Related papers: A sharp oracle inequality for Graph-Slope
Here we consider the problem of denoising features associated to complex data, modeled as signals on a graph, via a smoothness prior. This is motivated in part by settings such as single-cell RNA where the data is very high-dimensional, but…
This work studies the denoising of piecewise smooth graph signals that exhibit inhomogeneous levels of smoothness over a graph, where the value at each node can be vector-valued. We extend the graph trend filtering framework to denoising…
The maximization for the independence systems defined on graphs is a generalization of combinatorial optimization problems such as the maximum $b$-matching, the unweighted MAX-SAT, the matchoid, and the maximum timed matching problems. In…
The sparse inverse covariance estimation problem is commonly solved using an $\ell_{1}$-regularized Gaussian maximum likelihood estimator known as "graphical lasso", but its computational cost becomes prohibitive for large data sets. A…
Consider the following generalization of the classic binary search problem: A searcher is required to find a hidden target vertex $x$ in a graph $G$. To do so, they iteratively perform queries to an oracle, each about a chosen vertex $v$.…
Learning a graph topology to reveal the underlying relationship between data entities plays an important role in various machine learning and data analysis tasks. Under the assumption that structured data vary smoothly over a graph, the…
In this article we propose a new concept of a $(\delta,L)$-model of a function which generalizes the concept of the $(\delta,L)$-oracle (Devolder-Glineur-Nesterov). Using this concept we describe the gradient descent method and the fast…
We consider sum-type strongly convex optimization problem (first term) with smooth convex not proximal friendly composite (second term). We show that the complexity of this problem can be split into optimal number of incremental oracle…
We study a number of graph exploration problems in the following natural scenario: an algorithm starts exploring an undirected graph from some seed node; the algorithm, for an arbitrary node $v$ that it is aware of, can ask an oracle to…
The Frank-Wolfe optimization algorithm has recently regained popularity for machine learning applications due to its projection-free property and its ability to handle structured constraints. However, in the stochastic learning setting, it…
The fused lasso, also known as (anisotropic) total variation denoising, is widely used for piecewise constant signal estimation with respect to a given undirected graph. The fused lasso estimate is highly nontrivial to compute when the…
In this letter, we study distributed optimization, where a network of agents, abstracted as a directed graph, collaborates to minimize the average of locally-known convex functions. Most of the existing approaches over directed graphs are…
In this paper, a new numerical method based on adaptive gradient descent optimizers is provided for computing the implied volatility from the Black-Scholes (B-S) option pricing model. It is shown that the new method is more accurate than…
We consider the problem of signal recovery on graphs as graphs model data with complex structure as signals on a graph. Graph signal recovery implies recovery of one or multiple smooth graph signals from noisy, corrupted, or incomplete…
Solutions to the Traveling Salesperson Problem (TSP) have practical applications to processes in transportation, logistics, and automation, yet must be computed with minimal delay to satisfy the real-time nature of the underlying tasks.…
Spectral graph sparsification aims to find ultra-sparse subgraphs which can preserve spectral properties of original graphs. In this paper, a new spectral criticality metric based on trace reduction is first introduced for identifying…
There has been significant recent progress on algorithms for approximating graph spanners, i.e., algorithms which approximate the best spanner for a given input graph. Essentially all of these algorithms use the same basic LP relaxation, so…
Existing graph contrastive learning methods rely on augmentation techniques based on random perturbations (e.g., randomly adding or dropping edges and nodes). Nevertheless, altering certain edges or nodes can unexpectedly change the graph…
We consider the problem of jointly learning row-wise and column-wise dependencies of matrix-variate observations, which are modelled separately by two precision matrices. Due to the complicated structure of Kronecker-product precision…
The Restricted Shortest Path (RSP) problem, also known as the Delay-Constrained Least-Cost (DCLC) problem, is an NP-hard bicriteria optimization problem on graphs with $n$ vertices and $m$ edges. In a graph where each edge is assigned a…