相关论文: Wirtinger gradient descent methods for low-dose Po…
Natural gradient descent is a principled method for adapting the parameters of a statistical model on-line using an underlying Riemannian parameter space to redefine the direction of steepest descent. The algorithm is examined via methods…
The goal of this paper is to debunk and dispel the magic behind black-box optimizers and stochastic optimizers. It aims to build a solid foundation on how and why the techniques work. This manuscript crystallizes this knowledge by deriving…
Projective Norms are a class of tensor norms that map on the input and output spaces. These norms are useful for providing a measure of entanglement. Calculating the projective norms is an NP-hard problem, which creates challenges in…
In this paper, the problem of distributed optimization is studied via a network of agents. Each agent only has access to a noisy gradient of its own objective function, and can communicate with its neighbors via a network. To handle this…
In many problems in machine learning and operations research, we need to optimize a function whose input is a random variable or a probability density function, i.e. to solve optimization problems in an infinite dimensional space. On the…
Solving a Poisson equation is generally reduced to solving a linear system with a coefficient matrix $A$ of entries $a_{ij}$, $i,j=1,2,...,n$, from the discretized Poisson equation. Although the variational quantum algorithms are promising…
Gaussian Boson Sampling (GBS) is a near-term platform for photonic quantum computing. Applications have been developed which rely on directly programming GBS devices, but the ability to train and optimize circuits has been a key missing…
The principal limitation in many areas of astronomy, especially for directly imaging exoplanets, arises from instability in the point spread function (PSF) delivered by the telescope and instrument. To understand the transfer function, it…
Approximation of subdifferentials is one of the main tasks when computing descent directions for nonsmooth optimization problems. In this article, we propose a bisection method for weakly lower semismooth functions which is able to compute…
It seems that in the current age, computers, computation, and data have an increasingly important role to play in scientific research and discovery. This is reflected in part by the rise of machine learning and artificial intelligence,…
Prediction-correction algorithms are a highly effective class of methods for solving pseudo-convex optimization problems. The descent direction of these algorithms can be viewed as an adjustment to the gradient direction based on the…
This paper investigates the application of mini-batch gradient descent to semiflows (gradient flows). Given a loss function (potential), we introduce a continuous version of mini-batch gradient descent by randomly selecting sub-loss…
Robust Bayesian inference using density power divergence (DPD) has emerged as a promising approach for handling outliers in statistical estimation. Although the DPD-based posterior offers theoretical guarantees of robustness, its practical…
Particle-optimization-based sampling (POS) is a recently developed effective sampling technique that interactively updates a set of particles. A representative algorithm is the Stein variational gradient descent (SVGD). We prove, under…
A fundamental task in phase retrieval is to recover an unknown signal $\vx\in \Rn$ from a set of magnitude-only measurements $y_i=\abs{\nj{\va_i,\vx}}, \; i=1,\ldots,m$. In this paper, we propose two novel perturbed amplitude models (PAMs)…
In this study, we consider an optimization problem with uncertainty dependent on decision variables, which has recently attracted attention due to its importance in machine learning and pricing applications. In this problem, the gradient of…
In this paper, a methodology is investigated for signal recovery in the presence of non-Gaussian noise. In contrast with regularized minimization approaches often adopted in the literature, in our algorithm the regularization parameter is…
Most existing methodologies of estimating low-rank matrices rely on Burer-Monteiro factorization, but these approaches can suffer from slow convergence, especially when dealing with solutions characterized by a large condition number,…
Accurate quantum tomography is a vital tool in both fundamental and applied quantum science. It is a task that involves processing a noisy measurement record in order to construct a reliable estimate of an unknown quantum state, and is…
We propose a new algorithm to learn a dictionary for reconstructing and sparsely encoding signals from measurements without phase. Specifically, we consider the task of estimating a two-dimensional image from squared-magnitude measurements…