Approximating Likelihood Ratios with Calibrated Discriminative Classifiers

Cranmer, Pavez & Louppe (2015)

Approximating Likelihood Ratios with Calibrated Discriminative Classifiers establishes that a classifier trained to distinguish two samples learns a monotone function of their likelihood ratio and that calibration can recover the ratio. This directly supports CLASSIFIER-RATIO-ORACLE; it does not bound the Fisher-information loss caused by calibration or approximation error. Direct density-ratio estimation (KLIEP, uLSIF and related methods) is a mature alternative to separately estimating component densities. Classifier posterior odds are another route. For ScoreQuant these are model-access backends, not the quantizer itself. Useful reference: Sugiyama, Suzuki & Kanamori, Density Ratio Estimation in Machine Learning.

Research-agent instruction

When a theorem depends on a density-ratio/classifier assumption, search the ratio-estimation literature separately from the quantization literature. Do not infer exact Fisher preservation merely from classifier discrimination performance.