## Generative Probabilistic Novelty Detection with Adversarial Autoencoders

Stanislav Pidhorskyi, Ranya Almohsen, Donald Adjeroh, and Gianfranco Doretto

In: Advances in Neural Information Processing Systems (NeurIPS). 2018 , pp. 6821–6832 .

We propose a new method for approaching novelty/anomaly detection. Novelty detection is needed when you want to distinguish between inlier and outlier samples. However, you have training data only for inliers, while for outliers training data is not available. This is a very frequent scenario for real-world problems when outliers are infrequent and may have unknown distribution.

Please refer to the paper for all details, here I'll provide a brief summary of the method plus some implementation-related details.

### Model

We assume, that training data (inliers) $x_1, \dots, x_N; \ x_i\in \mathbb{R}^m; \ i = 1, \cdots, N$ are draw from a model:

$x_i = f(z_i) + \xi_i \qquad z_i \in \Omega \subset \mathbb{R}^n$

where $\xi_i$ - is noise, and $f(.)$ is a mapping $f:\Omega \rightarrow \mathbb{R}^m$ that defines a manifold $\mathcal{M} \equiv f(\Omega)$. Thus, $z_i$ - are coordinates of the point on the manifold.

We also definean an inverse function $g: \mathbb{R}^m \rightarrow \mathbb{R}^n$, such that for every point that belongs to the manifold$x \in \mathcal{M}$, composition of functions gives identity fucntion: $f(g(x))=x$.