Processing high-volume, streaming data is increasingly common in modern statistics and machine learning, where batch-mode algorithms are often impractical because they require repeated passes over the full dataset. This has motivated incremental stochastic estimation methods, including the incremental stochastic Expectation-Maximization (EM) algorithm formulated via stochastic approximation. In this work, we revisit and analyze an incremental stochastic variant of the Majorization-Minimization (MM) algorithm, which generalizes incremental stochastic EM as a special case. Our approach relaxes key EM requirements, such as explicit latent-variable representations, enabling broader applicability and greater algorithmic flexibility. We establish theoretical guarantees for the incremental stochastic MM algorithm, proving consistency in the sense that the iterates converge to a stationary point characterized by a vanishing gradient of the objective. We demonstrate these advantages on a softmax-gated mixture of experts (MoE) regression problem, for which no stochastic EM algorithm is available. Empirically, our method consistently outperforms widely used stochastic optimizers, including stochastic gradient descent, root mean square propagation, adaptive moment estimation, and second-order clipped stochastic optimization. These results support the development of new incremental stochastic algorithms, given the central role of softmax-gated MoE architectures in contemporary deep neural networks for heterogeneous data modeling. Beyond synthetic experiments, we also validate practical effectiveness on two real-world datasets, including a bioinformatics study of dent maize genotypes under drought stress that integrates high-dimensional proteomics with ecophysiological traits, where incremental stochastic MM yields stable gains in predictive performance.

We study grokking, the onset of generalization long after overfitting, in a classical ridge regression setting. We prove end-to-end grokking results for learning over-parameterized linear regression models using gradient descent with weight decay. Specifically, we prove that the following stages occur: (i) the model overfits the training data early during training; (ii) poor generalization persists long after overfitting has manifested; and (iii) the generalization error eventually becomes arbitrarily small. Moreover, we show, both theoretically and empirically, that grokking can be amplified or eliminated in a principled manner through proper hyperparameter tuning. To the best of our knowledge, these are the first rigorous quantitative bounds on the generalization delay (which we refer to as the "grokking time") in terms of training hyperparameters. Lastly, going beyond the linear setting, we empirically demonstrate that our quantitative bounds also capture the behavior of grokking on non-linear neural networks. Our results suggest that grokking is not an inherent failure mode of deep learning, but rather a consequence of specific training conditions, and thus does not require fundamental changes to the model architecture or learning algorithm to avoid.

Distributed high dimensional mean estimation is a common aggregation routine used often in distributed optimization methods. Most of these applications call for a communication-constrained setting where vectors, whose mean is to be estimated, have to be compressed before sharing. One could independently encode and decode these to achieve compression, but that overlooks the fact that these vectors are often close to each other. To exploit these similarities, recently Suresh et al., 2022, Jhunjhunwala et al., 2021, Jiang et al, 2023, proposed multiple correlation-aware compression schemes. However, in most cases, the correlations have to be known for these schemes to work. Moreover, a theoretical analysis of graceful degradation of these correlation-aware compression schemes with increasing dissimilarity is limited to only the $\ell_2$-error in the literature. In this paper, we propose four different collaborative compression schemes that agnostically exploit the similarities among vectors in a distributed setting. Our schemes are all simple to implement and computationally efficient, while resulting in big savings in communication. The analysis of our proposed schemes show how the $\ell_2$, $\ell_\infty$ and cosine estimation error varies with the degree of similarity among vectors.

Imputing missing node features in graphs is challenging, particularly under high missing rates. Existing methods based on latent representations or global diffusion often fail to produce reliable estimates, and may propagate errors across the graph. We propose FSD-CAP, a two-stage framework designed to improve imputation quality under extreme sparsity. A fractional diffusion operator adjusts propagation sharpness based on local structure. In the second stage, imputed features are refined using class-aware propagation, which incorporates pseudo-labels and neighborhood entropy to promote consistency. We evaluated FSD-CAP on multiple datasets. With 99 .5% of features missing across five benchmark datasets, FSD-CAP achieves average accuracies of 80 .06% For link prediction under the same setting, it reaches AUC scores of 91. Furthermore, FSD-CAP demonstrates superior performance on both large-scale and heterophily datasets when compared to other models. Graph Neural Networks (GNNs) are widely used for learning from graph-structured data, with successful applications in social networks (Bian et al., 2020), biology (Li et al., 2022), and recommendation systems (He et al., 2020). GNN architectures(Chen et al., 2023; Chien et al., 2020) always assume nodal features are fully observed, allowing information to be aggregated effectively from neighboring nodes. In practice, this assumption often fails. Node attributes are frequently missing due to privacy constraints, sensor failures, or incomplete data collection. High missing rates disrupt the message-passing process and significantly degrade model performance. A variety of methods have been proposed for imputing missing features, including statistical estimators (Srebro et al., 2004), machine learning models (Chen & Guestrin, 2016), and generative approaches (Vincent et al., 2008). Recent work has shifted toward deep learning techniques that model the distribution of node attributes. These include latent space models that align observed features with learned embeddings (Chen et al., 2020; Y oo et al., 2022), and GNN-based architectures designed to operate on incomplete inputs (Taguchi et al., 2021). These approaches, which rely on correlations in both feature and graph structure, are effective under moderate missing rates but experience significant performance degradation as sparsity increases, ultimately falling below simple baselines like zero-filling or mean imputation in highly incomplete settings(Y ou et al., 2020).

Explainable boosting machines (EBMs) are popular "glass-box" models that learn a set of univariate functions using boosting trees. These achieve explainability through visualizations of each feature's effect. However, unlike linear model coefficients, uncertainty quantification for the learned univariate functions requires computationally intensive bootstrapping, making it hard to know which features truly matter. We provide an alternative using recent advances in statistical inference for gradient boosting, deriving methods for statistical inference as well as end-to-end theoretical guarantees. Using a moving average instead of a sum of trees (Boulevard regularization) allows the boosting process to converge to a feature-wise kernel ridge regression. This produces asymptotically normal predictions that achieve the minimax-optimal mean squared error for fitting Lipschitz GAMs with $p$ features at rate $O(pn^{-2/3})$, successfully avoiding the curse of dimensionality. We then construct prediction intervals for the response and confidence intervals for each learned univariate function with a runtime independent of the number of datapoints, enabling further explainability within EBMs.

In modern biomedical and econometric studies, longitudinal processes are often characterized by complex time-varying associations and abrupt regime shifts that are shared across correlated outcomes. Standard functional data analysis (FDA) methods, which prioritize smoothness, often fail to capture these dynamic structural features, particularly in high-dimensional settings. This article introduces Adaptive Joint Learning (AJL), a hierarchical regularization framework designed to integrate functional variable selection with structural changepoint detection in multivariate time-varying coefficient models. Unlike standard simultaneous estimation approaches, we propose a theoretically grounded two-stage screening-and-refinement procedure. This framework first synergizes adaptive group-wise penalization with sure screening principles to robustly identify active predictors, followed by a refined fused regularization step that effectively borrows strength across multiple outcomes to detect local regime shifts. We provide a rigorous theoretical analysis of the estimator in the ultra-high-dimensional regime (p >> n). Crucially, we establish the sure screening consistency of the first stage, which serves as the foundation for proving that the refined estimator achieves the oracle property-performing as well as if the true active set and changepoint locations were known a priori. A key theoretical contribution is the explicit handling of approximation bias via undersmoothing conditions to ensure valid asymptotic inference. The proposed method is validated through comprehensive simulations and an application to Sleep-EDF data, revealing novel dynamic patterns in physiological states.

Many industries now deploy high-fidelity simulators (digital twins) to represent physical systems, yet their parameters must be calibrated to match the true system. This motivated the construction of simulation-driven parameter estimators, built by generating synthetic observations for sampled parameter values and learning a supervised mapping from observations to parameters. However, when the true parameters lie outside the sampled range, predictions suffer from an out-of-distribution (OOD) error. This paper introduces a fine-tuning approach for the Two-Stage estimator that mitigates OOD effects and improves accuracy. The effectiveness of the proposed method is verified through numerical simulations.

Full conformal prediction is a framework that implicitly formulates distribution-free confidence prediction regions for a wide range of estimators. However, a classical limitation of the full conformal framework is the computation of the confidence prediction regions, which is usually impossible since it requires training infinitely many estimators (for real-valued prediction for instance). The main purpose of the present work is to describe a generic strategy for designing a tight approximation to the full conformal prediction region that can be efficiently computed. Along with this approximate confidence region, a theoretical quantification of the tightness of this approximation is developed, depending on the smoothness assumptions on the loss and score functions. The new notion of thickness is introduced for quantifying the discrepancy between the approximate confidence region and the full conformal one.

Empirical investigations into unintended model behavior often show that the algorithm is predicting another outcome than what was intended. These exposes highlight the need to identify when algorithms predict unintended quantities - ideally before deploying them into consequential settings. We propose a falsification framework that provides a principled statistical test for discriminant validity: the requirement that an algorithm predict intended outcomes better than impermissible ones. Drawing on falsification practices from causal inference, econometrics, and psychometrics, our framework compares calibrated prediction losses across outcomes to assess whether the algorithm exhibits discriminant validity with respect to a specified impermissible proxy. In settings where the target outcome is difficult to observe, multiple permissible proxy outcomes may be available; our framework accommodates both this setting and the case with a single permissible proxy. Throughout we use nonparametric hypothesis testing methods that make minimal assumptions on the data-generating process. We illustrate the method in an admissions setting, where the framework establishes discriminant validity with respect to gender but fails to establish discriminant validity with respect to race. This demonstrates how falsification can serve as an early validity check, prior to fairness or robustness analyses. We also provide analysis in a criminal justice setting, where we highlight the limitations of our framework and emphasize the need for complementary approaches to assess other aspects of construct validity and external validity.

Task-oriented semantic communication (SemCom) prioritizes task execution over accurate symbol reconstruction and is well-suited to emerging intelligent applications. Cooperative multi-task SemCom (CMT-SemCom) further improves task execution performance. However, [1] demonstrates that cooperative multi-tasking can be either constructive or destructive. Moreover, the existing CMT-SemCom framework is not directly applicable to distributed multi-user scenarios, such as non-terrestrial satellite networks, where each satellite employs an individual semantic encoder. In this paper, we extend our earlier CMT-SemCom framework to distributed settings by proposing a federated learning (FL) based CMT-SemCom that enables cooperative multi-tasking across distributed users. Moreover, to address performance degradation caused by negative information transfer among heterogeneous tasks, we propose a semantic-aware task clustering method integrated in the FL process to ensure constructive cooperation based on an information-theoretic approach. Unlike common clustering methods that rely on high-dimensional data or feature space similarity, our proposed approach operates in the low-dimensional semantic domain to identify meaningful task relationships. Simulation results based on a LEO satellite network setup demonstrate the effectiveness of our approach and performance gain over unclustered FL and individual single-task SemCom.