Tutorial on logistic-regression calibration and fusion:converting a score to a likelihood ratio

Abstract

Logistic-regression calibration and fusion are potential steps in the calculation of forensic likelihood ratios. The present paper provides a tutorial on logisticregression calibration and fusion at a practical conceptual level with minimal mathematical complexity. A score is log-likelihood-ratio like in that it indicates the degree of similarity of a pair of samples while taking into consideration their typicality with respect to a model of the relevant population. A higher-valued score provides more support for the same-origin hypothesis over the differentorigin hypothesis than does a lower-valued score; however, the absolute values of scores are not interpretable as log likelihood ratios. Logistic-regression calibration is a procedure for converting scores to log likelihood ratios, and logistic-regression fusion is a procedure for converting parallel sets of scores from multiple forensic-comparison systems to log likelihood ratios. Logisticregression calibration and fusion were developed for automatic speaker recognition and are popular in forensic voice comparison. They can also be applied in other branches of forensic science, a fingerprint/finger-mark example is provided.

Avoiding overstating the strength of forensic evidence: Shrunk likelihood ratios/Bayes factors

“…In contrast, when the separation between the categories is greater and the amount of data is small, the increases in the ELUB 15 A potential alternative that avoids the sudden truncation could be to fit a sigmoidal function in the logistic space [45]. 16 We believe that this range of amount of sample data and range of separation between the categories is sufficient to gain an understanding of the relative behaviour of the procedures and to conceptually interpolate and extrapolate within and beyond these ranges. Other values can easily be substituted into the software we provide.…”

“…5 and 6 are based on 100 points per category, and with separations between the means of 2 and 4 variance units respectively. 16 Given a larger amount of training data (Figs. 5 and 6), the relative effect of shrinkage is less.…”

“…Another model which explicitly includes shrinkage is regularized logistic regression. In score-based approaches to likelihood ratio calculation, logistic regression is a popular model for score to likelihood ratio conversion (aka calibration; e.g., [14][15][16]). Small amounts of regularization can be applied to logistic regression to avoid numerical problems in parameter estimation.…”

Speech Replay Spoofing Attack Detection System Based on Fusion of Classification Algorithms

“…We use the state-of-the-art approach from Matlab Bosaris toolkit [4]. It provides a logistic regression solution, which can train combination weights to fuse multiple subsystems into a single subsystem, which outputs well-calibrated log-likelihoodratios.…”

“…The main idea behind our system is the fusion of scores [4] given by a set of binary classification algorithms to obtain better classification results. We opted for some common speaker modelling techniques such as Gaussian mixture models (GMM) [5], GMM based universal background models (UBM) and i-vectors [6,7].…”