Search Results for author:
Found 49 papers, 18 papers with code
Manopt, a Matlab toolbox for optimization on manifolds
Optimization on manifolds is a rapidly developing branch of nonlinear optimization.
Sparse plus low-rank autoregressive identification in neuroimaging time series
This paper considers the problem of identifying multivariate autoregressive (AR) sparse plus low-rank graphical models.
Heterogeneous Tensor Decomposition for Clustering via Manifold Optimization
In contrast to existing techniques, we propose a new clustering algorithm that alternates between different modes of the proposed heterogeneous tensor model.
Riemannian preconditioning for tensor completion
We propose a novel Riemannian preconditioning approach for the tensor completion problem with rank constraint.
Understanding symmetries in deep networks
Consequently, training the network boils down to using stochastic gradient descent updates on the unit-norm manifold.
Symmetry-invariant optimization in deep networks
Recent works have highlighted scale invariance or symmetry that is present in the weight space of a typical deep network and the adverse effect that it has on the Euclidean gradient based stochastic gradient descent optimization.
Scaled stochastic gradient descent for low-rank matrix completion
The paper looks at a scaled variant of the stochastic gradient descent algorithm for the matrix completion problem.
A Riemannian gossip approach to decentralized matrix completion
In this paper, we propose novel gossip algorithms for the low-rank decentralized matrix completion problem.
Riemannian stochastic variance reduced gradient on Grassmann manifold
In this paper, we propose a novel Riemannian extension of the Euclidean stochastic variance reduced gradient algorithm (R-SVRG) to a compact manifold search space.
Low-rank tensor completion: a Riemannian manifold preconditioning approach
We propose a novel Riemannian manifold preconditioning approach for the tensor completion problem with rank constraint.
Riemannian stochastic variance reduced gradient algorithm with retraction and vector transport
In recent years, stochastic variance reduction algorithms have attracted considerable attention for minimizing the average of a large but finite number of loss functions.
Riemannian stochastic quasi-Newton algorithm with variance reduction and its convergence analysis
The present paper proposes a Riemannian stochastic quasi-Newton algorithm with variance reduction (R-SQN-VR).
Structured low-rank matrix learning: algorithms and applications
We consider the problem of learning a low-rank matrix, constrained to lie in a linear subspace, and introduce a novel factorization for modeling such matrices.
A Riemannian gossip approach to subspace learning on Grassmann manifold
Interesting applications in this setting include low-rank matrix completion and low-dimensional multivariate regression, among others.
A two-dimensional decomposition approach for matrix completion through gossip
The problem of matrix completion especially uses it to decompose a sparse matrix into two non sparse, low rank matrices which can then be used to predict unknown entries of the original matrix.
A dual framework for low-rank tensor completion
One of the popular approaches for low-rank tensor completion is to use the latent trace norm regularization.
Inductive Framework for Multi-Aspect Streaming Tensor Completion with Side Information
Besides the tensors, in many real world scenarios, side information is also available in the form of matrices which also grow in size with time.
E-commerce Anomaly Detection: A Bayesian Semi-Supervised Tensor Decomposition Approach using Natural Gradients
In addition, we use Polya-Gamma data augmentation for the semi-supervised Bayesian tensor decomposition.
A Unified Framework for Domain Adaptation using Metric Learning on Manifolds
We present a novel framework for domain adaptation, whereby both geometric and statistical differences between a labeled source domain and unlabeled target domain can be integrated by exploiting the curved Riemannian geometry of statistical manifolds.
Low-rank geometric mean metric learning
We propose a low-rank approach to learning a Mahalanobis metric from data.
A Unified Framework for Structured Low-rank Matrix Learning
We consider the problem of learning a low-rank matrix, constrained to lie in a linear subspace, and introduce a novel factorization for modeling such matrices.
Riemannian Stochastic Recursive Gradient Algorithm with Retraction and Vector Transport and Its Convergence Analysis
Stochastic variance reduction algorithms have recently become popular for minimizing the average of a large, but finite number of loss functions on a Riemannian manifold.
Learning Multilingual Word Embeddings in Latent Metric Space: A Geometric Approach
Our approach decouples learning the transformation from the source language to the target language into (a) learning rotations for language-specific embeddings to align them to a common space, and (b) learning a similarity metric in the common space to model similarities between the embeddings.
McTorch, a manifold optimization library for deep learning
In this paper, we introduce McTorch, a manifold optimization library for deep learning that extends PyTorch.
Inexact trust-region algorithms on Riemannian manifolds
We consider an inexact variant of the popular Riemannian trust-region algorithm for structured big-data minimization problems.
Riemannian adaptive stochastic gradient algorithms on matrix manifolds
We propose novel stochastic gradient algorithms for problems on Riemannian matrix manifolds by adapting the row and column subspaces of gradients.
Riemannian joint dimensionality reduction and dictionary learning on symmetric positive definite manifold
Dictionary leaning (DL) and dimensionality reduction (DR) are powerful tools to analyze high-dimensional noisy signals.
Low-rank approximations of hyperbolic embeddings
While the hyperbolic manifold is well-studied in the literature, it has gained interest in the machine learning and natural language processing communities lately due to its usefulness in modeling continuous hierarchies.
Detection of Review Abuse via Semi-Supervised Binary Multi-Target Tensor Decomposition
In this paper, our focus is on detecting such abusive entities (both sellers and reviewers) by applying tensor decomposition on the product reviews data.
Riemannian optimization on the simplex of positive definite matrices
In this work, we generalize the probability simplex constraint to matrices, i. e., $\mathbf{X}_1 + \mathbf{X}_2 + \ldots + \mathbf{X}_K = \mathbf{I}$, where $\mathbf{X}_i \succeq 0$ is a symmetric positive semidefinite matrix of size $n\times n$ for all $i = \{1,\ldots, K \}$.
Geometry-aware Domain Adaptation for Unsupervised Alignment of Word Embeddings
We propose a novel manifold based geometric approach for learning unsupervised alignment of word embeddings between the source and the target languages.
A Simple Approach to Learning Unsupervised Multilingual Embeddings
Recent progress on unsupervised learning of cross-lingual embeddings in bilingual setting has given impetus to learning a shared embedding space for several languages without any supervision.
Learning Geometric Word Meta-Embeddings
We propose a geometric framework for learning meta-embeddings of words from different embedding sources.
Efficient Robust Optimal Transport with Application to Multi-Label Classification
Optimal transport (OT) is a powerful geometric tool for comparing two distributions and has been employed in various machine learning applications.
Manifold optimization for non-linear optimal transport problems
In this work, we discuss how to computationally approach general non-linear OT problems within the framework of Riemannian manifold optimization.
SPOT: A framework for selection of prototypes using optimal transport
In this work, we develop an optimal transport (OT) based framework to select informative prototypical examples that best represent a given target dataset.
On Riemannian Optimization over Positive Definite Matrices with the Bures-Wasserstein Geometry
We build on this to show that the BW metric is a more suitable and robust choice for several Riemannian optimization problems over ill-conditioned SPD matrices.
Learning with symmetric positive definite matrices via generalized Bures-Wasserstein geometry
Learning with symmetric positive definite (SPD) matrices has many applications in machine learning.
Riemannian block SPD coupling manifold and its application to optimal transport
In this work, we study the optimal transport (OT) problem between symmetric positive definite (SPD) matrix-valued measures.
Riemannian Hamiltonian methods for min-max optimization on manifolds
In this paper, we study min-max optimization problems on Riemannian manifolds.
Differentially private Riemannian optimization
We introduce a framework of differentially private Riemannian optimization by adding noise to the Riemannian gradient on the tangent space.
Riemannian accelerated gradient methods via extrapolation
In this paper, we propose a simple acceleration scheme for Riemannian gradient methods by extrapolating iterates on manifolds.
ProtoBandit: Efficient Prototype Selection via Multi-Armed Bandits
In this work, we propose a multi-armed bandit-based framework for identifying a compact set of informative data instances (i. e., the prototypes) from a source dataset $S$ that best represents a given target set $T$.
Rieoptax: Riemannian Optimization in JAX
We present Rieoptax, an open source Python library for Riemannian optimization in JAX.
Generalised Spherical Text Embedding
The proposed modelling and the novel similarity metric exploits the matrix structure of embeddings.
Light-weight Deep Extreme Multilabel Classification
Extreme multi-label (XML) classification refers to the task of supervised multi-label learning that involves a large number of labels.
A Framework for Bilevel Optimization on Riemannian Manifolds
We provide convergence and complexity analysis for the proposed hypergradient descent algorithm on manifolds.
A Gauss-Newton Approach for Min-Max Optimization in Generative Adversarial Networks
It modifies the Gauss-Newton method to approximate the min-max Hessian and uses the Sherman-Morrison inversion formula to calculate the inverse.
Federated Learning on Riemannian Manifolds with Differential Privacy
To the best of our knowledge, this is the first federated learning framework on Riemannian manifold with a privacy guarantee and convergence results.
