Subspace Learning with Partial Information

TL;DR

This paper investigates subspace learning when only partial attribute information is available per instance, proposing efficient algorithms and analyzing their sample complexity to address this challenge.

Contribution

It introduces novel algorithms for subspace learning with partial data and provides theoretical analysis of their sample complexity.

Findings

Algorithms achieve efficient subspace learning with limited attribute observations.

Sample complexity bounds are established for the proposed methods.

The methods perform well in partial information settings, reducing data requirements.

Abstract

The goal of subspace learning is to find a $k$-dimensional subspace of $\mathbb{R}^d$, such that the expected squared distance between instance vectors and the subspace is as small as possible. In this paper we study subspace learning in a partial information setting, in which the learner can only observe $r \le d$ attributes from each instance vector. We propose several efficient algorithms for this task, and analyze their sample complexity