Statistical Learning
Legendre Decomposition for Tensors
Mahito Sugiyama, Hiroyuki Nakahara, Koji Tsuda
We present a novel nonnegative tensor decomposition method, called Legendre decomposition, which factorizes an input tensor into a multiplicative combination of parameters. Thanks to the well-developed theory of information geometry, the reconstructed tensor is unique and always minimizes the KL divergence from an input tensor. We empirically show that Legendre decomposition can more accurately reconstruct tensors than other nonnegative tensor decomposition methods.
Generative Probabilistic Novelty Detection with Adversarial Autoencoders
Stanislav Pidhorskyi, Ranya Almohsen, Gianfranco Doretto
Novelty detection is the problem of identifying whether a new data point is considered to be an inlier or an outlier. We assume that training data is available to describe only the inlier distribution. Recent approaches primarily leverage deep encoder-decoder network architectures to compute a reconstruction error that is used to either compute a novelty score or to train a one-class classifier.