  Real-world datasets often exhibit imbalanced data distribution, where certain
class levels are severely underrepresented. In such cases, traditional pattern
classifiers have shown a bias towards the majority class, impeding accurate
predictions for the minority class. This paper introduces an imbalanced
data-oriented approach using probabilistic neural networks (PNNs) with a skew
normal probability kernel to address this major challenge. PNNs are known for
providing probabilistic outputs, enabling quantification of prediction
confidence and uncertainty handling. By leveraging the skew normal
distribution, which offers increased flexibility, particularly for imbalanced
and non-symmetric data, our proposed Skew Probabilistic Neural Networks
(SkewPNNs) can better represent underlying class densities. To optimize the
performance of the proposed approach on imbalanced datasets, hyperparameter
fine-tuning is imperative. To this end, we employ a population-based heuristic
algorithm, Bat optimization algorithms, for effectively exploring the
hyperparameter space. We also prove the statistical consistency of the density
estimates which suggests that the true distribution will be approached smoothly
as the sample size increases. Experimental simulations have been conducted on
different synthetic datasets, comparing various benchmark-imbalanced learners.
Our real-data analysis shows that SkewPNNs substantially outperform
state-of-the-art machine learning methods for both balanced and imbalanced
datasets in most experimental settings.
