  This paper proposes a novel optimization principle and its implementation for
unsupervised anomaly detection in sound (ADS) using an autoencoder (AE). The
goal of unsupervised-ADS is to detect unknown anomalous sound without training
data of anomalous sound. Use of an AE as a normal model is a state-of-the-art
technique for unsupervised-ADS. To decrease the false positive rate (FPR), the
AE is trained to minimize the reconstruction error of normal sounds and the
anomaly score is calculated as the reconstruction error of the observed sound.
Unfortunately, since this training procedure does not take into account the
anomaly score for anomalous sounds, the true positive rate (TPR) does not
necessarily increase. In this study, we define an objective function based on
the Neyman-Pearson lemma by considering ADS as a statistical hypothesis test.
The proposed objective function trains the AE to maximize the TPR under an
arbitrary low FPR condition. To calculate the TPR in the objective function, we
consider that the set of anomalous sounds is the complementary set of normal
sounds and simulate anomalous sounds by using a rejection sampling algorithm.
Through experiments using synthetic data, we found that the proposed method
improved the performance measures of ADS under low FPR conditions. In addition,
we confirmed that the proposed method could detect anomalous sounds in real
environments.
