Learning Trees of $\ell_0$-Minimization Problems
The problem of computing minimally sparse solutions of under-determined linear systems is $NP$ hard in general. Subsets with extra properties, may allow efficient algorithms, most notably problems with the restricted isometry property (RIP) can be solved by convex $\ell_1$-minimization. While these classes have been very successful, they leave out many practical applications. In this paper, we consider adaptable classes that are tractable after training on a curriculum of increasingly difficult samples. The setup is intended as a candidate model for a human mathematician, who may not be able to tackle an arbitrary proof right away, but may be successful in relatively flexible subclasses, or areas of expertise, after training on a suitable curriculum.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Multivariate Dyadic Regression Trees for Sparse Learning Problems
We propose a new nonparametric learning method based on multivariate dyadic regression trees (MDRTs). Unlike traditional dyadic decision trees (DDTs) or classification and regression trees (CARTs), MDRTs are constructed…
General ClassificationregressionSparse LearningVariable SelectionNew characterizations of minimum spanning trees and of saliency maps based on quasi-flat zones
We study three representations of hierarchies of partitions: dendrograms (direct representations), saliency maps, and minimum spanning trees. We provide a new bijection between saliency maps and hierarchies based on quas…
Ease of dependency distance minimization in star-like structures
The syntactic structure of a sentence can be represented as a tree where edges indicate syntactic dependencies between words. When that structure is a star, it has been demonstrated that the head should be placed in the …
Positive-Unlabeled Learning using Random Forests via Recursive Greedy Risk Minimization
The need to learn from positive and unlabeled data, or PU learning, arises in many applications and has attracted increasing interest. While random forests are known to perform well on many tasks with positive and negati…
Feature ImportanceWeakly Supervised ClassificationRobust Optimal Classification Trees Against Adversarial Examples
Decision trees are a popular choice of explainable model, but just like neural networks, they suffer from adversarial examples. Existing algorithms for fitting decision trees robust against adversarial examples are greed…
Classification