# DAVIDSTUTZ

21thOCTOBER2019

Jie Ren, Peter J. Liu, Emily Fertig, Jasper Snoek, Ryan Poplin, Mark A. DePristo, Joshua V. Dillon, Balaji Lakshminarayanan. Likelihood Ratios for Out-of-Distribution Detection. ICML Workshop, 2019.

Ren et al. propose a simple likelihood ratio test for out-of-distribution detection. The idea is based on the input samples consisting of background information and semantic, category-specific information. Thus, the likelihood $p(x)$ can be split up into $p(x_B)p(x_S)$ of background features $x_B$ and semantic features $x_S$. Then, given a in-distribution model $p_\theta(x)$ and a background model $p_{\theta_0}$, the likelihood test considers

$LLR(x) = \frac{p_\theta(x)}{p_{\theta_0}(x)}$.

Assuming that both models capture the background information equally well ($p_\theta(x_B) \approx p_{\theta_0}(x_B)$) and substituting the factorization, leads to a simple test:

$LLR(x) \approx \log p_\theta(x_S) - \log p_{\theta_0}(x_S)$.

In practice, the models are obtained using PixelCNN++; for the background model, random noise is applied (see the paper for details). Unfortunately, it is not entirely clear how the semantic features $x_S$ are determined to compute the likelihood ratio.