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Found 18 papers, 6 papers with code
A Stochastic-Gradient-based Interior-Point Algorithm for Solving Smooth Bound-Constrained Optimization Problems
A stochastic-gradient-based interior-point algorithm for minimizing a continuously differentiable objective function (that may be nonconvex) subject to bound constraints is presented, analyzed, and demonstrated through experimental results.
Boosting RANSAC via Dual Principal Component Pursuit
In this paper, we revisit the problem of local optimization in RANSAC.
A Stochastic Sequential Quadratic Optimization Algorithm for Nonlinear Equality Constrained Optimization with Rank-Deficient Jacobians
A sequential quadratic optimization algorithm is proposed for solving smooth nonlinear equality constrained optimization problems in which the objective function is defined by an expectation of a stochastic function.
A Subspace Acceleration Method for Minimization Involving a Group Sparsity-Inducing Regularizer
We consider the problem of minimizing an objective function that is the sum of a convex function and a group sparsity-inducing regularizer.
Optimization and Control 49M37, 65K05, 65K10, 65Y20, 68Q25, 90C30, 90C60
Sequential Quadratic Optimization for Nonlinear Equality Constrained Stochastic Optimization
It is assumed in this setting that it is intractable to compute objective function and derivative values explicitly, although one can compute stochastic function and gradient estimates.
Self-Representation Based Unsupervised Exemplar Selection in a Union of Subspaces
When the dataset is drawn from a union of independent subspaces, our method is able to select sufficiently many representatives from each subspace.
Is an Affine Constraint Needed for Affine Subspace Clustering?
Specifically, our analysis provides conditions that guarantee the correctness of affine subspace clustering methods both with and without the affine constraint, and shows that these conditions are satisfied for high-dimensional data.
Basis Pursuit and Orthogonal Matching Pursuit for Subspace-preserving Recovery: Theoretical Analysis
The goal is to have the representation $c$ correctly identify the subspace, i. e. the nonzero entries of $c$ should correspond to columns of $A$ that are in the subspace $\mathcal{S}_0$.
What is the Largest Sparsity Pattern that Can Be Recovered by 1-Norm Minimization?
In the case of the partial discrete Fourier transform, our characterization of the largest sparsity pattern that can be recovered requires the unknown signal to be real and its dimension to be a prime number.
Gradient flows and proximal splitting methods: A unified view on accelerated and stochastic optimization
We show that similar discretization schemes applied to Newton's equation with an additional dissipative force, which we refer to as accelerated gradient flow, allow us to obtain accelerated variants of all these proximal algorithms -- the majority of which are new although some recover known cases in the literature.
Conformal Symplectic and Relativistic Optimization
Arguably, the two most popular accelerated or momentum-based optimization methods in machine learning are Nesterov's accelerated gradient and Polyaks's heavy ball, both corresponding to different discretizations of a particular second order differential equation with friction.
Dual Principal Component Pursuit: Probability Analysis and Efficient Algorithms
However, its geometric analysis is based on quantities that are difficult to interpret and are not amenable to statistical analysis.
Scalable Exemplar-based Subspace Clustering on Class-Imbalanced Data
Our experiments demonstrate that the proposed method outperforms state-of-the-art subspace clustering methods in two large-scale image datasets that are imbalanced.
A Nonsmooth Dynamical Systems Perspective on Accelerated Extensions of ADMM
Recently, there has been great interest in connections between continuous-time dynamical systems and optimization methods, notably in the context of accelerated methods for smooth and unconstrained problems.
Provable Self-Representation Based Outlier Detection in a Union of Subspaces
While outlier detection methods based on robust statistics have existed for decades, only recently have methods based on sparse and low-rank representation been developed along with guarantees of correct outlier detection when the inliers lie in one or more low-dimensional subspaces.
Oracle Based Active Set Algorithm for Scalable Elastic Net Subspace Clustering
Our geometric analysis also provides a theoretical justification and a geometric interpretation for the balance between the connectedness (due to $\ell_2$ regularization) and subspace-preserving (due to $\ell_1$ regularization) properties for elastic net subspace clustering.
Ranked #7 on
Image Clustering
on coil-100
(Accuracy metric)
Trading-Off Cost of Deployment Versus Accuracy in Learning Predictive Models
For the challenging real-world application of risk prediction for sepsis in intensive care units, the use of our regularizer leads to models that are in harmony with the underlying cost structure and thus provide an excellent prediction accuracy versus cost tradeoff.
Scalable Sparse Subspace Clustering by Orthogonal Matching Pursuit
Subspace clustering methods based on $\ell_1$, $\ell_2$ or nuclear norm regularization have become very popular due to their simplicity, theoretical guarantees and empirical success.
Ranked #6 on
Image Clustering
on Extended Yale-B
