An efficient model-free estimation of multiclass conditional probability

TL;DR

This paper introduces a model-free approach to estimate multiclass conditional probabilities using conditional quantile regression, which is computationally efficient and effective for large class numbers.

Contribution

It proposes a novel model-free estimation method based on conditional quantile regression functions, avoiding restrictive distributional assumptions.

Findings

Highly competitive with existing methods

Efficient computation regardless of class number

Performs well with large class sets

Abstract

Conventional multiclass conditional probability estimation methods, such as Fisher's discriminate analysis and logistic regression, often require restrictive distributional model assumption. In this paper, a model-free estimation method is proposed to estimate multiclass conditional probability through a series of conditional quantile regression functions. Specifically, the conditional class probability is formulated as difference of corresponding cumulative distribution functions, where the cumulative distribution functions can be converted from the estimated conditional quantile regression functions. The proposed estimation method is also efficient as its computation cost does not increase exponentially with the number of classes. The theoretical and numerical studies demonstrate that the proposed estimation method is highly competitive against the existing competitors, especially when the number of classes is relatively large.