Related papers: Low-complexity subspace-descent over symmetric pos…
The goal of this paper is to show how different machine learning tools on the Riemannian manifold $\mathcal{P}_d$ of Symmetric Positive Definite (SPD) matrices can be united under a probabilistic framework. For this, we will need several…
In this paper, we utilize stochastic optimization to reduce the space complexity of convex composite optimization with a nuclear norm regularizer, where the variable is a matrix of size $m \times n$. By constructing a low-rank estimate of…
We propose new Riemannian preconditioned algorithms for low-rank tensor completion via the polyadic decomposition of a tensor. These algorithms exploit a non-Euclidean metric on the product space of the factor matrices of the low-rank…
Symmetric Positive Definite (SPD) matrices have been widely used for data representation in many visual recognition tasks. The success mainly attributes to learning discriminative SPD matrices with encoding the Riemannian geometry of the…
Large-scale optimization problems arising from the discretization of problems involving PDEs sometimes admit solutions that can be well approximated by low-rank matrices. In this paper, we will exploit this low-rank approximation property…
In this paper, we introduce some new iterative optimisation algorithms on Riemannian manifolds and Hilbert spaces which have good global convergence guarantees to local minima. More precisely, these algorithms have the following properties:…
As the problem of minimizing functionals on the Wasserstein space encompasses many applications in machine learning, different optimization algorithms on $\mathbb{R}^d$ have received their counterpart analog on the Wasserstein space. We…
Subspace learning and matrix factorization problems have great many applications in science and engineering, and efficient algorithms are critical as dataset sizes continue to grow. Many relevant problem formulations are non-convex, and in…
This paper considers a stochastic optimization problem over the fixed point sets of quasinonexpansive mappings on Riemannian manifolds. The problem enables us to consider Riemannian hierarchical optimization problems over complicated sets,…
In recent years, various subspace algorithms have been developed to handle large-scale optimization problems. Although existing subspace Newton methods require fewer iterations to converge in practice, the matrix operations and full…
Riemannian meta-optimization provides a promising approach to solving non-linear constrained optimization problems, which trains neural networks as optimizers to perform optimization on Riemannian manifolds. However, existing Riemannian…
Direct search methods represent a robust and reliable class of algorithms for solving black-box optimization problems. In this paper, we explore the application of those strategies to Riemannian optimization, wherein minimization is to be…
The subgradient method is a classical and foundational approach in non-smooth convex optimization; its simplicity, robustness, and role as a conceptual and algorithmic starting point have made it the backbone of many significant…
Low-rank tensor completion aims to recover a tensor from partially observed entries, and it is widely applicable in fields such as quantum computing and image processing. Due to the significant advantages of the tensor train (TT) format in…
We propose an L-BFGS optimization algorithm on Riemannian manifolds using minibatched stochastic variance reduction techniques for fast convergence with constant step sizes, without resorting to linesearch methods designed to satisfy Wolfe…
Orthogonality constraints naturally appear in many machine learning problems, from principal component analysis to robust neural network training. They are usually solved using Riemannian optimization algorithms, which minimize the…
The Symmetric Positive Definite (SPD) matrices have received wide attention for data representation in many scientific areas. Although there are many different attempts to develop effective deep architectures for data processing on the…
Spectral compressed sensing involves reconstructing a spectral-sparse signal from a subset of uniformly spaced samples, with applications in radar imaging and wireless channel estimation. By fully exploiting the signal structures, this…
Stochastic gradient descent type methods are ubiquitous in machine learning, but they are only applicable to the optimization of differentiable functions. Proximal algorithms are more general and applicable to nonsmooth functions. We…
Nonsmooth Riemannian optimization has attracted increasing attention, especially in problems with sparse structures. While existing formulations typically involve convex nonsmooth terms, incorporating nonsmooth difference-of-convex (DC)…