The least-squares probabilistic classifier (LSPC) is a computationally-efficient alternative to kernel logistic regression. However, to assure its learned probabilities to be non-negative, LSPC involves a post-processing step of rounding up negative parameters to zero, which can unexpectedly influence classification performance. In order to mitigate this problem, we propose a simple alternative scheme that directly rounds up the classifier's negative outputs, not negative parameters. Through extensive experiments including real-world image classification and audio tagging tasks, we demonstrate that the proposed modification significantly improves classification accuracy, while the computational advantage of the original LSPC remains unchanged.

Estimating the ratio of two probability density functions (a.k.a. the importance) has recently gathered a great deal of attention since importance estimators can be used for solving various machine learning and data mining problems. In this paper, we propose a new importance estimation method using a mixture of probabilistic principal component analyzers. The proposed method is more flexible than existing approaches, and is expected to work well when the target importance function is correlated and rank-deficient. Through experiments, we illustrate the validity of the proposed approach.