  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.
