Papers

We study whether otherwise-idle inference resources could reduce the scarce-GPU cost of training. Our analysis uses a simulated compute ledger in which fleet work is billed at a fraction of a scarce-GPU forward; all experiments run on a regular GPU. Our algorithm predicts gradients with a reduced-precision, inference-style reverse-mode program and combines many predictions with a few exact gradients through a control variate, so approximation error becomes variance rather than bias. On a 124M-parameter language model and selected short training windows, the method can lower simulated ledger cost relative to the tested baselines when fleet work is sufficiently cheap. Experiments spanning 10M-774M parameters show both transfers and failures. We do not test inference-only hardware, end-to-end distributed latency, or a full optimizer-by-batch-size baseline sweep.

Convex clustering is a well-regarded clustering method, resembling the similar centroid-based approach of Lloyd's $k$-means, without requiring a predefined cluster count. It starts with each data point as its centroid and iteratively merges them. Despite its advantages, this method can fail when dealing with data exhibiting linearly non-separable or non-convex structures. To mitigate the limitations, we propose a kernelized extension of the convex clustering method. This approach projects the data points into a Reproducing Kernel Hilbert Space (RKHS) using a feature map, enabling convex clustering in this transformed space. This kernelization not only allows for better handling of complex data distributions but also produces an embedding in a finite-dimensional vector space. We provide a comprehensive theoretical underpinning for our kernelized approach, proving algorithmic convergence and establishing finite sample bounds for our estimates. The effectiveness of our method is demonstrated through extensive experiments on both synthetic and real-world datasets, showing superior performance compared to state-of-the-art clustering techniques. This work marks a significant advancement in the field, offering an effective solution for clustering in non-linear and non-convex data scenarios.

We provide a unified approach to MM-estimation with auxiliary scale for balanced linear models with structured covariance matrices. This approach leads to estimators that are highly robust against outliers and highly efficient for normal data. These properties not only hold for estimators of the regression parameter, but also for estimators of scale invariant transformations of the variance parameters. Of main interest are MM-estimators for linear mixed effects models, but our approach also includes MM-estimators in several other standard multivariate models. We provide sufficient conditions for the existence of MM-functionals and MM-estimators, establish asymptotic properties such as consistency and asymptotic normality, and derive their robustness properties in terms of breakdown point and influence function. All the results are obtained for general identifiable covariance structures and are established under mild conditions on the distribution of the observations, which goes far beyond models with elliptically contoured densities.

Every year, over one million EU students choose a secondary school track based on teacher recommendations, yet little evidence shows this yields optimal assignments. Using Dutch data, we examine whether access to standardized test scores improves recommendation quality. We develop a Principal-Stratification metric in a quasi-randomized setting, conduct a welfare analysis that flexibly weights short- and long-term losses, and assess principal fairness by examining whether test-score access affects equity across protected attributes. Results are robust to replacing the Exclusion Restriction assumption underlying our main identification strategy with alternative assumptions. Allowing recommendation upgrades when test scores exceed expectations increases successful placement in more demanding tracks by at least 6%, while misplacing 7% of weaker students. Only unrealistically high weights on short-term losses would justify banning such upgrades. Test-score access also yields fairer recommendations for immigrant and low-SES students. Our methodology and findings contribute to the literature on algorithm-assisted human decisions.

This paper introduces a spatiotemporal exponential generalised autoregressive conditional heteroscedasticity (spatiotemporal E-GARCH) model, extending traditional spatiotemporal GARCH models by incorporating asymmetric volatility spillovers, while also generalising the time-series E-GARCH model to a spatiotemporal setting with instantaneous, potentially asymmetric volatility spillovers across space. The model allows for both temporal and spatial dependencies in volatility dynamics, capturing how financial shocks propagate across time, space, and network structures. We establish the theoretical properties of the model, deriving stationarity conditions and moment existence results. For estimation, we propose a quasi-maximum likelihood (QML) estimator and assess its finite-sample performance through Monte Carlo simulations. Empirically, we apply the model to financial networks, specifically analysing volatility spillovers in stock markets. We compare different network structures and analyse asymmetric effects in instantaneous volatility interactions.

Statistical inference on histograms and frequency counts plays a central role in categorical data analysis. Moving beyond classical methods that directly analyze labeled frequencies, we introduce a framework that models the multiset of unlabeled histograms via a mixture distribution to better capture unseen domain elements in large-alphabet regime. We study the nonparametric maximum likelihood estimator (NPMLE) under this framework, and establish its optimal convergence rate under the Poisson setting. The NPMLE also immediately yields flexible and efficient plug-in estimators for functional estimation problems, where a localized variant further achieves the optimal sample complexity for a wide range of symmetric functionals. Extensive experiments on synthetic, real-world datasets, and large language models highlight the practical benefits of the proposed method.

The quantification of the interannual component of variability in climatological time series is essential for the assessment and prediction of the El Niño - Southern Oscillation phenomenon. This is achieved by estimating the deviation of a climate variable (e.g., temperature, pressure, precipitation, or wind strength) from its normal conditions, defined by its baseline level and seasonal patterns. Climate normals are currently estimated by simple arithmetic averages calculated over the most recent 30-year period ending in a year divisible by 10. The suitability of the standard methodology has been questioned in the context of a changing climate, characterized by nonstationary conditions. The literature has focused on the choice of the bandwidth and the ability to account for trends induced by climate change. The paper contributes to the literature by proposing a regularized real time filter based on local trigonometric regression, optimizing the estimation bias-variance trade-off in the presence of climate change, and by introducing a class of seasonal kernels enhancing the localization of the estimates of climate normals. Application to sea surface temperature series in the Niño 3.4 region and zonal and trade winds strength in the equatorial and tropical Pacific region, illustrates the relevance of our proposal.

In this study, a scalable online kernel learning framework is proposed for estimating bidirectional causal effects in systems characterized by mutual dependence and heteroskedasticity. Traditional causal inference often focuses on unidirectional effects, overlooking the common bidirectional relationships in real-world phenomena. Building on heteroskedasticity-based identification, the proposed method integrates a quasi-maximum likelihood estimator for simultaneous equation models with large scale online kernel learning. It employs random Fourier feature approximations to flexibly model nonlinear conditional means and variances, while an adaptive online gradient descent algorithm ensures computational efficiency for streaming and high-dimensional data. Results from extensive simulations demonstrate that the proposed method achieves superior accuracy and stability than single equation and polynomial approximation baselines, exhibiting lower bias and root mean squared error across various data-generating processes. These results confirm that the proposed approach effectively captures complex bidirectional causal effects with near-linear computational scaling. By combining econometric identification with modern machine learning techniques, the proposed framework offers a practical, scalable, and theoretically grounded solution for large scale causal inference in natural/social science, policy making, business, and industrial applications.

By amalgamating data from disparate sources, the resulting integrated dataset becomes a valuable resource for statistical analysis. In probabilistic record linkage, the effectiveness of such integration relies on the availability of linkage variables free from errors. Where this is lacking, the linked data set would suffer from linkage errors and the resultant analyses, linkage bias. This paper proposes a methodology leveraging the bootstrap technique to devise linkage bias-corrected estimators. Additionally, it introduces a test to assess whether increasing the number of bootstrap iterations meaningfully reduces linkage bias or merely inflates variance without further improving accuracy. An application of these methodologies is demonstrated through the analysis of a simulated dataset featuring hormone information, along with a dataset obtained from linking two data sets from the Australian Bureau of Statistics' labour mobility surveys.

This study presents a comprehensive framework for uncertainty quantification (UQ) and design optimization of plasma etching in semiconductor manufacturing. The framework is demonstrated using experimental measurements of etched depth collected at nine wafer locations under various plasma conditions. A heteroscedastic Gaussian process (hetGP) surrogate model is employed to capture the complex uncertainty structure in the data, enabling distinct quantification of (a) spatial variability across the wafer and (b) process-related uncertainty arising from variations in chamber pressure, gas flow rate, and RF power. Epistemic uncertainty due to sparse data is further quantified and incorporated into a reliability-based design optimization (RBDO) scheme. The proposed method identifies optimal process parameters that minimize spatial variability of etch depth while maintaining reliability under both aleatory and epistemic uncertainties. The results demonstrate that this framework effectively integrates data-driven surrogate modeling with robust optimization, enhancing predictive accuracy and process reliability. Moreover, the proposed approach is generalizable to other semiconductor processes, such as photolithography, where performance is highly sensitive to multifaceted uncertainties.

The ROC-SVM, originally proposed by Rakotomamonjy, directly maximizes the area under the ROC curve (AUC) and has become an attractive alternative of the conventional binary classification under the presence of class imbalance. However, its practical use is limited by high computational cost, as training involves evaluating all $O(n^2)$. To overcome this limitation, we develop a scalable variant of the ROC-SVM that leverages incomplete U-statistics, thereby substantially reducing computational complexity. We further extend the framework to nonlinear classification through a low-rank kernel approximation, enabling efficient training in reproducing kernel Hilbert spaces. Theoretical analysis establishes an error bound that justifies the proposed approximation, and empirical results on both synthetic and real datasets demonstrate that the proposed method achieves comparable AUC performance to the original ROC-SVM with drastically reduced training time.

We consider the discrete-time filtering problem in scenarios where the observation noise is degenerate or low. More precisely, one is given access to a discrete time observation sequence which at any time $k$ depends only on the state of an unobserved Markov chain. We specifically assume that the functional relationship between observations and hidden Markov chain has either degenerate or low noise. In this article, under suitable assumptions, we derive the filtering density and its recursions for this class of problems on a specific sequence of manifolds defined through the observation function. We then design sequential Markov chain Monte Carlo methods to approximate the filter serially in time. For a certain linear observation model, we show that using sequential Markov chain Monte Carlo for low noise will converge as the noise disappears to that of using sequential Markov chain Monte Carlo for degenerate noise. We illustrate the performance of our methodology on several challenging stochastic models arising in statistics and applied mathematics.

An enhancement in seismic measuring instrumentation has been proven to have implications in the quantity of observed earthquakes, since denser networks usually allow recording more events. However, phenomena such as strong earthquakes or even aseismic transients, as slow slip earthquakes, may alter the occurrence of earthquakes. In the field of seismology, it is a standard practice to model background seismicity as a Poisson process. Based on this idea, this work proposes a model that can incorporate the evolving spatial intensity of Poisson processes over time (i.e., we include temporal changes in the background seismicity when modeling). In recent years, novel methodologies have been developed for quantifying the uncertainty in the estimation of the background seismicity in homogeneous cases using Bayesian non-parametric techniques. This work proposes a novel methodology based on graphical Dirichlet processes for incorporating spatial and temporal inhomogeneities in background seismicity. The proposed model in this work is applied to study the seismicity in the southern Mexico, using recorded data from 2000 to 2015.

As predictive algorithms grow in popularity, using the same dataset to both train and test a new model has become routine across research, policy, and industry. Sample-splitting attains valid inference on model properties by using separate subsamples to estimate the model and to evaluate it. However, this approach has two drawbacks, since each task uses only part of the data, and different splits can lead to widely different estimates. Averaging across multiple splits, I develop an inference approach that uses more data for training, uses the entire sample for testing, and improves reproducibility. I address the statistical dependence from reusing observations across splits by proving a new central limit theorem for a large class of split-sample estimators under arguably mild and general conditions. Importantly, I make no restrictions on model complexity or convergence rates. I show that confidence intervals based on the normal approximation are valid for many applications, but may undercover in important cases of interest, such as comparing the performance between two models. I develop a new inference approach for such cases, explicitly accounting for the dependence across splits. Moreover, I provide a measure of reproducibility for p-values obtained from split-sample estimators. Finally, I apply my results to two important problems in development and public economics: predicting poverty and learning heterogeneous treatment effects in randomized experiments. I show that my inference approach with repeated cross-fitting achieves better power than existing alternatives, often enough to reveal statistical significance that would otherwise be missed.

Multicalibration [HJKRR18] is an algorithmic fairness perspective that demands that the predictions of a predictor are correct conditional on themselves and membership in a collection of potentially overlapping subgroups of a population. The work of [NR23] established a surprising connection between multicalibration for an arbitrary property $\Gamma$ (e.g., mean or median) and property elicitation: a property $\Gamma$ can be multicalibrated if and only if it is elicitable, where elicitability is the notion that the true property value of a distribution can be obtained by solving a regression problem over the distribution. In the online setting, [NR23] proposed an inefficient algorithm that achieves $\sqrt T$ $\ell_2$-multicalibration error for a hypothesis class of group membership functions and an elicitable property $\Gamma$, after $T$ rounds of interaction between a forecaster and adversary. In this paper, we generalize multicalibration for an elicitable property $\Gamma$ from group membership functions to arbitrary bounded hypothesis classes and introduce a stronger notion – swap multicalibration, following [GKR23]. Subsequently, we propose an oracle-efficient algorithm which, when given access to an online agnostic learner, achieves $T^{1/(r+1)}$ $\ell_r$-swap multicalibration error with high probability (for $r\ge2$) for a hypothesis class with bounded sequential Rademacher complexity and an elicitable property $\Gamma$. For the special case of $r=2$, this implies an oracle-efficient algorithm that achieves $T^{1/3}$ $\ell_2$-swap multicalibration error, which significantly improves on the previously established bounds for the problem [NR23, GMS25, LSS25a], and completely resolves an open question raised in [GJRR24] on the possibility of an oracle-efficient algorithm that achieves $\sqrt{T}$ $\ell_2$-mean multicalibration error by answering it in a strongly affirmative sense.

The problem of optimal estimation of linear functionals constructed from unobserved values of stochastic sequence with periodically stationary increments based on observations of the sequence with a periodically stationary noise is considered. For sequences with known spectral densities, we obtain formulas for calculating values of the mean square errors and the spectral characteristics of the optimal estimates of the functionals. Formulas that determine the least favorable spectral densities and minimax (robust) spectral characteristics of the optimal linear estimates of functionals are proposed in the case where spectral densities of the sequence are not exactly known while some sets of admissible spectral densities are given.

Efficacy testing is a cornerstone of clinical trials, ensuring that medical interventions achieve their intended therapeutic effects. Over the decades, a wide range of statistical methodologies have been developed to address the complexities of clinical trial data, including parametric, nonparametric, Bayesian, and machine learning approaches. Parametric methods, such as t-tests, ANOVA, and LMMs, have traditionally been the foundation of efficacy testing due to their efficiency under well-defined assumptions. Nonparametric techniques, including the Friedman test, Brunner-Munzel test, and modern extensions like nparLD, have emerged as robust alternatives, particularly for skewed, ordinal, or non-normal data. Bayesian methodologies have enabled the incorporation of prior information and uncertainty quantification, while machine learning techniques, such as deep learning and reinforcement learning, are revolutionizing trial designs and outcome predictions. Despite these advancements, significant gaps remain, including challenges in handling high-dimensional data, missingness, and ensuring equitable efficacy testing across diverse populations. This review provides a comprehensive overview of these statistical methods, highlighting their applications, strengths, limitations, and future directions. By bridging traditional statistical frameworks with modern computational techniques, the field can continue to advance toward more reliable and personalized clinical trial methodologies.

Modern sensing technologies have enabled the collection of unstructured point cloud data (PCD) of varying sizes, which are used to monitor the geometric accuracy of 3D objects. PCD are widely applied in advanced manufacturing processes, including additive, subtractive, and hybrid manufacturing. To ensure the consistency of analysis and avoid false alarms, preprocessing steps such as registration and mesh reconstruction are commonly applied prior to monitoring. However, these steps are error-prone, time-consuming and may introduce artifacts, potentially affecting monitoring outcomes. In this paper, we present a novel registration-free approach for monitoring PCD of complex shapes, eliminating the need for both registration and mesh reconstruction. Our proposal consists of two alternative feature learning methods and a common monitoring scheme designed to handle hundreds of features. Feature learning methods leverage intrinsic geometric properties of the shape, captured via the Laplacian and geodesic distances. In the monitoring scheme, thresholding techniques are used to further select intrinsic features most indicative of potential out-of-control conditions. Numerical experiments and case studies highlight the effectiveness of the proposed approach in identifying different types of defects.

We study worst-case dynamic regret of specific multi-armed bandit algorithms on piecewise-stationary instances with at most one breakpoint. Our constructions exploit belief inertia: observations collected before a change can make an algorithm slow to revise the empirical ordering on which its decisions are based. We first illustrate this mechanism for Explore-Then-Commit, $\epsilon$-greedy, and UCB, for which deterministic one-breakpoint instances can produce linear regret. Our principal result concerns standard sliding-window UCB (SW-UCB), which was designed to forget outdated observations. For every $K\geq 2$ and every window $K\leq\tau\leq T$, we prove the finite gap-free lower bound $\frac{1}{20}\min\{T,(K\ln T)^{1/3}T^{2/3}\}$ on its worst-case regret. The proof combines two deterministic obstructions: a stationary small-gap instance that makes repeated forgetting costly, and a one-breakpoint instance that creates a strict post-change index lock. This yields an algorithmic separation. The class with at most one breakpoint admits regret $O(\sqrt{KT\ln(KT)})$, whereas SW-UCB necessarily incurs $\Omega((K\ln T)^{1/3}T^{2/3})$ until the linear cap becomes active, regardless of how its window is tuned. Thus, with respect to the horizon, the class admits essentially $T^{1/2}$ regret while SW-UCB necessarily incurs $T^{2/3}$ regret. This shows that the $T^{2/3}$ behavior appearing in gap-free analyses of forgetting policies is not merely an artifact of an upper-bound proof for SW-UCB. The comparison does not resolve the different dependence on $K$ or the logarithmic factors. All constants are explicit, and the SW-UCB proof permits arbitrary non-anticipating randomized tie-breaking.

We develop a symmetry-aware toolkit for finite mixtures whose components are only identifiable up to a finite folding group action. The correct estimand is the multiset of parameter orbits in the quotient space, not an ordered list of raw parameters. We design invariant tensor summaries via the Reynolds projector, show that mixtures become convex combinations in a low-dimensional invariant feature space, and prove identifiability, stability, and asymptotic normality on the quotient. Our loss is a Hausdorff distance on orbit multisets; we prove it coincides with a bottleneck assignment metric and is thus computable in polynomial time. We give finite-sample Hausdorff bounds, a two-step efficient GMM formulation, consistent selection of the number of components, robustness to contamination, and minimax lower bounds that certify Poly-LAN rates $n^{-1/D}$ when the first nonzero invariant curvature appears at order $D$. The framework is illustrated for the hyperoctahedral group (signed permutations) and dihedral symmetries in the plane.

Prototype selection methods compress a training set, but the existing taxonomy of condensation, edition, hybrid, competence-based, optimization-based, and clustering-based families does not include methods that operate on the multi-scale topological structure of the data. This paper introduces two different persistence-based prototype selector variants, Topological Prototype Selector (TPS) and Boundary-Conscious Topological Prototype Selector (BoundaryTPS). TPS uses two sequential Rips filtrations to retain boundary-relevant and interior-typical points. BoundaryTPS is a single-stage variant whose vertex-weighted filtration concentrates retention near the decision boundary. We evaluate both methods against seven classical baselines on fifteen real datasets and find that the topological methods occupy a different operating point in the prototype-selection design space than existing methods. BoundaryTPS achieves the lowest mean Friedman rank on $H_1$ persistence-diagram preservation and is significantly better than five of the seven baselines (Nemenyi, $\alpha = 0.05$). TPS ranks third on the same endpoint. Both methods are more stable under fold perturbation than any chained-decision selector tested, and both inherit the source set's class proportions without label-aware machinery. On aggregate G-Mean both methods are competitive but not leading, with rank-1 frequencies of $11.3\%$ (TPS) and $9.9\%$ (BoundaryTPS) across fold combinations. Empirically, both methods scale sub-quadratically in sample size.

Diffusion-weighted magnetic resonance imaging (DW-MRI) derived scalar maps are effective for assessing neurodegenerative diseases and microstructural properties of white matter in large number of brain conditions. However, DW-MRI inherently limits the combination of data from multiple acquisition sites without harmonization to mitigate scanner-specific biases. While the widely used ComBAT method reduces site effects in research, its reliance on linear covariate relationships, homogeneous populations, fixed site numbers, and well populated sites constrains its clinical use. To overcome these limitations, we propose Clinical-ComBAT, a method designed for real-world clinical scenarios. Clinical-ComBAT harmonizes each site independently, enabling flexibility as new data and clinics are introduced. It incorporates a non-linear polynomial data model, site-specific harmonization referenced to a normative site, and variance priors adaptable to small cohorts. It further includes hyperparameter tuning and a goodness-of-fit metric for harmonization assessment. We demonstrate its effectiveness on simulated and real data, showing improved alignment of diffusion metrics and enhanced applicability for normative modeling.

We extend a theorem of Maa, Pearl, and Bartoszynski, which links equality of interpoint distance distributions to equality of underlying multivariate distributions, beyond the restrictive class of homogeneous, translation-invariant distance functions. Our approach replaces geometric assumptions on the distance with analytic conditions: volume-regularity of distance-induced balls, Lebesgue differentiability with respect to the distance, and bounded centered oscillations of densities. Under these conditions, equality of interpoint distance distributions continues to imply equality of the generating laws. The result persists under monotone continuous transformations of homogeneous, translation-invariant distances, recovering the original statement, and it extends to compact Riemannian manifolds equipped with the geodesic metric. We further develop a quantitative version of the theorem, i.e., inequalities that connect discrepancies of interpoint distance distributions to the $L^2$-distance between densities, and obtain explicit rates under Ahlfors $\alpha$-regularity of the distance function and $\beta$-Hölder continuity of densities, capturing dependence on dimensionality. Several representative examples illustrate the applicability of the generalization to domain-specific distances used in modern statistics. The examples include non-homogeneous non-translation invariant distances such as Canberra, entropic distances, and the Bray–Curtis dissimilarity.

Large Language Models (LLMs) often lack meaningful confidence estimates for their outputs. While base LLMs are known to exhibit next-token calibration, it remains unclear whether they can assess confidence in the actual meaning of their responses beyond the token level. We find that, when using a certain sampling-based notion of semantic calibration, base LLMs are remarkably well-calibrated: they can meaningfully assess confidence in open-domain question-answering tasks, despite not being explicitly trained to do so. Our main theoretical contribution establishes a mechanism for why semantic calibration emerges as a byproduct of next-token prediction, leveraging a recent connection between calibration and local loss optimality. The theory relies on a general definition of "B-calibration," which is a notion of calibration parameterized by a choice of equivalence classes (semantic or otherwise). This theoretical mechanism leads to a testable prediction: base LLMs will be semantically calibrated when they can easily predict their own distribution over semantic answer classes before generating a response. We state three implications of this prediction, which we validate through experiments: (1) Base LLMs are semantically calibrated across question-answering tasks, (2) RL instruction-tuning systematically breaks this calibration, and (3) chain-of-thought reasoning breaks calibration. To our knowledge, our work provides the first principled explanation of when and why semantic calibration emerges in LLMs.

This manuscript studies latent space graph-fused LASSO methods for clustering graphs with multivariate nodal attributes. The framework includes node-specific priors of low-dimensional representations coupled with a neural decoder that bridges the observed attributes with the latent variables. Both structural and attribute information are incorporated for the clustering through a graph-fused LASSO regularization on prior nodal means. The optimization problem is solved via the alternating direction method of multipliers with Langevin dynamics for posterior inference. Simulations on grid and block graphs, together with applications to California county temperatures and Los Angeles traffic data, demonstrate the effectiveness of the proposed method.

Multiple studies have shown that scalar summaries of objectively measured physical activity (PA) using accelerometers are the strongest predictors of mortality, outperforming all traditional risk factors, including age, sex, body mass index (BMI), and smoking. Here we show that diurnal patterns of PA and their day-to-day variability provide additional information about mortality. To do that, we introduce a class of extended functional Cox models and corresponding inferential tools designed to quantify the association between multiple functional and scalar predictors with time-to-event outcomes in large-scale (large $n$) high-dimensional (large $p$) datasets. Methods are applied to the UK Biobank study, which collected PA at every minute of the day for up to seven days, as well as time to mortality ($93{,}370$ participants with good quality accelerometry data and $931$ events). Simulation studies show that methods perform well in realistic scenarios and scale up to studies an order of magnitude larger than the UK Biobank accelerometry study. Establishing the feasibility and scalability of these methods for such complex and large data sets is a major milestone in applied Functional Data Analysis (FDA).

SDE-based methods such as denoising diffusion probabilistic models (DDPMs) have shown remarkable success in real-world sample generation tasks. Prior analyses of DDPMs have been focused on the exponential Euler discretization, showing guarantees that generally depend at least linearly on the dimension or initial Fisher information. Inspired by works in log-concave sampling (Shen and Lee, 2019), we analyze an integrator – the denoising diffusion randomized midpoint method (DDRaM) – that leverages an additional randomized midpoint to better approximate the SDE. Using a recently-developed analytic framework called the "shifted composition rule", we show that this algorithm enjoys favorable discretization properties under appropriate smoothness assumptions, with sublinear $\widetilde{O}(\sqrt{d})$ score evaluations needed to ensure convergence. This is the first sublinear complexity bound for pure DDPM sampling – prior works which obtained such bounds worked instead with ODE-based sampling and had to make modifications to the sampler which deviate from how they are used in practice. We also provide experimental validation of the advantages of our method, showing that it performs well in practice with pre-trained image synthesis models.

Missing values pose a persistent challenge in modern data science. Consequently, there is an ever-growing number of publications introducing new imputation methods in various fields. While many studies compare imputation approaches, they often focus on a limited subset of algorithms and evaluate performance primarily through pointwise metrics such as RMSE, which are not suitable to measure the preservation of the true data distribution. In this work, we provide a systematic benchmarking method based on the idea of treating imputation as a distributional prediction task. We consider a large number of algorithms and, for the first time, evaluate them not only on synthetic missing mechanisms, but also on real-world missingness scenarios, using the concept of Imputation Scores. Finally, while the focus of previous benchmark has often been on numerical data, we also consider mixed data sets in our study. The analysis overwhelmingly confirms the superiority of iterative imputation algorithms, especially the methods implemented in the mice R package.

Understanding the biological and behavioral heterogeneity underlying psychiatric disorders is critical for advancing precision diagnosis, treatment, and prevention. This paper addresses the scientific question of how multimodal data, spanning clinical, cognitive, and neuroimaging measures, can be integrated to identify biologically meaningful subtypes of mental disorders. We introduce Mixed INtegrative Data Subtyping (MINDS), a Bayesian hierarchical model designed to jointly analyze mixed-type data for simultaneous dimension reduction and clustering. Using data from the Adolescent Brain Cognitive Development (ABCD) Study, MINDS integrates clinical symptoms, cognitive performance, and brain structure measures to subtype Attention-Deficit/Hyperactivity Disorder (ADHD) and Obsessive-Compulsive Disorder (OCD). Our method leverages Polya-Gamma augmentation for computational efficiency and robust inference. Simulations demonstrate improved stability and accuracy compared to existing clustering approaches. Application to the ABCD data reveals clinically interpretable subtypes of ADHD and OCD with distinct cognitive and neurodevelopmental profiles. These findings show how integrative multimodal modeling can enhance the reproducibility and clinical relevance of psychiatric subtyping, supporting data-driven policies for early identification and targeted interventions in mental health.

Massive data collection holds the promise of a better understanding of complex phenomena and, ultimately, better decisions. Representation learning has become a key driver of deep learning applications, as it allows learning latent spaces that capture important properties of the data without requiring any supervised annotations. Although representation learning has been hugely successful in predictive tasks, it can fail miserably in causal tasks including predicting the effect of a perturbation/intervention. This calls for a marriage between representation learning and causal inference. An exciting opportunity in this regard stems from the growing availability of multi-modal data (observational and perturbational, imaging-based and sequencing-based, at the single-cell level, tissue-level, and organism-level). We outline a statistical and computational framework for causal structure and representation learning motivated by fundamental biomedical questions: how to effectively use observational and perturbational data to perform causal discovery on observed causal variables; how to use multi-modal views of the system to learn causal variables; and how to design optimal perturbations.