This paper studies the task of estimating heterogeneous treatment effects in causal panel data models with covariate effects. We propose a novel Covariate-Adjusted Deep Causal Learning (CoDEAL) framework that cohesively deals with the underlying heterogeneity and nonlinearity of both panel units and covariate effects. CoDEAL integrates nonlinear covariate effect components (parameterized by a feed-forward neural network) with nonlinear factor structures (modeled by a multi-output autoencoder) to form a heterogeneous causal panel model. The nonlinear covariate component flexibly captures complex covariate influences on outcomes, and the nonlinear factor decomposition enables CoDEAL to effectively capture both cross-sectional and temporal dependencies inherent in the data panel. This latent structural information is subsequently integrated into a customized matrix completion algorithm, thereby facilitating more accurate counterfactual imputation. Moreover, the use of a multi-output autoencoder explicitly accounts for heterogeneity across units and enhances the model interpretability of the latent factors. We establish theoretical guarantees on the convergence of the estimated counterfactuals and demonstrate the compelling performance of the proposed method using extensive simulation studies and real-world data applications.
Handling missing values is a common challenge in biostatistical analyses, typically addressed by imputation methods. We propose a novel, fast, and easy-to-use imputation method called missing value imputation with adversarial random forests (MissARF), based on generative machine learning, that provides both single and multiple imputation. MissARF employs adversarial random forest (ARF) for density estimation and data synthesis. To impute a missing value of an observation, we condition on the non-missing values and sample from the estimated conditional distribution generated by ARF. Our experiments demonstrate that MissARF performs comparably to state-of-the-art single and multiple imputation methods in terms of imputation quality and fast runtime with no additional costs for multiple imputation.
Recent years have witnessed a growing interest for time series foundation models, with a strong emphasis on the forecasting task. Yet, the crucial task of out-of-domain imputation of missing values remains largely underexplored. We propose a first step to fill this gap by leveraging implicit neural representations (INRs). INRs model time series as continuous functions and naturally handle various missing data scenarios and sampling rates. While they have shown strong performance within specific distributions, they struggle under distribution shifts. To address this, we introduce MoTM (Mixture of Timeflow Models), a step toward a foundation model for time series imputation. Building on the idea that a new time series is a mixture of previously seen patterns, MoTM combines a basis of INRs, each trained independently on a distinct family of time series, with a ridge regressor that adapts to the observed context at inference. We demonstrate robust in-domain and out-of-domain generalization across diverse imputation scenarios (e.g., block and pointwise missingness, variable sampling rates), paving the way for adaptable foundation imputation models.
Large language models (LLMs) trained on text demonstrated remarkable results on natural language processing (NLP) tasks. These models have been adapted to decipher the language of DNA, where sequences of nucleotides act as "words" that encode genomic functions. However, the genome differs fundamentally from natural language, as it lacks clearly defined words or a consistent grammar. Although DNA language models (DNALMs) such as DNABERT, GENA-LM have achieved high level of performance on genome-related biological tasks, these models do not encode biological functions in the presence of sequence variations. To address this problem, we pre-train foundation models that effectively integrate sequence variations, in particular Single Nucleotide Polymorphisms (SNPs), as they underlie important biological functions. Specifically, we use ModernBERT to pre-train two different Biomedical Foundation Models (BMFM), namely, BMFM-DNA-REF in which the model is trained with sequences of varying lengths along with their reverse complements derived from the reference genome and BMFM-DNA-SNP in which the model is trained with sequences created using a novel representation scheme that encodes sequence variations. Our findings indicate that integrating sequence variations into DNALMs helps capture the biological functions as seen in improvements on all fine-tuning tasks. To explore the model's practical utility, we experimented with various strategies for SNP imputation on promoter detection task introduced in DNABERT-2. However, we acknowledge that the current benchmarks are limited in their ability to fully evaluate these models. To enable more comprehensive assessment in the future and encourage community contributions, we release our models through HuggingFace and the code to reproduce the results at https://github.com/BiomedSciAI/biomed-multi-omic
Time series with missing or irregularly sampled data are a persistent challenge in machine learning. Many methods operate on the frequency-domain, relying on the Fast Fourier Transform (FFT) which assumes uniform sampling, therefore requiring prior interpolation that can distort the spectra. To address this limitation, we introduce a differentiable Lomb--Scargle layer that enables a reliable computation of the power spectrum of irregularly sampled data. We integrate this layer into a novel score-based diffusion model (LSCD) for time series imputation conditioned on the entire signal spectrum. Experiments on synthetic and real-world benchmarks demonstrate that our method recovers missing data more accurately than purely time-domain baselines, while simultaneously producing consistent frequency estimates. Crucially, our method can be easily integrated into learning frameworks, enabling broader adoption of spectral guidance in machine learning approaches involving incomplete or irregular data.
Single-cell transcriptomics has become a great source for data-driven insights into biology, enabling the use of advanced deep learning methods to understand cellular heterogeneity and transcriptional regulation at the single-cell level. With the advent of spatial transcriptomics data we have the promise of learning about cells within a tissue context as it provides both spatial coordinates and transcriptomic readouts. However, existing models either ignore spatial resolution or the gene regulatory information. Gene regulation in cells can change depending on microenvironmental cues from neighboring cells, but existing models neglect gene regulatory patterns with hierarchical dependencies across levels of abstraction. In order to create contextualized representations of cells and genes from spatial transcriptomics data, we introduce HEIST, a hierarchical graph transformer-based foundation model for spatial transcriptomics and proteomics data. HEIST models tissue as spatial cellular neighborhood graphs, and each cell is, in turn, modeled as a gene regulatory network graph. The framework includes a hierarchical graph transformer that performs cross-level message passing and message passing within levels. HEIST is pre-trained on 22.3M cells from 124 tissues across 15 organs using spatially-aware contrastive learning and masked auto-encoding objectives. Unsupervised analysis of HEIST representations of cells, shows that it effectively encodes the microenvironmental influences in cell embeddings, enabling the discovery of spatially-informed subpopulations that prior models fail to differentiate. Further, HEIST achieves state-of-the-art results on four downstream task such as clinical outcome prediction, cell type annotation, gene imputation, and spatially-informed cell clustering across multiple technologies, highlighting the importance of hierarchical modeling and GRN-based representations.
In phylogenomics, species-tree methods must contend with two major sources of noise; stochastic gene-tree variation under the multispecies coalescent model (MSC) and finite-sequence substitutional noise. Fast agglomerative methods such as GLASS, STEAC, and METAL combine multi-locus information via distance-based clustering. We derive the exact covariance matrix of these pairwise distance estimates under a joint MSC-plus-substitution model and leverage it for reliable confidence estimation, and we algebraically decompose it into components attributable to coalescent variation versus sequence-level stochasticity. Our theory identifies parameter regimes where one source of variance greatly exceeds the other. For both very low and very high mutation rates, substitutional noise dominates, while coalescent variance is the primary contributor at intermediate mutation rates. Moreover, the interval over which coalescent variance dominates becomes narrower as the species-tree height increases. These results imply that in some settings one may legitimately ignore the weaker noise source when designing methods or collecting data. In particular, when gene-tree variance is dominant, adding more loci is most beneficial, while when substitution noise dominates, longer sequences or imputation are needed. Finally, leveraging the derived covariance matrix, we implement a Gaussian-sampling procedure to generate split support values for METAL trees and demonstrate empirically that this approach yields more reliable confidence estimates than traditional bootstrapping.
Probabilistic models are often used to make predictions in regions of the data space where no observations are available, but it is not always clear whether such predictions are well-informed by previously seen data. In this paper, we propose a knowledge score for predictions from Gaussian process regression (GPR) models that quantifies the extent to which observing data have reduced our uncertainty about a prediction. The knowledge score is interpretable and naturally bounded between 0 and 1. We demonstrate in several experiments that the knowledge score can anticipate when predictions from a GPR model are accurate, and that this anticipation improves performance in tasks such as anomaly detection, extrapolation, and missing data imputation. Source code for this project is available online at https://github.com/KurtButler/GP-knowledge.
Cross-domain time series imputation is an underexplored data-centric research task that presents significant challenges, particularly when the target domain suffers from high missing rates and domain shifts in temporal dynamics. Existing time series imputation approaches primarily focus on the single-domain setting, which cannot effectively adapt to a new domain with domain shifts. Meanwhile, conventional domain adaptation techniques struggle with data incompleteness, as they typically assume the data from both source and target domains are fully observed to enable adaptation. For the problem of cross-domain time series imputation, missing values introduce high uncertainty that hinders distribution alignment, making existing adaptation strategies ineffective. Specifically, our proposed solution tackles this problem from three perspectives: (i) Data: We introduce a frequency-based time series interpolation strategy that integrates shared spectral components from both domains while retaining domain-specific temporal structures, constructing informative priors for imputation. (ii) Model: We design a diffusion-based imputation model that effectively learns domain-shared representations and captures domain-specific temporal dependencies with dedicated denoising networks. (iii) Algorithm: We further propose a cross-domain consistency alignment strategy that selectively regularizes output-level domain discrepancies, enabling effective knowledge transfer while preserving domain-specific characteristics. Extensive experiments on three real-world datasets demonstrate the superiority of our proposed approach. Our code implementation is available here.
Missing data in spatiotemporal systems presents a significant challenge for modern applications, ranging from environmental monitoring to urban traffic management. The integrity of spatiotemporal data often deteriorates due to hardware malfunctions and software failures in real-world deployments. Current approaches based on machine learning and deep learning struggle to model the intricate interdependencies between spatial and temporal dimensions effectively and, more importantly, suffer from cumulative errors during the data imputation process, which propagate and amplify through iterations. To address these limitations, we propose CoFILL, a novel Conditional Diffusion Model for spatiotemporal data imputation. CoFILL builds on the inherent advantages of diffusion models to generate high-quality imputations without relying on potentially error-prone prior estimates. It incorporates an innovative dual-stream architecture that processes temporal and frequency domain features in parallel. By fusing these complementary features, CoFILL captures both rapid fluctuations and underlying patterns in the data, which enables more robust imputation. The extensive experiments reveal that CoFILL's noise prediction network successfully transforms random noise into meaningful values that align with the true data distribution. The results also show that CoFILL outperforms state-of-the-art methods in imputation accuracy. The source code is publicly available at https://github.com/joyHJL/CoFILL.
Evaluating the abilities of learners is a fundamental objective in the field of education. In particular, there is an increasing need to assess higher-order abilities such as expressive skills and logical thinking. Constructed-response tests such as short-answer and essay-based questions have become widely used as a method to meet this demand. Although these tests are effective, they require substantial manual grading, making them both labor-intensive and costly. Item response theory (IRT) provides a promising solution by enabling the estimation of ability from incomplete score data, where human raters grade only a subset of answers provided by learners across multiple test items. However, the accuracy of ability estimation declines as the proportion of missing scores increases. Although data augmentation techniques for imputing missing scores have been explored in order to address this limitation, they often struggle with inaccuracy for sparse or heterogeneous data. To overcome these challenges, this study proposes a novel method for imputing missing scores by leveraging automated scoring technologies for accurate IRT-based ability estimation. The proposed method achieves high accuracy in ability estimation while markedly reducing manual grading workload.
Time series imputation models have traditionally been developed using complete datasets with artificial masking patterns to simulate missing values. However, in real-world infrastructure monitoring, practitioners often encounter datasets where large amounts of data are missing and follow complex, heterogeneous patterns. We introduce DIM-SUM, a preprocessing framework for training robust imputation models that bridges the gap between artificially masked training data and real missing patterns. DIM-SUM combines pattern clustering and adaptive masking strategies with theoretical learning guarantees to handle diverse missing patterns actually observed in the data. Through extensive experiments on over 2 billion readings from California water districts, electricity datasets, and benchmarks, we demonstrate that DIM-SUM outperforms traditional methods by reaching similar accuracy with lower processing time and significantly less training data. When compared against a large pre-trained model, DIM-SUM averages 2x higher accuracy with significantly less inference time.
Accurate weather forecasts are essential for supporting a wide range of activities and decision-making processes, as well as mitigating the impacts of adverse weather events. While traditional numerical weather prediction (NWP) remains the cornerstone of operational forecasting, machine learning is emerging as a powerful alternative for fast, flexible, and scalable predictions. We introduce PeakWeather, a high-quality dataset of surface weather observations collected every 10 minutes over more than 8 years from the ground stations of the Federal Office of Meteorology and Climatology MeteoSwiss's measurement network. The dataset includes a diverse set of meteorological variables from 302 station locations distributed across Switzerland's complex topography and is complemented with topographical indices derived from digital height models for context. Ensemble forecasts from the currently operational high-resolution NWP model are provided as a baseline forecast against which to evaluate new approaches. The dataset's richness supports a broad spectrum of spatiotemporal tasks, including time series forecasting at various scales, graph structure learning, imputation, and virtual sensing. As such, PeakWeather serves as a real-world benchmark to advance both foundational machine learning research, meteorology, and sensor-based applications.
Objectives: We propose a novel imputation method tailored for Electronic Health Records (EHRs) with structured and sporadic missingness. Such missingness frequently arises in the integration of heterogeneous EHR datasets for downstream clinical applications. By addressing these gaps, our method provides a practical solution for integrated analysis, enhancing data utility and advancing the understanding of population health. Materials and Methods: We begin by demonstrating structured and sporadic missing mechanisms in the integrated analysis of EHR data. Following this, we introduce a novel imputation framework, Macomss, specifically designed to handle structurally and heterogeneously occurring missing data. We establish theoretical guarantees for Macomss, ensuring its robustness in preserving the integrity and reliability of integrated analyses. To assess its empirical performance, we conduct extensive simulation studies that replicate the complex missingness patterns observed in real-world EHR systems, complemented by validation using EHR datasets from the Duke University Health System (DUHS). Results: Simulation studies show that our approach consistently outperforms existing imputation methods. Using datasets from three hospitals within DUHS, Macomss achieves the lowest imputation errors for missing data in most cases and provides superior or comparable downstream prediction performance compared to benchmark methods. Conclusions: We provide a theoretically guaranteed and practically meaningful method for imputing structured and sporadic missing data, enabling accurate and reliable integrated analysis across multiple EHR datasets. The proposed approach holds significant potential for advancing research in population health.
Postoperative stroke remains a critical complication in elderly surgical intensive care unit (SICU) patients, contributing to prolonged hospitalization, elevated healthcare costs, and increased mortality. Accurate early risk stratification is essential to enable timely intervention and improve clinical outcomes. We constructed a combined cohort of 19,085 elderly SICU admissions from the MIMIC-III and MIMIC-IV databases and developed an interpretable machine learning (ML) framework to predict in-hospital stroke using clinical data from the first 24 hours of Intensive Care Unit (ICU) stay. The preprocessing pipeline included removal of high-missingness features, iterative Singular Value Decomposition (SVD) imputation, z-score normalization, one-hot encoding, and class imbalance correction via the Adaptive Synthetic Sampling (ADASYN) algorithm. A two-stage feature selection process-combining Recursive Feature Elimination with Cross-Validation (RFECV) and SHapley Additive exPlanations (SHAP)-reduced the initial 80 variables to 20 clinically informative predictors. Among eight ML models evaluated, CatBoost achieved the best performance with an AUROC of 0.8868 (95% CI: 0.8802--0.8937). SHAP analysis and ablation studies identified prior cerebrovascular disease, serum creatinine, and systolic blood pressure as the most influential risk factors. Our results highlight the potential of interpretable ML approaches to support early detection of postoperative stroke and inform decision-making in perioperative critical care.
The large underlying assumption of climate models today relies on the basis of a "confident" initial condition, a reasonably plausible snapshot of the Earth for which all future predictions depend on. However, given the inherently chaotic nature of our system, this assumption is complicated by sensitive dependence, where small uncertainties in initial conditions can lead to exponentially diverging outcomes over time. This challenge is particularly salient at global spatial scales and over centennial timescales, where data gaps are not just common but expected. The source of uncertainty is two-fold: (1) sparse, noisy observations from satellites and ground stations, and (2) internal variability stemming from the simplifying approximations within the models themselves. In practice, data assimilation methods are used to reconcile this missing information by conditioning model states on partial observations. Our work builds on this idea but operates at the extreme end of sparsity. We propose a conditional data imputation framework that reconstructs full temperature fields from as little as 1% observational coverage. The method leverages a diffusion model guided by a prekriged mask, effectively inferring the full-state fields from minimal data points. We validate our framework over the Southern Great Plains, focusing on afternoon (12:00-6:00 PM) temperature fields during the summer months of 2018-2020. Across varying observational densities--from swath data to isolated in-situ sensors--our model achieves strong reconstruction accuracy, highlighting its potential to fill in critical data gaps in both historical reanalysis and real-time forecasting pipelines.
Pathogen genome data offers valuable structure for spatial models, but its utility is limited by incomplete sequencing coverage. We propose a probabilistic framework for inferring genetic distances between unsequenced cases and known sequences within defined transmission chains, using time-aware evolutionary distance modeling. The method estimates pairwise divergence from collection dates and observed genetic distances, enabling biologically plausible imputation grounded in observed divergence patterns, without requiring sequence alignment or known transmission chains. Applied to highly pathogenic avian influenza A/H5 cases in wild birds in the United States, this approach supports scalable, uncertainty-aware augmentation of genomic datasets and enhances the integration of evolutionary information into spatiotemporal modeling workflows.
In cognitive neuroscience research, Representational Dissimilarity Matrices (RDMs) are often incomplete because pairwise similarity judgments cannot always be exhaustively collected as the number of pairs rapidly increases with the number of conditions. Existing methods to fill these missing values, such as deep neural network imputation, are powerful but computationally demanding and relatively opaque. We introduce a simple algorithm based on geometric inference that fills missing dissimilarity matrix entries using known distances. We use tests on publicly available empirical cognitive neuroscience datasets, as well as simulations, to demonstrate the method's effectiveness and robustness across varying sparsity and matrix sizes. We have made this geometric reconstruction algorithm, implemented in Python and MATLAB, publicly available. This method provides a fast and accurate solution for completing partial dissimilarity matrices in the cognitive neurosciences.
Cell-free DNA (cfDNA) analysis is a powerful, minimally invasive tool for monitoring disease progression, treatment response, and early detection. A major challenge, however, is accurately determining the tissue of origin, especially in complex or heterogeneous disease contexts. To address this, we developed a machine learning framework that leverages tissue-specific DNA methylation signatures to classify both tissue and disease origin from cfDNA data. Our model integrates methylation datasets across diverse epigenomic platforms, including Whole Genome Bisulfite Sequencing (WGBS), Illumina Infinium Bead Arrays, and Enzymatic Methyl-seq (EM-seq). To account for platform variability and data sparsity, we applied imputation strategies and harmonized CpG features to enable cross-platform learning. Dimensionality reduction revealed clear tissue-specific clustering of methylation profiles. A random forest classifier trained on these features achieved consistent classification performance (accuracy 0.75-0.8 across test sets and platforms). Notably, our model distinguished clinically relevant tissues such as inflamed synovium and peripheral blood mononuclear cells (PBMCs) in arthritis patients and deconvoluted synthetic cfDNA mixtures mimicking real-world liquid biopsy samples. The predicted tissue proportions closely matched the true values, demonstrating the model's potential for both classification and quantitative inference. These results support the feasibility of using cross-platform methylation data and machine learning for scalable, generalizable cfDNA diagnostics and lay the groundwork for future integration of disease-specific epigenetic features to guide clinical decision-making in precision medicine.
This tutorial aims to provide signal processing (SP) and machine learning (ML) practitioners with vital tools, in an accessible way, to answer the question: How to deal with missing data? There are many strategies to handle incomplete signals. In this paper, we propose to group these strategies based on three common tasks: i) missing-data imputation, ii) estimation with missing values and iii) prediction with missing values. We focus on methodological and experimental results through specific case studies on real-world applications. Promising and future research directions, including a better integration of informative missingness, are also discussed. We hope that the proposed conceptual framework and the presentation of recent missing-data problems related will encourage researchers of the SP and ML communities to develop original methods and to efficiently deal with new applications involving missing data.