Abstract
Binary classification is one of the central problems in machine-learning research and, as such, investigations of its general statistical properties are of interest. We studied the ranking statistics of items in binary classification problems and observed that there is a formal and surprising relationship between the probability of a sample belonging to one of the two classes and the Fermi-Dirac distribution determining the probability that a fermion occupies a given single-particle quantum state in a physical system of noninteracting fermions. Using this equivalence, it is possible to compute a calibrated probabilistic output for binary classifiers. We show that the area under the receiver operating characteristics curve (AUC) in a classification problem is related to the temperature of an equivalent physical system. In a similar manner, the optimal decision threshold between the two classes is associated with the chemical potential of an equivalent physical system. Using our framework, we also derive a closed-form expression to calculate the variance for the AUC of a classifier. Finally, we introduce FiDEL (Fermi-Dirac-based ensemble learning), an ensemble learning algorithm that uses the calibrated nature of the classifier's output probability to combine possibly very different classifiers.
Highlights
We explore the application of the FD statistics in machine learning in the context of binary classification problems
We present a conceptual parallel between certain statistical properties in binary classification problems and the FD
The problem of binary classification is a fundamental task in machine learning
Summary
Where sP,i and sN ,k are the scores assigned by the classifier to the ith positive examples and the k th negative examples, respectively, and H(s) is the Heaviside function that takes the value of 1 for positive arguments and 0 for negative arguments. To determine the extent to which class-conditional dependence influences the performance of the FiDEL ensemble we developed a model (SI Appendix) that simulates the situation in which all pairs of classifiers in the ensemble have a conditional rank correlation given both the positive and the negative class equal to a parameter r, which we varied between 0 (uncorrelated case) and 0.6. The WoC ensemble is a classifier whose score for a given item can be computed as the average of the ranks assigned by the base classifiers to that item The results of these simulations, summarized in SI Appendix, Figs. In a previous section we demonstrated that the threshold for segregating the positive and the negative classes that zeroes the log-likelihood ratio is the threshold that maximizes the balance accuracy, and we did so by expressing the balance accuracy in terms of the class-conditioned rank probabilities of the classifier. Given that yr can take only the values 1 and 0, its mean value yr in the (N , N1) ensemble is equal
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
