相关论文: Ultrametric OGP - parametric RDT \emph{symmetric} …
In this paper, we address the challenge of solving large-scale graph-structured nonlinear programs (gsNLPs) in a scalable manner. GsNLPs are problems in which the objective and constraint functions are associated with nodes on a graph and…
Recent studies show that a reproducing kernel Hilbert space (RKHS) is not a suitable space to model functions by neural networks as the curse of dimensionality (CoD) cannot be evaded when trying to approximate even a single ReLU neuron…
We present a fast algorithm for global rigid symmetry detection with approximation guarantees. The algorithm is guaranteed to find the best approximate symmetry of a given shape, to within a user-specified threshold, with very high…
A frame is a generalization of a basis of a vector space to a redundant overspanning set whose vectors are linearly dependent. Frames find applications in signal processing and quantum information theory. We present a genetic algorithm that…
Parameter retrieval and model inversion are key problems in remote sensing and Earth observation. Currently, different approximations exist: a direct, yet costly, inversion of radiative transfer models (RTMs); the statistical inversion with…
We present a new algorithmic paradigm for the decentralized solution of graph-structured optimization problems that arise in the estimation and control of network systems. A key and novel design concept of the proposed approach is that it…
Given a point $A$ in the convex hull of a given adjoint orbit $\mathcal{O}(F)$ of a compact Lie group $G$, we give a polynomial time algorithm to compute the probability density supported on $\mathcal{O}(F)$ whose expectation is $A$ and…
Mirror descent (MD) is a powerful first-order optimization technique that subsumes several optimization algorithms including gradient descent (GD). In this work, we develop a semi-definite programming (SDP) framework to analyze the…
There has been considerable progress in implicit neural representation to upscale an image to any arbitrary resolution. However, existing methods are based on defining a function to predict the Red, Green and Blue (RGB) value from just four…
The Orthogonal Frequency Division Multiplexing (OFDM) is one of the most widely adopted schemes in wireless technologies such as Wi-Fi and LTE due to its high transmission rates, and the robustness against Intersymbol Interference (ISI).…
$ $We study the $d$-Uniform Hypergraph Matching ($d$-UHM) problem: given an $n$-vertex hypergraph $G$ where every hyperedge is of size $d$, find a maximum cardinality set of disjoint hyperedges. For $d\geq3$, the problem of finding the…
The radius and diameter are fundamental graph parameters. They are defined as the minimum and maximum of the eccentricities in a graph, respectively, where the eccentricity of a vertex is the largest distance from the vertex to another…
We study the theoretical limits of the $\ell_0$ (quasi) norm based optimization algorithms when employed for solving classical compressed sensing or sparse regression problems. Considering standard contexts with deterministic signals and…
Optimal transport (OT) distances between probability distributions are parameterized by the ground metric they use between observations. Their relevance for real-life applications strongly hinges on whether that ground metric parameter is…
A single McCulloch-Pitts neuron, that is, the simple perceptron is studied, with focus on the region beyond storage capacity. It is shown that Parisi's hierarchical ansatz for the overlap matrix of the synaptic couplings with so called…
We study the problem of approximately counting matchings in hypergraphs of bounded maximum degree and maximum size of hyperedges. With an activity parameter $\lambda$, each matching $M$ is assigned a weight $\lambda^{|M|}$. The counting…
We study the problem of detecting local geometry in random graphs. We introduce a model $\mathcal{G}(n, p, d, k)$, where a hidden community of average size $k$ has edges drawn as a random geometric graph on $\mathbb{S}^{d-1}$, while all…
We study the problem of detecting the presence of a single unknown spike in a rectangular data matrix, in a high-dimensional regime where the spike has fixed strength and the aspect ratio of the matrix converges to a finite limit. This…
This paper deals with the problem of detecting non-isotropic high-dimensional geometric structure in random graphs. Namely, we study a model of a random geometric graph in which vertices correspond to points generated randomly and…
Decentralized optimization with orthogonality constraints is found widely in scientific computing and data science. Since the orthogonality constraints are nonconvex, it is quite challenging to design efficient algorithms. Existing…