Quick sensitivity analysis for incremental data modification and its application to leave-one-out CV in linear classification problems

TL;DR

This paper presents a new sensitivity analysis framework for efficiently estimating the impact of small incremental data modifications on large-scale linear classifiers without full re-optimization, reducing computational costs.

Contribution

The paper introduces a novel framework that computes bounds on classifier updates efficiently, depending only on the number of updated instances, applicable to various sensitivity analysis tasks.

Findings

Framework provides tight bounds for classifier updates

Computational cost depends only on number of updated instances

Applicable to practical sensitivity analysis scenarios

Abstract

We introduce a novel sensitivity analysis framework for large scale classification problems that can be used when a small number of instances are incrementally added or removed. For quickly updating the classifier in such a situation, incremental learning algorithms have been intensively studied in the literature. Although they are much more efficient than solving the optimization problem from scratch, their computational complexity yet depends on the entire training set size. It means that, if the original training set is large, completely solving an incremental learning problem might be still rather expensive. To circumvent this computational issue, we propose a novel framework that allows us to make an inference about the updated classifier without actually re-optimizing it. Specifically, the proposed framework can quickly provide a lower and an upper bounds of a quantity on the unknown updated classifier. The main advantage of the proposed framework is that the computational cost of computing these bounds depends only on the number of updated instances. This property is quite advantageous in a typical sensitivity analysis task where only a small number of instances are updated. In this paper we demonstrate that the proposed framework is applicable to various practical sensitivity analysis tasks, and the bounds provided by the framework are often sufficiently tight for making desired inferences.