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A latent space model for a family of random graphs assigns real-valued vectors to nodes of the graph such that edge probabilities are determined by latent positions. Latent space models provide a natural statistical framework for graph…
This paper presents distributed conjugate gradient algorithms for distributed parameter estimation and spectrum estimation over wireless sensor networks. In particular, distributed conventional conjugate gradient (CCG) and modified…
Computing the stationary distributions of a continuous-time Markov chain (CTMC) involves solving a set of linear equations. In most cases of interest, the number of equations is infinite or too large, and the equations cannot be solved…
In recent years, electric vehicle (EV) charging station has experienced an increasing supply-demand mismatch due to its fluctuating renewables and unpredictable charging demand. To reduce its operating cost, this paper proposes a…
We propose a novel distributed inference algorithm for continuous graphical models, by extending Stein variational gradient descent (SVGD) to leverage the Markov dependency structure of the distribution of interest. Our approach combines…
An optimization problem is at the heart of many robotics estimating, planning, and optimum control problems. Several attempts have been made at model-based multi-robot localization, and few have formulated the multi-robot collaborative…
This paper studies the statistical model of the non-centered mixture of scaled Gaussian distributions (NC-MSG). Using the Fisher-Rao information geometry associated to this distribution, we derive a Riemannian gradient descent algorithm.…
The stochastic gradient descent (SGD) algorithm is the algorithm we use to train neural networks. However, it remains poorly understood how the SGD navigates the highly nonlinear and degenerate loss landscape of a neural network. In this…
Motivated by a geometric problem, we introduce a new non-convex graph partitioning objective where the optimality criterion is given by the sum of the Dirichlet eigenvalues of the partition components. A relaxed formulation is identified…
This paper considers a distributed stochastic strongly convex optimization, where agents connected over a network aim to cooperatively minimize the average of all agents' local cost functions. Due to the stochasticity of gradient estimation…
This paper presents distributed adaptive algorithms based on the conjugate gradient (CG) method for distributed networks. Both incremental and diffusion adaptive solutions are all considered. The distributed conventional (CG) and modified…
The configuration model is a standard tool for uniformly generating random graphs with a specified degree sequence, and is often used as a null model to evaluate how much of an observed network's structure can be explained by its degree…
This paper investigates the optimal allocation of large language model (LLM) inference workloads across heterogeneous edge data centers over time. Each data center features on-site renewable generation and faces dynamic electricity prices…
We compute the stationary distribution of a continuous-time Markov chain which is constructed by gluing together two finite, irreducible Markov chains by identifying a pair of states of one chain with a pair of states of the other and…
We give computable bounds on the rate of convergence of the transition probabilities to the stationary distribution for a certain class of geometrically ergodic Markov chains. Our results are different from earlier estimates of Meyn and…
The in-memory graph layout or organization has a considerable impact on the time and energy efficiency of distributed memory graph computations. It affects memory locality, inter-task load balance, communication time, and overall memory…
We derive and analyze new diffusion approximations of stationary distributions of Markov chains that are based on second- and higher-order terms in the expansion of the Markov chain generator. Our approximations achieve a higher degree of…
In this paper, we investigate a distributed learning scheme for a broad class of stochastic optimization problems and games that arise in signal processing and wireless communications. The proposed algorithm relies on the method of matrix…
This paper presents the formulation and analysis of a novel distributed maximum likelihood algorithm that utilizes a first-order optimization scheme. The proposed approach utilizes a static average consensus algorithm to reach agreement on…
This work provides a simplified proof of the statistical minimax optimality of (iterate averaged) stochastic gradient descent (SGD), for the special case of least squares. This result is obtained by analyzing SGD as a stochastic process and…