A New Probabilistic Output Constrained Optimization Extreme Learning Machine

In near decades machine learning approaches have received overwhelming attention from many researchers for solving problems that cannot be ironed out by traditional approaches. However, most of these approaches produces output that is not equivalent to the probability estimates of how credible and reliable the output can be for each prediction. One widely utilized, highly accorded for generalized performance but non-probabilistic machine learning algorithm is the Extreme Learning Machine (ELM). As with other classification systems, ELM generates outputs that cannot be treated as probabilities. Current literature shows approaches attempt to assimilate probabilistic concept in ELM however their outputs are not equivalent to probabilities. Furthermore, these methods invoke two-stage post processing procedures with iterative learning procedures which are against the salient features of ELM that highlight no iterative operations involved in learning. Hence, we want to probe in this paper the ability of ELM to produce probabilistic output from the original architecture of ELM itself while preserving the merits of ELM without the need for a post processing two-stage procedures to convert the output to probability and eliminates iterative learning to compute output weights. Two methodologies of unified probabilistic ELM framework are presented, i.e., Probabilistic Output Extreme Learning Machine (PO-ELM) and Constrained Optimization Posterior Probabilistic Outputs based Extreme Learning Machine (CPP-POELM). The proposed models are evaluated empirically on several benchmark datasets as well as real world power system applications to demonstrate its validity and efficacy in handling pattern classification problems as well as decision making process.