  In this work, we propose Sum-Product-Transform Networks (SPTN), an extension
of sum-product networks that uses invertible transformations as additional
internal nodes. The type and placement of transformations determine properties
of the resulting SPTN with many interesting special cases. Importantly, SPTN
with Gaussian leaves and affine transformations pose the same inference task
tractable that can be computed efficiently in SPNs. We propose to store affine
transformations in their SVD decompositions using an efficient parametrization
of unitary matrices by a set of Givens rotations. Last but not least, we
demonstrate that G-SPTNs achieve state-of-the-art results on the density
estimation task and are competitive with state-of-the-art methods for anomaly
detection.
