Related papers: Autonomous Gaussian Decomposition
This work proposes A$^2$GD, a novel adaptive accelerated gradient descent method for convex and composite optimization. Smoothness and convexity constants are updated via Lyapunov analysis. Inspired by stability analysis in ODE solvers, the…
We present a novel computational approach for extracting weak signals, whose exact location and width may be unknown, from complex background distributions with an arbitrary functional form. We focus on datasets that can be naturally…
Dictionary learning is a cutting-edge area in imaging processing, that has recently led to state-of-the-art results in many signal processing tasks. The idea is to conduct a linear decomposition of a signal using a few atoms of a learned…
We present a systematic analysis of automatic differentiation (AD) applications in astrophysics, identifying domains where gradient-based optimization could provide significant computational advantages. Building on our previous work with…
Using gradient descent (GD) with fixed or decaying step-size is a standard practice in unconstrained optimization problems. However, when the loss function is only locally convex, such a step-size schedule artificially slows GD down as it…
By using the gravitational decoupling through the minimal geometric deformation approach (MGD-decoupling), we show a simple and powerful method to generate physically acceptable exact analytical solutions for anisotropic stellar…
Spectroscopic data may often contain unwanted extrinsic signals. For example, in ARPES experiment, a wire mesh is typically placed in front of the CCD to block stray photo-electrons, but could cause a grid-like structure in the spectra…
We present a cost-effective new approach for generating denser depth maps for Autonomous Driving (AD) and Autonomous Vehicles (AVs) by integrating the images obtained from deep neural network (DNN) 4D radar detectors with conventional…
Distributed Gaussian processes (DGPs) are prominent local approximation methods to scale Gaussian processes (GPs) to large datasets. Instead of a global estimation, they train local experts by dividing the training set into subsets, thus…
Gradient Descent (GD) is a ubiquitous algorithm for finding the optimal solution to an optimization problem. For reduced computational complexity, the optimal solution $\mathrm{x^*}$ of the optimization problem must be attained in a minimum…
3D Gaussian Splatting (3DGS) has emerged as a mainstream solution for novel view synthesis and 3D reconstruction. By explicitly encoding a 3D scene using a collection of Gaussian kernels, 3DGS achieves high-quality rendering with superior…
Nesterov's accelerated gradient descent (AGD), an instance of the general family of "momentum methods", provably achieves faster convergence rate than gradient descent (GD) in the convex setting. However, whether these methods are superior…
The goal of this paper is to present a theoretical and practical introduction to generalized eigendecomposition (GED), which is a robust and flexible framework used for dimension reduction and source separation in multichannel signal…
3D Gaussian Splatting reconstructs scenes by starting from a sparse Structure-from-Motion initialization and refining under-reconstructed regions. This process is slow, as it requires multiple densification steps where Gaussians are…
Context. Mathematical optimization can be used as a computational tool to obtain the optimal solution to a given problem in a systematic and efficient way. For example, in twice-differentiable functions and problems with no constraints, the…
Stochastic gradient descent (SGD) has taken the stage as the primary workhorse for large-scale machine learning. It is often used with its adaptive variants such as AdaGrad, Adam, and AMSGrad. This paper proposes an adaptive stochastic…
This paper introduces a novel error estimator for the Proper Generalized Decomposition (PGD) approximation of parametrized equations. The estimator is intrinsically random: It builds on concentration inequalities of Gaussian maps and an…
Coherent ptychographic imaging experiments often discard over 99.9 % of the flux from a light source to define the coherence of an illumination. Even when coherent flux is sufficient, the stability required during an exposure is another…
Stochastic Gradient Descent (SGD) is an out-of-equilibrium algorithm used extensively to train artificial neural networks. However very little is known on to what extent SGD is crucial for to the success of this technology and, in…
In this paper, we propose a probabilistic model with automatic relevance determination (ARD) for learning interpolative decomposition (ID), which is commonly used for low-rank approximation, feature selection, and identifying hidden…