Decentralized optimization has become vital for leveraging distributed data without central control, enhancing scalability and privacy. However, practical deployments face fundamental challenges due to heterogeneous computation speeds and unpredictable communication delays. This paper introduces a refined model of Asynchronous Decentralized Stochastic Gradient Descent (ADSGD) under practical assumptions of bounded computation and communication times. To understand the convergence of ADSGD, we first analyze Asynchronous Stochastic Block Coordinate Descent (ASBCD) as a tool, and then show that ADSGD converges under computation-delay-independent step sizes. The convergence result is established without assuming bounded data heterogeneity. Empirical experiments reveal that ADSGD outperforms existing methods in wall-clock convergence time across various scenarios. With its simplicity, efficiency in memory and communication, and resilience to communication and computation delays, ADSGD is well-suited for real-world decentralized learning tasks.

Community detection, a vital technology for real-world applications, uncovers cohesive node groups (communities) by leveraging both topological and attribute similarities in social networks. However, existing Graph Convolutional Networks (GCNs) trained to maximize modularity often converge to suboptimal solutions. Additionally, directly using human-labeled communities for training can undermine topological cohesiveness by grouping disconnected nodes based solely on node attributes. We address these issues by proposing a novel Topological and Attributive Similarity-based Community detection (TAS-Com) method. TAS-Com introduces a novel loss function that exploits the highly effective and scalable Leiden algorithm to detect community structures with global optimal modularity. Leiden is further utilized to refine human-labeled communities to ensure connectivity within each community, enabling TAS-Com to detect community structures with desirable trade-offs between modularity and compliance with human labels. Experimental results on multiple benchmark networks confirm that TAS-Com can significantly outperform several state-of-the-art algorithms.

We study the out-of-sample performance of multi-pass stochastic gradient descent (SGD) in the fundamental stochastic convex optimization (SCO) model. While one-pass SGD is known to achieve an optimal $Θ(1/\sqrt{n})$ excess population loss given a sample of size $n$, much less is understood about the multi-pass version of the algorithm which is widely used in practice. Somewhat surprisingly, we show that in the general non-smooth case of SCO, just a few epochs of SGD can already hurt its out-of-sample performance significantly and lead to overfitting. In particular, using a step size $η= Θ(1/\sqrt{n})$, which gives the optimal rate after one pass, can lead to population loss as large as $Ω(1)$ after just one additional pass. More generally, we show that the population loss from the second pass onward is of the order $Θ(1/(ηT) + η\sqrt{T})$, where $T$ is the total number of steps. These results reveal a certain phase-transition in the out-of-sample behavior of SGD after the first epoch, as well as a sharp separation between the rates of overfitting in the smooth and non-smooth cases of SCO. Additionally, we extend our results to with-replacement SGD, proving that the same asymptotic bounds hold after $O(n \log n)$ steps. Finally, we also prove a lower bound of $Ω(η\sqrt{n})$ on the generalization gap of one-pass SGD in dimension $d = \smash{\widetilde O}(n)$, improving on recent results of Koren et al.(2022) and Schliserman et al.(2024).

Time Series Classification (TSC) is an important problem with numerous applications in science and technology. Dissimilarity-based approaches, such as Dynamic Time Warping (DTW), are classical methods for distinguishing time series when time deformations are confounding information. In this paper, starting from a deformation-based model for signal classes we define a problem statement for time series classification problem. We show that, under theoretically ideal conditions, a continuous version of classic 1NN-DTW method can solve the stated problem, even when only one training sample is available. In addition, we propose an alternative dissimilarity measure based on Optimal Transport and show that it can also solve the aforementioned problem statement at a significantly reduced computational cost. Finally, we demonstrate the application of the newly proposed approach in simulated and real time series classification data, showing the efficacy of the method.

We introduce the first one-stage Top-$k$ Learning-to-Defer framework, which unifies prediction and deferral by learning a shared score-based model that selects the $k$ most cost-effective entities-labels or experts-per input. While existing one-stage L2D methods are limited to deferring to a single expert, our approach jointly optimizes prediction and deferral across multiple entities through a single end-to-end objective. We define a cost-sensitive loss and derive a novel convex surrogate that is independent of the cardinality parameter $k$, enabling generalization across Top-$k$ regimes without retraining. Our formulation recovers the Top-1 deferral policy of prior score-based methods as a special case, and we prove that our surrogate is both Bayes-consistent and $\mathcal{H}$-consistent under mild assumptions. We further introduce an adaptive variant, Top-$k(x)$, which dynamically selects the number of consulted entities per input to balance predictive accuracy and consultation cost. Experiments on CIFAR-10 and SVHN confirm that our one-stage Top-$k$ method strictly outperforms Top-1 deferral, while Top-$k(x)$ achieves superior accuracy-cost trade-offs by tailoring allocations to input complexity.

Bayesian inference with Markov Chain Monte Carlo (MCMC) is challenging when the likelihood function is irregular and expensive to compute. We explore several sampling algorithms that make use of subset evaluations to reduce computational overhead. We adapt the subset samplers for this setting where gradient information is not available or is unreliable. To achieve this, we introduce data-driven proxies in place of Taylor expansions and define a novel computation-cost aware adaptive controller. We undertake an extensive evaluation for a challenging disease modelling task and a configurable task with similar irregularity in the likelihood surface. We find our improved version of Hierarchical Importance with Nested Training Samples (HINTS), with adaptive proposals and a data-driven proxy, obtains the best sampling error in a fixed computational budget. We conclude that subset evaluations can provide cheap and naturally-tempered exploration, while a data-driven proxy can pre-screen proposals successfully in explored regions of the state space. These two elements combine through hierarchical delayed acceptance to achieve efficient, exact sampling.

In many scientific and industrial applications, we are given a handful of instances (a 'small ensemble') of a spatially distributed quantity (a 'field') but would like to acquire many more. For example, a large ensemble of global temperature sensitivity fields from a climate model can help farmers, insurers, and governments plan appropriately. When acquiring more data is prohibitively expensive -- as is the case with climate models -- statistical emulation offers an efficient alternative for simulating synthetic yet realistic fields. However, parameter inference using maximum likelihood estimation (MLE) is computationally prohibitive, especially for large, non-stationary fields. Thus, many recent works train neural networks to estimate parameters given spatial fields as input, sidestepping MLE completely. In this work we focus on a popular class of parametric, spatially autoregressive (SAR) models. We make a simple yet impactful observation; because the SAR parameters can be arranged on a regular grid, both inputs (spatial fields) and outputs (model parameters) can be viewed as images. Using this insight, we demonstrate that image-to-image (I2I) networks enable faster and more accurate parameter estimation for a class of non-stationary SAR models with unprecedented complexity.

We consider the problem of estimating differences in two multi-attribute Gaussian graphical models (GGMs) which are known to have similar structure, using a penalized D-trace loss function with non-convex penalties. The GGM structure is encoded in its precision (inverse covariance) matrix. Existing methods for multi-attribute differential graph estimation are based on a group lasso penalized loss function. In this paper, we consider a penalized D-trace loss function with non-convex (log-sum and smoothly clipped absolute deviation (SCAD)) penalties. Two proximal gradient descent methods are presented to optimize the objective function. Theoretical analysis establishing sufficient conditions for consistency in support recovery, convexity and estimation in high-dimensional settings is provided. We illustrate our approaches with numerical examples based on synthetic and real data.

Multimodal data modeling has emerged as a powerful approach in clinical research, enabling the integration of diverse data types such as imaging, genomics, wearable sensors, and electronic health records. Despite its potential to improve diagnostic accuracy and support personalized care, modeling such heterogeneous data presents significant technical challenges. This systematic review synthesizes findings from 69 studies to identify common obstacles, including missing modalities, limited sample sizes, dimensionality imbalance, interpretability issues, and finding the optimal fusion techniques. We highlight recent methodological advances, such as transfer learning, generative models, attention mechanisms, and neural architecture search that offer promising solutions. By mapping current trends and innovations, this review provides a comprehensive overview of the field and offers practical insights to guide future research and development in multimodal modeling for medical applications.

This study underscores the potential of machine learning in stroke risk prediction, addressing key challenges such as class imbalance and feature selection. Our findings highlight the significant role of demographic, clinical, and lifestyle factors, with age, average glucose level, and BMI emerging as key predictors. Notably, the analysis reveals the importance of age-specific models, as the predictive influence of factors shifts across different age groups. In elderly patients (65-80 years), work type and glucose level become more influential, while hypertension and heart disease gain prominence. By achieving high predictive accuracy and identifying im-pactful features, this research supports the development of stroke risk assessment tools with potential integration into clinical decision systems. These tools could assist clinicians in early intervention planning and personalized prevention strategies. However, challenges such as data variability, model interpretability, and deployment in real-world healthcare settings remain. Future research should focus on improving model sensitivity, incorporating diverse datasets, and validating predictions in clinical environments. Advancing these models could enhance early detection strategies, ultimately improving patient outcomes and stroke prevention.