Unsupervised Out-of-distribution Detection with DLSGAN

DLSGAN proposed a learning-based GAN inversion method with maximum likelihood estimation. In this paper, I propose a method for unsupervised out-of-distribution detection using the encoder of DLSGAN. When the DLSGAN converged, since the entropy of the scaled latent random variable is optimal to express in-distribution data, in-distribution data is densely mapped to latent codes with high likelihood. This enables the log-likelihood of the predicted latent code to be used for out-ofdistribution detection. 1. Out-of-distribution detection with DLSGAN DLSGAN [4] proposed a learning-based GAN inversion method with maximum likelihood estimation of the encoder. The encoder of DLSGAN maps input data to predicted latent code. In this paper, I propose a method for unsupervised out-of-distribution (OOD) detection using the encoder of DLSGAN. Simply, the log-likelihood of the predicted latent code of input data can be used for out-of-distribution detection. There are two characteristics that allow the DLSGAN encoder to be utilized for OOD detection. First is the entropy optimality. As DLSGAN training progresses, the entropy of scaled latent random variable decreases, and the entropy of the scaled encoder output increases. When DLSGAN is converged, the generator perfectly generates in-distribution data with a scaled latent random variable, and the entropy of scaled latent random variable and scaled encoder output becomes optimal entropy for expressing in-distribution data with generator and encoder. It means that indistribution data generated by the generator is densely mapped to latent codes with high likelihood. Therefore, by the pigeonhole principle, OOD data can only be mapped to latent codes with low likelihood. Secondly, elements of DLSGAN encoder output are independent of each other and follow a simple distribution (the same as latent distribution). Therefore, it is very easy to calculate the log-likelihood of predicted latent code. The following equation shows the negative log-likelihood of the predicted latent code of