Out-of-Distribution Detection using Maximum Entropy Coding

TL;DR

This paper introduces a novel out-of-distribution detection method using maximum entropy coding in latent space, combining theoretical foundations with neural network transformations, and demonstrates improved anomaly detection performance over existing methods.

Contribution

It generalizes Kolmogorov-Martin-Löf randomness to continuous distributions using maximum entropy distributions and develops a new out-of-distribution detection approach with neural networks.

Findings

Outperforms existing anomaly detection methods in most cases

Provides a theoretical framework with desirable properties

Utilizes maximum entropy distributions in latent space for detection

Abstract

Given a default distribution $P$ and a set of test data $x^M=\{x_1,x_2,\ldots,x_M\}$ this paper seeks to answer the question if it was likely that $x^M$ was generated by $P$. For discrete distributions, the definitive answer is in principle given by Kolmogorov-Martin-L\"{o}f randomness. In this paper we seek to generalize this to continuous distributions. We consider a set of statistics $T_1(x^M),T_2(x^M),\ldots$. To each statistic we associate its maximum entropy distribution and with this a universal source coder. The maximum entropy distributions are subsequently combined to give a total codelength, which is compared with $-\log P(x^M)$. We show that this approach satisfied a number of theoretical properties. For real world data $P$ usually is unknown. We transform data into a standard distribution in the latent space using a bidirectional generate network and use maximum entropy coding there. We compare the resulting method to other methods that also used generative neural networks to detect anomalies. In most cases, our results show better performance.