# Random Coordinate Descent Methods for Minimizing Decomposable Submodular Functions

@article{Ene2015RandomCD, title={Random Coordinate Descent Methods for Minimizing Decomposable Submodular Functions}, author={Alina Ene and Huy L. Nguyen}, journal={ArXiv}, year={2015}, volume={abs/1502.02643} }

Submodular function minimization is a fundamental optimization problem that arises in several applications in machine learning and computer vision. The problem is known to be solvable in polynomial time, but general purpose algorithms have high running times and are unsuitable for large-scale problems. Recent work have used convex optimization techniques to obtain very practical algorithms for minimizing functions that are sums of "simple" functions. In this paper, we use random coordinate… Expand

#### 36 Citations

Quadratic Decomposable Submodular Function Minimization

- Computer Science, Mathematics
- NeurIPS
- 2018

This work introduces a new convex optimization problem, termed quadratic decomposable submodular function minimization, and describes an objective that may be optimized via random coordinate descent methods and projections onto cones and establishes the linear convergence rate of the RCD algorithm. Expand

Fast Decomposable Submodular Function Minimization using Constrained Total Variation

- Mathematics, Computer Science
- NeurIPS
- 2019

A modified convex problem requiring constrained version of the total variation oracles that can be solved with significantly fewer calls to the simple minimization oracles is considered. Expand

Quadratic Decomposable Submodular Function Minimization: Theory and Practice

- 2020

We introduce a new convex optimization problem, termed quadratic decomposable submodular function minimization (QDSFM), which allows to model a number of learning tasks on graphs and hypergraphs. The… Expand

Quadratic Decomposable Submodular Function Minimization: Theory and Practice

- Computer Science, Mathematics
- J. Mach. Learn. Res.
- 2020

A new convex optimization problem, termed quadratic decomposable submodular function minimization (QDSFM), which allows to model a number of learning tasks on graphs and hypergraphs and two new applications of QDSFM are described: hypergraph-adapted PageRank and semi-supervised learning. Expand

Decomposable Submodular Function Minimization via Maximum Flow

- Computer Science
- ICML
- 2021

This paper bridges discrete and continuous optimization approaches for decomposable submodular function minimization, in both the standard and parametric settings. We provide improved running times… Expand

Geometric Rescaling Algorithms for Submodular Function Minimization

- Computer Science, Mathematics
- SODA
- 2018

A new class of polynomial-time algorithms for submodular function minimization (SFM), as well as a unified framework to obtain stronglyPolynomial SFM algorithms, which can be applied to a wide range of combinatorial and continuous algorithms, including pseudo-polynomial ones. Expand

Subquadratic submodular function minimization

- Mathematics, Computer Science
- STOC
- 2017

For integer-valued submodular functions, this paper gives an SFM algorithm which runs in O(nM3logn· EO) time giving the first nearly linear time algorithm in any known regime. Expand

Minimizing a Submodular Function from Samples

- Computer Science, Mathematics
- NIPS
- 2017

There is a class of submodular functions with range in [0, 1] such that, despite being PAC-learnable and minimizable in polynomial-time, no algorithm can obtain an approximation strictly better than 1/2 − o(1) using polynomially-many samples drawn from any distribution. Expand

Greed is good : greedy optimization methods for large-scale structured problems

- Computer Science
- 2018

This dissertation shows that greedy coordinate descent and Kaczmarz methods have efficient implementations and can be faster than their randomized counterparts for certain common problem structures in machine learning, and shows linear convergence for greedy (block) coordinate descent methods under a revived relaxation of strong convexity from 1963. Expand

Convex Optimization for Parallel Energy Minimization

- Computer Science, Mathematics
- ArXiv
- 2015

This work reformulates the quadratic energy minimization problem as a total variation denoising problem, which, when viewed geometrically, enables the use of projection and reflection based convex methods and performs an extensive empirical evaluation comparing state-of-the-art combinatorial algorithms and convex optimization techniques. Expand

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