Estimation of the conditional independence graph (CIG) of high-dimensional multivariate Gaussian time series from multi-attribute data is considered. Existing methods for graph estimation for such data are based on single-attribute models where one associates a scalar time series with each node. In multi-attribute graphical models, each node represents a random vector or vector time series. In this paper we provide a unified theoretical analysis of multi-attribute graph learning for dependent time series using a penalized log-likelihood objective function formulated in the frequency domain using the discrete Fourier transform of the time-domain data. We consider both convex (sparse-group lasso) and non-convex (log-sum and SCAD group penalties) penalty/regularization functions. We establish sufficient conditions in a high-dimensional setting for consistency (convergence of the inverse power spectral density to true value in the Frobenius norm), local convexity when using non-convex penalties, and graph recovery. We do not impose any incoherence or irrepresentability condition for our convergence results. We also empirically investigate selection of the tuning parameters based on the Bayesian information criterion, and illustrate our approach using numerical examples utilizing both synthetic and real data.

Estimation of differences in conditional independence graphs (CIGs) of two time series Gaussian graphical models (TSGGMs) is investigated where the two TSGGMs are known to have similar structure. The TSGGM structure is encoded in the inverse power spectral density (IPSD) of the time series. In several existing works, one is interested in estimating the difference in two precision matrices to characterize underlying changes in conditional dependencies of two sets of data consisting of independent and identically distributed (i.i.d.) observations. In this paper we consider estimation of the difference in two IPSDs to characterize the underlying changes in conditional dependencies of two sets of time-dependent data. Our approach accounts for data time dependencies unlike past work. We analyze a penalized D-trace loss function approach in the frequency domain for differential graph learning, using Wirtinger calculus. We consider both convex (group lasso) and non-convex (log-sum and SCAD group penalties) penalty/regularization functions. An alternating direction method of multipliers (ADMM) algorithm is presented to optimize the objective function. We establish sufficient conditions in a high-dimensional setting for consistency (convergence of the inverse power spectral density to true value in the Frobenius norm) and graph recovery. Both synthetic and real data examples are presented in support of the proposed approaches. In synthetic data examples, our log-sum-penalized differential time-series graph estimator significantly outperformed our lasso based differential time-series graph estimator which, in turn, significantly outperformed an existing lasso-penalized i.i.d. modeling approach, with $F_1$ score as the performance metric.

Recently, there has been an explosion in statistical learning literature to represent data using topological principles to capture structure and relationships. We propose a topological data analysis (TDA)-based framework, named Topological Prototype Selector (TPS), for selecting representative subsets (prototypes) from large datasets. We demonstrate the effectiveness of TPS on simulated data under different data intrinsic characteristics, and compare TPS against other currently used prototype selection methods in real data settings. In all simulated and real data settings, TPS significantly preserves or improves classification performance while substantially reducing data size. These contributions advance both algorithmic and geometric aspects of prototype learning and offer practical tools for parallelized, interpretable, and efficient classification.

Most Differentially Private (DP) approaches focus on limiting privacy leakage from learners based on the data that they are trained on, there are fewer approaches that consider leakage when procedures involve a calibration dataset which is common in uncertainty quantification methods such as Conformal Prediction (CP). Since there is a limited amount of approaches in this direction, in this work we deliver a general DP approach for CP that we call Private Conformity via Quantile Search (P-COQS). The proposed approach adapts an existing randomized binary search algorithm for computing DP quantiles in the calibration phase of CP thereby guaranteeing privacy of the consequent prediction sets. This however comes at a price of slightly under-covering with respect to the desired $(1 - α)$-level when using finite-sample calibration sets (although broad empirical results show that the P-COQS generally targets the required level in the considered cases). Confirming properties of the adapted algorithm and quantifying the approximate coverage guarantees of the consequent CP, we conduct extensive experiments to examine the effects of privacy noise, sample size and significance level on the performance of our approach compared to existing alternatives. In addition, we empirically evaluate our approach on several benchmark datasets, including CIFAR-10, ImageNet and CoronaHack. Our results suggest that the proposed method is robust to privacy noise and performs favorably with respect to the current DP alternative in terms of empirical coverage, efficiency, and informativeness. Specifically, the results indicate that P-COQS produces smaller conformal prediction sets while simultaneously targeting the desired coverage and privacy guarantees in all these experimental settings.

The task of statistical inference, which includes the building of confidence intervals and tests for parameters and effects of interest to a researcher, is still an open area of investigation in a differentially private (DP) setting. Indeed, in addition to the randomness due to data sampling, DP delivers another source of randomness consisting of the noise added to protect an individual's data from being disclosed to a potential attacker. As a result of this convolution of noises, in many cases it is too complicated to determine the stochastic behavior of the statistics and parameters resulting from a DP procedure. In this work, we contribute to this line of investigation by employing a simulation-based matching approach, solved through tools from the fiducial framework, which aims to replicate the data generation pipeline (including the DP step) and retrieve an approximate distribution of the estimates resulting from this pipeline. For this purpose, we focus on the analysis of categorical (nominal) data that is common in national surveys, for which sensitivity is naturally defined, and on additive privacy mechanisms. We prove the validity of the proposed approach in terms of coverage and highlight its good computational and statistical performance for different inferential tasks in simulated and applied data settings.

We consider the problem of inferring the conditional independence graph (CIG) of high-dimensional Gaussian vectors from multi-attribute data. Most existing methods for graph estimation are based on single-attribute models where one associates a scalar random variable with each node. In multi-attribute graphical models, each node represents a random vector. In this paper we provide a unified theoretical analysis of multi-attribute graph learning using a penalized log-likelihood objective function. We consider both convex (sparse-group lasso) and sparse-group non-convex (log-sum and smoothly clipped absolute deviation (SCAD) penalties) penalty/regularization functions. An alternating direction method of multipliers (ADMM) approach coupled with local linear approximation to non-convex penalties is presented for optimization of the objective function. For non-convex penalties, theoretical analysis establishing local consistency in support recovery, local convexity and precision matrix estimation in high-dimensional settings is provided under two sets of sufficient conditions: with and without some irrepresentability conditions. We illustrate our approaches using both synthetic and real-data numerical examples. In the synthetic data examples the sparse-group log-sum penalized objective function significantly outperformed the lasso penalized as well as SCAD penalized objective functions with $F_1$-score and Hamming distance as performance metrics.

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.

Statistical topic modeling is widely used in political science to study text. Researchers examine documents of varying lengths, from tweets to speeches. There is ongoing debate on how document length affects the interpretability of topic models. We investigate the effects of aggregating short documents into larger ones based on natural units that partition the corpus. In our study, we analyze one million tweets by U.S. state legislators from April 2016 to September 2020. We find that for documents aggregated at the account level, topics are more associated with individual states than when using individual tweets. This finding is replicated with Wikipedia pages aggregated by birth cities, showing how document definitions can impact topic modeling results.

The increasing complexity and scale of modern telecommunications networks demand intelligent automation to enhance efficiency, adaptability, and resilience. Agentic AI has emerged as a key paradigm for intelligent communications and networking, enabling AI-driven agents to perceive, reason, decide, and act within dynamic networking environments. However, effective decision-making in telecom applications, such as network planning, management, and resource allocation, requires integrating retrieval mechanisms that support multi-hop reasoning, historical cross-referencing, and compliance with evolving 3GPP standards. This article presents a forward-looking perspective on generative information retrieval-inspired intelligent communications and networking, emphasizing the role of knowledge acquisition, processing, and retrieval in agentic AI for telecom systems. We first provide a comprehensive review of generative information retrieval strategies, including traditional retrieval, hybrid retrieval, semantic retrieval, knowledge-based retrieval, and agentic contextual retrieval. We then analyze their advantages, limitations, and suitability for various networking scenarios. Next, we present a survey about their applications in communications and networking. Additionally, we introduce an agentic contextual retrieval framework to enhance telecom-specific planning by integrating multi-source retrieval, structured reasoning, and self-reflective validation. Experimental results demonstrate that our framework significantly improves answer accuracy, explanation consistency, and retrieval efficiency compared to traditional and semantic retrieval methods. Finally, we outline future research directions.

Mutation analysis of deep neural networks (DNNs) is a promising method for effective evaluation of test data quality and model robustness, but it can be computationally expensive, especially for large models. To alleviate this, we present DEEPMAACC, a technique and a tool that speeds up DNN mutation analysis through neuron and mutant clustering. DEEPMAACC implements two methods: (1) neuron clustering to reduce the number of generated mutants and (2) mutant clustering to reduce the number of mutants to be tested by selecting representative mutants for testing. Both use hierarchical agglomerative clustering to group neurons and mutants with similar weights, with the goal of improving efficiency while maintaining mutation score. DEEPMAACC has been evaluated on 8 DNN models across 4 popular classification datasets and two DNN architectures. When compared to exhaustive, or vanilla, mutation analysis, the results provide empirical evidence that neuron clustering approach, on average, accelerates mutation analysis by 69.77%, with an average -26.84% error in mutation score. Meanwhile, mutant clustering approach, on average, accelerates mutation analysis by 35.31%, with an average 1.96% error in mutation score. Our results demonstrate that a trade-off can be made between mutation testing speed and mutation score error.