Related papers: Adjusting PageRank parameters and Comparing result…

We study the PageRank mass of principal components in a bow-tie Web Graph, as a function of the damping factor c. Using a singular perturbation approach, we show that the PageRank share of IN and SCC components remains high even for very…

This paper is concerned with distributed computation of several commonly used centrality measures in complex networks. In particular, we propose deterministic algorithms, which converge in finite time, for the distributed computation of the…

Randomized algorithms are overwhelming methods for low-rank approximation that can alleviate the computational expenditure with great reliability compared to deterministic algorithms. A crucial thought is generating a standard Gaussian…

Learning-to-Rank (LTR) is a supervised machine learning approach that constructs models specifically designed to order a set of items or documents based on their relevance or importance to a given query or context. Despite significant…

We propose two basic assumptions, under which the rate of convergence of the augmented Lagrange method for a class of composite optimization problems is estimated. We analyze the rate of local convergence of the augmented Lagrangian method…

The question of knowing whether the policy Iteration algorithm (PI) for solving Markov Decision Processes (MDPs) has exponential or (strongly) polynomial complexity has attracted much attention in the last 50 years. Recently, Fearnley…

PageRank (PR) is a fundamental tool for assessing the relative importance of the nodes in a network. In this paper, we propose a measure, weighted PageRank (WPR), extended from the classical PR for weighted, directed networks with possible…

Low-Rank Adaptation (LoRA) lowers the computational and memory overhead of fine-tuning large models by updating a low-dimensional subspace of the pre-trained weight matrix. Albeit efficient, LoRA exhibits suboptimal convergence and…

Ranked search results have become the main mechanism by which we find content, products, places, and people online. Thus their ordering contributes not only to the satisfaction of the searcher, but also to career and business opportunities,…

Aligning large language models (LLMs) to human preferences is a crucial step in building helpful and safe AI tools, which usually involve training on supervised datasets. Popular algorithms such as Direct Preference Optimization (DPO) rely…

Ranking algorithms are fundamental to various online platforms across e-commerce sites to content streaming services. Our research addresses the challenge of adaptively ranking items from a candidate pool for heterogeneous users, a key…

Consider a random graph model where each possible edge $e$ is present independently with some probability $p_e$. Given these probabilities, we want to build a large/heavy matching in the randomly generated graph. However, the only way we…

It is known that the common factors in a large panel of data can be consistently estimated by the method of principal components, and principal components can be constructed by iterative least squares regressions. Replacing least squares…

Learning-to-rank (LTR) is a set of supervised machine learning algorithms that aim at generating optimal ranking order over a list of items. A lot of ranking models have been studied during the past decades. And most of them treat each…

Over the last decade, PageRank has gained importance in a wide range of applications and domains, ever since it first proved to be effective in determining node importance in large graphs (and was a pioneering idea behind Google's search…

Chance-constrained problems involve stochastic components in the constraints which can be violated with a small probability. We investigate the impact of different types of chance constraints on the performance of iterative search…

Previous researches have shown that adding local memory can accelerate the consensus. It is natural to ask questions like what is the fastest rate achievable by the $M$-tap memory acceleration, and what are the corresponding control…

Low Rank Approximation is among most fundamental subjects of numerical linear algebra having important applications to various areas of modern computing and %they range from machine learning theory and %neural networks to data mining and…

In this paper, we consider large-scale ranking problems where one is given a set of (possibly non-redundant) pairwise comparisons and the underlying ranking explained by those comparisons is desired. We show that stochastic gradient descent…

Graph matching---aligning a pair of graphs to minimize their edge disagreements---has received wide-spread attention from both theoretical and applied communities over the past several decades, including combinatorics, computer vision, and…