication-computation overlap reduces training time and that the delay-corrected merge outperforms naive overwriting.

We develop an adaptive jump test for discretely observed high-frequency semimartingales by combining the A"it-Sahalia–Jacod ratio statistic (A"it-Sahalia and Jacod, 2009) and the Lee–Mykland extreme-return statistic (Lee and Mykland, 2008) with the Cauchy combination rule. Allowing stochastic It^o drift, volatility, and leverage, we show asymptotic independence under the continuous-path null and dense local alternatives, yielding an analytically calibrated test with closed-form power; under finite-activity jumps, the test is consistent. We also extend the method to additive microstructure noise. Simulations show that the combined procedure performs well under both dense and sparse alternatives and is typically best overall.

The intersection set of Bayesian and nonparametric statistics was almost empty until about 1973, but now is growing at a healthy rate. This chapter, for the Highly Structured Stochastic Systems book (Oxford University Press, 2003) gives an overview of various theoretical and applied research themes inside this field, partly complementing and extending recent reviews of Dey, Müller and Sinha (1998) and Walker, Damien, Laud and Smith (1999). The intention is not to be complete or exhaustive, but rather to touch on research areas of interest, partly by example.

This paper proposes a novel, nonparametric, interpoint distance-based measure to investigate whether there exist any groups in a set of given data, and if so then, how many groups are prevailing in total. It is a cluster accuracy index useful for arbitrary-dimensional data set, in association with any clustering algorithm having the number of groups specified as a priori. We perform univariate, nonparametric, multiple statistical tests of hypotheses, where as many dependent tests as the sample size are carried out using the interpoint distances. They possess $p$-values to be combined to reach a decision, which is taken in a step-wise process for a possible number of clusters. It reduces the unnecessary computations compared with the other accuracy measures from the literature. Data study establishes the proposed index's efficiency and superiority.

Large language models (LLMs) show potential as simulators of human behavior, offering a scalable way to study responses to interventions. However, because LLMs are trained largely on observational data, interventions in experiments with LLM-simulated synthetic users can induce unintended shifts in latent user attributes, causing user drift where the implicit simulated population differs across treatment conditions, potentially distorting effect estimates. We formalize the confounding or selection bias that can arise due to user drift and show how intervention-dependent shifts can inflate or attenuate observed differences in user responses under intervention. To diagnose confounding, we propose using negative control outcomes–attributes that should remain invariant under intervention–to identify distribution shifts across intervention conditions, providing evidence of user drift. To mitigate drift, we study adjusting the persona specification by eliciting additional confounders, finding that targeted, setting-relevant confounders can substantially reduce bias across survey-style and multi-turn agent evaluations.

Preconditioned optimizers are central to language model training, but their stochastic update rules are usually treated as direct approximations to population preconditioned descent. We show that this view misses two finite-sample biases. First, the gradient and preconditioner are typically estimated from the same minibatch, introducing gradient–preconditioner coupling bias. Second, even when the preconditioner estimate is unbiased, its inverse or inverse-root is generally biased because inversion is nonlinear. We propose a single-batch bias-correction framework that addresses both effects: cross-fitted preconditioning estimates the numerator and preconditioner from independent microbatch groups, while variance-corrected inversion uses microbatch variability to subtract the leading delta-method bias term. The framework applies to diagonal moment, diagonal curvature, and matrix preconditioning methods, instantiated in AdamW, Sophia, and Shampoo. Bias correction reduces held-out pretraining loss on Qwen2.5-0.5B by $0.15$, $0.07$, and $0.11$ nats, respectively; the effects on mixed-quality pretraining and downstream instruction tuning are consistently neutral-to-positive. Together, these results establish bias correction as a practical mechanism for reducing finite-sample update bias and improving the performance of preconditioned optimizers.

Estimation under model misspecification arises in many signal processing problems, where the assumed observation model deviates from the true data-generating mechanism due to errors or simplifications. The misspecified Cramér-Rao bound (MCRB) is a widely recognized mean-squared-error (MSE) lower bound for this case, which has originally been used to describe the asymptotic behavior of the misspecified maximum likelihood (MML) estimator. Despite its widespread use, the MCRB lacks a rigorous characterization of the class of estimators for which it is valid. In this paper, we revisit the theory of parameter estimation under model misspecification and re-examine the foundations of the MCRB. We first demonstrate these limitations and examine a naive version of the MCRB, which relies only on local misspecified unbiasedness. We show that this bound is generally not tight and may be unattainable. To obtain a meaningful bound, we develop a new derivation based on the concept of pointwise equivalent models. By maximizing the naive bound for these models, we recover the classical MCRB, now supported by a constructive derivation, an explicit characterization of the associated estimator class, and an equality condition. This formulation establishes a formal link between local unbiasedness conditions and achievable bounds, offering new insights into the MCRB structure and its relevance to practical estimators. Finally, we define the notion of an efficient misspecified estimator and show that if it exists, it is achieved by the MML estimator.

Text-to-image models now generate graphic design at production scale, yet their supervision still comes primarily from photo-style preference datasets with a single overall verdict per comparison. Designers evaluate designs along several distinct axes (e.g., typography, layout, color harmony) that a single preference label collapses. We release TASTE (Typography, Aesthetics, Spatial, Tone, Etc.), a multi-dimensional preference dataset in which two disjoint cohorts of five professional designers each ranked outputs from four current text-to-image models across nine criteria along with per-image hallucination flags. We pair the dataset with two contributions. First, a criterion-agnostic signal-validation framework based on Kendall's $\tau$, majority-vote probability, and Condorcet cycles against exact iid-uniform nulls; the analysis reveals significant but moderate designer agreement, with every TASTE criterion rejecting the random-rater null. Second, we benchmark preference models on TASTE and find that off-the-shelf VLM judges and dedicated T2I scorers fail to reach majority agreement with the designer panel, while a small MLP head trained directly on TASTE substantially narrows the gap to the single-rater ceiling, setting a baseline for future TASTE-trained preference models.

Modern applications of conformal inference to multiple testing problems, such as outlier detection and candidate selection, often involve selecting test samples whose conformal p-values fall below a threshold. The quality of such methods is often measured by the false discovery proportion (FDP), defined as the fraction of incorrect selections. Existing approaches typically control the expected value of the FDP, using methods such as the Benjamini-Hochberg procedure. This approach fails to provide high-probability bounds on the realized false discovery proportion and invalidates statistical guarantees if the rejection threshold is selected after inspecting the data. This paper establishes finite-sample, distribution-free upper bounds on the FDP that hold simultaneously over all possible rejection thresholds, enabling arbitrary post hoc selection of the threshold. Simultaneous validity is achieved by constructing a high-probability envelope for the empirical distribution function of null conformal p-values by sampling from their joint distribution. Furthermore, our framework allows practitioners to modulate the envelope's shape, thereby producing tight bounds in rejection regions of primary interest. We use this flexible approach to derive simultaneous FDP upper bounds for both outlier detection and conformal selection. We demonstrate through synthetic and real-data experiments that the resulting bounds are both valid and substantially less conservative than those derived from existing approaches.

Random forests construct each tree with a different, randomised representation of the feature space. Their uniform voting cannot correct errors in regions where trees with incorrect representations probabilistically outnumber correct ones, even when the ensemble collectively holds enough correct information - a reducible error that this paper addresses. We propose using the structural pattern of each tree's decision path as an instance-adaptive reliability signal to identify and differentially weight the more reliable trees. At inference, a random forest reaches its prediction through the root-to-leaf path the sample traverses in each tree, so path-level reliability offers a finer granularity than tree-level weighting can access. We show that this signal reflects the actual reliability of each tree's decision, and that using it yields a statistically significant accuracy improvement over RF on 36 binary classification benchmarks (Wilcoxon p < 0.0001). Class-recall regression - the typical failure mode of RF correction methods - is measured: zero minority-recall regressions and a single majority-recall regression at the 0.2 pp threshold, indicating bias reduction rather than a class trade-off. We further quantify the reducible error accessible to the method from the fitted RF alone; this estimate correlates strongly with per-dataset gain (Pearson r = +0.840, p < 0.0001). On the qualifying group it identifies, the method delivers a mean +0.99 pp accuracy improvement with strict wins on every dataset (7/0/0); an optional amplification mechanism further raises this to +1.48 pp.

Conditional average treatment effects (CATEs) are increasingly estimated from observational data and used to guide policy and individualized treatment decisions. Before such estimates can be trusted in practice, their predictive fitness needs to be assessed, yet observational data alone offer limited opportunities for doing so. We propose CATE Assessment via Fitness Evaluation (CAFE), a formal framework for directly assessing the goodness-of-fit of a CATE estimate learned from observational data, rather than the full underlying outcome model, using evidence from a randomized trial. CAFE partitions the trial covariate space according to estimated propensity scores (or the like) and compares observationally derived conditional treatment effects with group-level experimental averages. The framework accommodates a broad class of CATE learners, including parametric models and flexible machine learning methods such as causal forest and boosting. We establish theoretical guarantees under both the null and alternative hypotheses, and introduce a maximum-type extension to improve sensitivity to localized lack of fit. When both randomized trial and observational data are available, we further develop a two-stage procedure to detect the existence of unobserved confounders. Extensive numerical studies show the utility of the CAFE approach when assessing observational-derived CATE estimates.

Interpretable text representations should expose coordinates that are not only predictive, but also meaningful enough for independent auditors to apply. Existing discriminative representations often use anonymous embedding directions, while concept-bottleneck and LLM-assisted methods attach natural-language names to features without ensuring that those definitions are reproducible or distinct from the target label. We propose an operational criterion for interpretable discriminative text representations: each coordinate should satisfy conceptual clarity, measured by chance-adjusted agreement between independent annotators applying the feature definition, and label disentanglement, meaning the feature should not merely paraphrase the prediction target. We instantiate this criterion in LLM-assisted Feature Discovery (LFD), an iterative method that proposes lexical and semantic features from contrastive outcome-opposed text pairs, screens candidates using cross-LLM Cohen's $\kappa$, and selects features by residual held-out predictive gain. A stylized analysis connects the $\kappa$ screen to a per-feature annotation-noise bound, formalizing agreement as a reliability check. Across ten text-classification tasks spanning seven corpora, LFD matches the predictive performance of a strong text bottleneck baseline while producing substantially clearer and less label-entangled features. Human audits with 232 raters show that LFD features achieve higher human–human and human–LLM agreement than baseline concepts, and raters consistently judge them as less label-leaking. These results suggest that agreement-tested, label-disentangled coordinates provide a practical auditability standard for interpretable text classification.

During an infectious disease outbreak, providing accurate answers to policy questions about transmission requires a detailed model of the natural history of infectiousness. Unfortunately, direct measures of infectiousness are generally unavailable. Instead, we often rely on indirect proxies, such as viral load measured by PCR or antigen tests, viral culture to detect replication-competent virus, or symptom onset, each of which reflects different aspects of viral dynamics or host response. However, these proxies vary in terms of the ease of collection, scalability, and their relationship to viral shedding and therefore underlying infectiousness. Here, we use data from five prospective, densely sampled cohorts with longitudinal data on multiple proxies of viral shedding for approximately 2,000 infections to develop a Bayesian joint model for the within-host viral kinetics of SARS-CoV-2 infection. Modeling the joint distribution allows us to infer the trajectory of infectious virus shedding – the most direct correlate of infectiousness – for individuals who contribute only PCR data, and to compute derived quantities that are inaccessible from any single proxy alone. These include the population-level probability and expected duration of ongoing infectiousness as a function of time since diagnosis, stratified by variant, vaccination status, and infection history; the residual risk of releasing an individual from isolation; and personalized, real-time estimates of infectiousness that are sequentially updated as new test results become available.

Distributed principal component analysis (PCA) produces node-level estimates of both a mean vector and a principal subspace. Robustly aggregating these heterogeneous objects requires a relative scale between mean error and subspace error. We study a scale-calibrated median-of-means estimator for this problem using the product geometry of Euclidean space and the Grassmann manifold. A node-level PCA expansion shows that the mean component has the usual linear influence, whereas the subspace component is an eigengap-weighted covariance perturbation. We prove a local reduction showing that the proposed product-manifold median-of-means estimator is asymptotically equivalent to a scaled spatial median of node influence errors. This yields fixed-node non-Gaussian limits, growing-node Gaussian limits with finite-block bias, and an explicit scale-dependent covariance formula. We propose robust block-scale and inference-optimal calibration rules, establish high-probability median-of-means bounds, characterize factorwise bad-node influence, and prove node-bootstrap validity. Simulations and large-scale single-cell RNA-seq data show that scale calibration adapts to eigengap-driven subspace uncertainty and provides a robust distributed PCA summary.

Thermal management is a major challenge in next-generation high-performance computing systems, particularly for heterogeneous multi-chip packages such as the NVIDIA GB200 Grace Blackwell Superchip. In this work, a physics-based computational framework is developed to optimize embedded cooling channel layouts for high-power multi-chip modules. The model couples steady-state heat conduction with a porous media-based representation of coolant transport, coupled with a row-wise coolant energy balance, to estimate chip temperature fields within microchannel networks. Unlike conventional designs, an interdigitated cooling architecture is parameterized using geometric variables, including channel count, width, and expansion over chip regions, enabling systematic design exploration. To enable efficient optimization, a surrogate-based approach is employed to approximate the relationship between geometric parameters and temperature metrics. The resulting model is optimized using a mixed-integer quadratic programming algorithm to minimize a weighted objective based on peak and average chip temperatures. To improve physical relevance, channel placement is further constrained to increase cooling coverage near GPU regions, where thermal loads are highest. The framework is applied to a representative multi-chip configuration based on NVIDIA GB200 architecture, consisting of two graphics processing units and one central processing unit. The results demonstrate that the optimal design reduces the peak chip temperature by 140.45{\deg}C and the average chip temperature by 35.87{\deg}C compared to the baseline configuration.

This paper proposes a general machine learning framework called the localization method, which is fundamentally built on two core concepts: localization kernels and local means – key components that underpin the self-attention mechanism. To establish a rigorous theoretical foundation, the framework is formally defined through two essential pillars: the formulation of the local(-ized) model and the localization trick. We systematically investigate the connections between the localization method and a wide range of existing machine learning models/methods, including (but not limited to) kernel methods, lazy learning, the MeanShift algorithm, relaxation labeling, Hopfield networks, local linear embedding (LLE), fuzzy inference, and denoising autoencoders (DAEs). By dissecting these relationships, we clarify the broader theoretical significance of the localization method and demonstrate its practical applicability across diverse machine learning tasks. Furthermore, we explore advanced extensions of the framework, such as adaptive kernels, hierarchical local models, and non-local models. Notably, we show that the Transformer – a cornerstone of modern sequence modeling – can be constructed using hierarchical local models, revealing the ability of the localization method to unify and generalize state-of-the-art architectures. This work not only provides a unified theoretical lens to reinterpret existing models but also offers new methodological tools for designing flexible, data-adaptive learning systems.

We develop joint confidence regions for linear regression coefficients when the regressors and errors are jointly stationary and ergodic with unspecified serial dependence. The method applies random smoothing, using an independent auxiliary sample and shrinking bandwidth, to a vector of regression and second-moment statistics. Under stationarity, ergodicity, and finite second moments, the estimator is asymptotically normal and yields Wald confidence regions and simultaneous confidence intervals without direct long-run variance estimation or a parametric dependence model. For implementation, we introduce a scaled estimator with data-driven bandwidth selection and a mild truncation that improves finite-sample stability. Simulations under ARMA, ARFIMA, copula-based Markov errors, and fractional Gaussian noise, with Gaussian and heavy-tailed margins, show near-nominal coverage and competitive region volumes relative to Newey-West HAC and MAC. A winter Beijing PM2.5 application illustrates the procedure. Keywords: Random smoothing, Joint inference, Confidence regions, Dependent errors, Long memory, Regression inference

Propensity score (PS) methods are widely used in observational studies to reduce confounding and estimate causal treatment effects. However, the validity of PS-based causal estimators depends heavily on correct model specification, and model misspecification may lead to substantial bias and instability. In this study, we systematically evaluate the performance of commonly used causal estimators, including response surface modeling (RSM), inverse probability weighting (IPW), and augmented inverse probability weighting (AIPW), under varying levels of PS and outcome model misspecification. We compare classical logistic regression with several machine learning approaches for PS estimation, including random forests (RF), support vector machines (SVM), and linear discriminant analysis (LDA). Extensive simulation studies were conducted under multiple scenarios defined by combinations of correctly specified and misspecified PS and outcome models, varying sample sizes, and different covariate correlation structures. Estimator performance was assessed using bias, absolute bias, root mean squared error, empirical standard error, and confidence interval width. Results demonstrate that AIPW consistently provides robust and stable estimates across most scenarios due to its doubly robust property, whereas IPW is highly sensitive to PS misspecification and unstable PS estimates produced by flexible machine learning methods. RSM performs well only when the outcome model is correctly specified. Real-world applications using the ACTG175 clinical trial and the Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset further illustrate the practical implications of estimator choice and PS modeling strategy. Overall, our findings highlight the importance of integrating flexible machine learning approaches within doubly robust frameworks to improve causal effect estimation in observational studies.

Changepoints are essential for homogenizing categorical time series and analyzing their trends and variations. The original total cloud cover in Canada was recorded hourly in tenths (or eighths), exhibiting inherent seasonality and serial correlation. Lu and Wang (2012) introduced an extended cumulative logit model to detect shifts in the annual frequencies of cloud cover conditions. While annual aggregation mitigates seasonality and serial correlation, it shortens the time series and may lead to overdispersion. This article introduces a marginalized transition model to detect a single changepoint in periodic and serially correlated categorical time series. The model captures serial dependence using a first-order Markov chain and enables category-specific changepoint specification. To enhance computational efficiency, we develop a new parameter estimation procedure for obtaining maximum likelihood estimates. A maximally selected likelihood ratio test statistic is then proposed to test for sudden changes in categorical time series, and the method is illustrated using daily total cloud cover observations recorded at 9 a.m. and 3 p.m. at Fort St. John Airport, British Columbia, Canada.

Scalarization is widely used in multi-objective optimization owing to its simplicity and scalability. In many applications, the goal is to generate solutions that represent diverse user preferences, ideally with uniform coverage of the Pareto front (PF). However, uniformly sampling scalarization weights usually induces non-uniform coverage of the PF. We explain this mismatch through the geometry of the scalarization path. As the weight varies, the corresponding solutions traverse the PF at a generally nonuniform speed. Integrating this speed gives cumulative arc length. After normalization by the total length, it defines a cumulative distribution function (CDF) on weights whose inverse selects points at equal arc-length intervals. Building on this insight, we propose SURF (Sampling Uniformly along the Pareto Front). For structured problems, including bi-objective bandits, we derive analytical expressions for this CDF map and the resulting PF-aware weight sampling rule. For general problems, SURF alternates between CDF reconstruction and weight sampling. Theoretically, we show that under provable conditions for bi-objective LS, SURF's CDF reconstruction error converges linearly to an $O(N^{-2})$ discretization floor. Empirically, experiments on bandits, multi-objective-gymnasium, and multi-objective LLM alignment demonstrate that SURF efficiently achieves more uniform PF coverage than baselines.

Causal mediation analysis is essential for disentangling the mechanisms by which investigational therapeutic and preventive agents impact clinical outcomes. However, the measurement of biological mediators is often subject to left-censoring by technical measurement limitations, most commonly an assay's limit of quantification. This form of censoring can pose severe challenges for both identification and estimation of causal mediation estimands, particularly when the censoring mechanism is deterministic and the resulting missingness is missing not at random (MNAR) or nonignorable. Motivated by the question of assessing the role of viral RNA in the action mechanism of monoclonal antibody therapies for COVID-19 in the Accelerating COVID-19 Therapeutics and Vaccine (ACTIV)-2 platform trial, we develop a semi-parametric framework for estimation of the natural direct and indirect effects when the mediator of interest is partially subject to this form of left-censoring. Our proposed strategy combines fractional imputation with a semi-parametric EM algorithm to flexibly estimate key components of the factorized data likelihood. Applying the proposed strategy to circumvent the left-censoring, we discuss both traditional plug-in and asymptotically efficient estimators of the direct and indirect effect estimands, introducing a data-adaptive $m$-out-of-$n$ bootstrap for robust inference under the imputation procedure. We demonstrate in numerical experiments that our approach significantly reduces bias and allows for reliable inference. An application to data from the ACTIV-2 platform trial confirms that monoclonal antibody therapies reduce the risk of hospitalization and death due to COVID-19, while suggesting that changes in viral RNA mediate only a modest proportion of the overall treatment effect.

Many functional datasets are observed sparsely and irregularly. Ordering such data is challenging because only limited information is available from each observation, while the underlying trajectories remain infinite-dimensional. This paper develops a novel depth notion for sparse functional data, called the conditional regularized halfspace depth (CRHD). CRHD is defined as the infimum of conditional halfspace probabilities of the underlying trajectory given the observed sparse measurements, thereby enabling depth evaluation directly at sparse observations without requiring trajectory reconstruction. We study several basic theoretical properties of CRHD that clarify its behavior as a depth measure. The proposed depth is applicable even to extremely sparsely observed functional data, overcoming key limitations of existing sparse functional depths that often rely on reconstructed curves. In addition, CRHD induces meaningful rankings for complex functional data. Its numerical performance is demonstrated through rank-based tests, and its practical utility is illustrated using an infant growth dataset.

We study design-unbiased estimation of the finite-population total $\sum_{i=1}^N y_i$ when each outcome satisfies known bounds $y_i\in[a_i,b_i]$. For any sampling design with inclusion probabilities $\pi_i>0$, we prove a sharp lower bound on the worst-case squared error over the rectangular parameter space. This bound is attained if and only if the unit inclusion indicators are pairwise independent, in which case the minimax estimator is the midpoint-differenced Horvitz-Thompson estimator $\sum_{i=1}^N m_i+\sum_{i\in S}(y_i-m_i)/\pi_i$, with $m_i=(a_i+b_i)/{2}$. We then solve the joint design-and-estimation problem under the constraint $\sum_i \pi_i\le n$. We find that a minimax strategy samples units independently with probabilities $\pi_i^\ast=\min(1,c (b_i-a_i))$ where $c>0$ is chosen so that $\sum_i \pi_i^\ast=n$, and uses the midpoint-differenced estimator. This extends Gabler (1990)'s linear minimax result to the full class of design-unbiased estimators. We also show that the estimator is admissible among unbiased estimators and affine equivariant.

Remote sensing techniques have been increasingly utilised in aquatic applications in recent years. A common challenge in using optical satellite data is the presence of missing observations due to cloud cover. These data gaps can lead to missed detection of critical events, such as algal blooms, in lakes of high interest to water authorities. As a result, enhancing the completeness of optical satellite datasets is crucial for improving the monitoring and prediction of algal blooms. In this study, we compared a traditional data imputation method (i.e., linear interpolation) with deep learning models for reconstructing missing spectral bands across four lakes with historical records of algal blooms. The deep learning models adopted include CNN-based architectures (i.e., CNN, Inception Resnet, and Autoencoder) and CNN-LSTM-based architectures (i.e., CNN-LSTM, Resnet-LSTM, and Autoencoder-LSTM). Our results demonstrated that deep learning models substantially outperformed the baseline linear interpolation method in imputing spectral band values within artificially masked regions. Among these models, CNN delivered the best performance across most lakes. Furthermore, we evaluated the performance of algal bloom indices (i.e., Green/Red and NDCI) derived from the imputed imagery by comparing them with the observed data. Our results demonstrate that deep learning models are effective for imputing missing data in PlanetScope SuperDove imagery, enabling more reliable applications in water monitoring.

We introduce Pairwise Distance-Diffusion Analysis (PDDA), a geometric framework that connects the Hurst exponent to the scaling of pairwise distances in long-memory stochastic processes. From a single distance-plot representation, PDDA yields three complementary routes to persistence: R/S-PDDA, based on the growth of geometric extrema; MSD-PDDA, based on the scaling of the second moment of lagged distances; and recurrence-volume scaling, in which the decay of close returns with increasing temporal separation reflects the expansion of the lagged displacement cloud. The framework extends naturally to multivariate isotropic and anisotropic processes, where the local spatial dimension specifies the available degrees of freedom while the Hurst exponents govern their temporal expansion. These results establish the distance plot as a common geometric representation of persistence, providing a unified distance-based foundation for Hurst analysis.

Protein-protein interactions (PPIs) govern nearly all cellular processes, yet computational methods for identifying binding partners typically produce ranked predictions without mechanistic justification. This creates a fundamental barrier to adoption because biologists cannot assess whether predictions reflect genuine biochemical insight or spurious correlations. We present Protein Thoughts, a framework that reformulates PPI discovery as an interpretable search problem with explicit reasoning. The system decomposes binding evidence into four biologically meaningful signals: sequence similarity reflecting evolutionary relationships, structural complementarity capturing geometric fit, interface balance, and chemical compatibility encoding residue-level interactions. Rather than collapsing these signals into an opaque score, we preserve their individual contributions through a transparent value function that enables both ranking and auditing. To navigate large candidate spaces efficiently, we introduce hypothesis-guided entropy-regularized Tree-of-Thoughts search. A fine-tuned language model generates search directives from embedding-derived features, classifying candidates as high-priority, exploratory, or skippable. These directives condition a Boltzmann policy that balances exploitation with entropy-driven exploration, while hypothesis-aware pruning prevents premature abandonment of promising candidates. For candidates exhibiting score disagreement, hypothesis-conditioned embedding-space flow matching transports protein embeddings toward the binder manifold. On the SHS148k benchmark, Protein Thoughts achieves mean best-binder rank of 11.2 versus 47.7 for an entropic tree search baseline, a 76% improvement, and for binding prediction the trained value function achieves $91.08 \pm 0.19$ Micro-F1, outperforming existing PPI methods on the same dataset.

Background: Often when undertaking meta-analyses of time-to-event (TTE) outcomes, especially in a Health Technology Assessment context, a hazard ratio (HR) scale is used. However, issues arise when there is evidence of non-proportional hazards in some of the studies included. A number of methods have been advocated, but their use has been limited by either their complexity and/or the ease with which their results can be used in HTA. An alternative approach is to assume a treatment-log(time) interaction within a Cox proportional hazards model for each study, and to then undertake a bivariate meta-analysis of the resulting treatment and interaction coefficients, so that an overall time-varying HR (TVHR) can be obtained. Methods: A TVHR approach was applied to a meta-analysis of chemotherapy compared to Standard of Care for advanced recurrent gastric cancer, and in which Progression-Free Survival (PFS) was an outcome. The approach was also applied to a network meta-analysis (NMA) evaluating overall survival (OS) in advanced BRAF-mutated melanoma. Results: Five trials in the advanced gastric cancer meta-analysis displayed evidence of non-proportional hazards for PFS. Using a TVHR model produced HRs ranging from 0.83 (CrI:0.75-0.91) at 0.5 years to 0.99 (CrI:0.79-1.23) at 3.5 years. Three studies showed evidence of non-proportional hazards in the advanced BRAF-mutated melanoma NMA for OS. Using a TVHR model, nivolumab plus ipilimumab demonstrated consistent superiority from month 7 onwards, with a HR improving from 0.37 (CrI:0.26-0.51) at one year to 0.24 (CrI:0.12-0.45) at five years. Conclusions: A TVHR approach to the meta-analysis or NMA of TTE outcomes when the proportional hazards assumption appears not to hold, produces an intuitive solution which can be readily used in HTA.

Modern matrix completion problems often involve heterogeneous data whose rows simultaneously belong to many meta-categories, such as demographic and age groups in recommendation systems, or region and recording session labels in neural electrophysiological experiments. Standard low-rank estimators impose a single global latent geometry, which can recover average structure but may smooth away subgroup-specific variation, especially when observations are unevenly distributed across groups. We introduce Group-Aware Matrix Estimation (GAME), a convex estimator for overlapping subgroup-wise low-rank matrix estimation. GAME regularizes category-specific submatrices through overlapping nuclear-norm penalties, allowing related groups to borrow information while preserving local latent structure in a shared coordinate system. We provide finite-sample guarantees for both reconstruction error and subgroup-specific subspace recovery, showing how performance depends on sampling density, subgroup rank, and overlap structure. Experiments on synthetic, recommendation, ecological, and neuroscience datasets show that GAME is most beneficial in structured missingness regimes, where subgroup-aware regularization improves both reconstruction accuracy and latent subspace fidelity. Across these benchmarks, GAME is competitive or best among global low-rank, side-information, and modern imputation baselines, with the largest gains when subgroups exhibit distinct low-rank structure.

Smooth functions on graphs have wide applications in manifold and semi-supervised learning. In this paper, we study a bandit problem where the payoffs of arms are smooth on a graph. This framework is suitable for solving online learning problems that involve graphs, such as content-based recommendation. In this problem, each recommended item is a node and its expected rating is similar to its neighbors. The goal is to recommend items that have high expected ratings. We aim for the algorithms where the cumulative regret would not scale poorly with the number of nodes. In particular, we introduce the notion of an effective dimension, which is small in real-world graphs, and propose two algorithms for solving our problem that scale linearly in this dimension. Our experiments on real-world content recommendation problem show that a good estimator of user preferences for thousands of items can be learned from just tens nodes evaluations.