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Found 12 papers, 0 papers with code
Semidefinite Relaxations of the Gromov-Wasserstein Distance
The Gromov-Wasserstein (GW) distance is a variant of the optimal transport problem that allows one to match objects between incomparable spaces.
Dictionary Learning under Symmetries via Group Representations
We apply our paradigm to investigate the dictionary learning problem for the groups SO(2) and SO(3).
Optimal Regularization for a Data Source
In this paper, we seek a systematic understanding of the power and the limitations of convex regularization by investigating the following questions: Given a distribution, what is the optimal regularizer for data drawn from the distribution?
Conjugation Invariant Learning with Neural Networks
Thus, a naturally significant class of functions consists of those that are intrinsic to the problem, in the sense of being independent of such base change or relabelling; in other words invariant under the conjugation action by a group.
Multiplicative updates for symmetric-cone factorizations
Given a matrix $X\in \mathbb{R}^{m\times n}_+$ with non-negative entries, the cone factorization problem over a cone $\mathcal{K}\subseteq \mathbb{R}^k$ concerns computing $\{ a_1,\ldots, a_{m} \} \subseteq \mathcal{K}$ and $\{ b_1,\ldots, b_{n} \} \subseteq~\mathcal{K}^*$ belonging to its dual so that $X_{ij} = \langle a_i, b_j \rangle$ for all $i\in [m], j\in [n]$.
A Non-commutative Extension of Lee-Seung's Algorithm for Positive Semidefinite Factorizations
The most widely used algorithm for computing NMFs of a matrix is the Multiplicative Update algorithm developed by Lee and Seung, in which nonnegativity of the updates is preserved by scaling with positive diagonal matrices.
Group Invariant Dictionary Learning
The dictionary learning problem concerns the task of representing data as sparse linear sums drawn from a smaller collection of basic building blocks.
Collaborative Inference for Efficient Remote Monitoring
While current machine learning models have impressive performance over a wide range of applications, their large size and complexity render them unsuitable for tasks such as remote monitoring on edge devices with limited storage and computational power.
A Note on Convex Relaxations for the Inverse Eigenvalue Problem
The affine inverse eigenvalue problem consists of identifying a real symmetric matrix with a prescribed set of eigenvalues in an affine space.
Optimization and Control 15A18, 15A29, 90C22
Fitting Tractable Convex Sets to Support Function Evaluations
Our numerical experiments highlight the utility of our framework over previous approaches in settings in which the measurements available are noisy or small in number as well as those in which the underlying set to be reconstructed is non-polyhedral.
Statistics Theory Computational Geometry Optimization and Control Statistics Theory
Learning Semidefinite Regularizers
The regularizers obtained using our framework can be employed effectively in semidefinite programming relaxations for solving inverse problems.
High-Dimensional Change-Point Estimation: Combining Filtering with Convex Optimization
We consider change-point estimation in a sequence of high-dimensional signals given noisy observations.
Statistics Theory Information Theory Information Theory Optimization and Control Statistics Theory
