Many modern unsupervised or semi-supervised machine learning algorithms rely on
Bayesian probabilistic models. These models are usually intractable and thus require …

We propose a new regularization method based on virtual adversarial loss: a new measure
of local smoothness of the conditional label distribution given input. Virtual adversarial loss …

Sure to be influential, Watanabe's book lays the foundations for the use of algebraic
geometry in statistical learning theory. Many models/machines are singular: mixture models …

Face verification systems are prone to spoofing attacks on photos, videos, and 3D masks.
Face spoofing detection, ie, face anti-spoofing, face liveness detection, or face presentation …

Mathematical Theory of Bayesian Statistics introduces the mathematical foundation of
Bayesian inference which is well-known to be more accurate in many real-world problems …

In singular models, the optimal set of parameters forms an analytic set with singularities, and
a classical statistical inference cannot be applied to such models. This is significant for deep …

Recently, variational Bayesian (VB) techniques have been applied to probabilistic matrix
factorization and shown to perform very well in experiments. In this paper, we theoretically …

A learning machine is called singular if its Fisher information matrix is singular. Almost all
learning machines used in information processing are singular, for example, layered neural …

In this work, we advocate for the importance of singular learning theory (SLT) as it pertains to
the theory and practice of variational inference in Bayesian neural networks (BNNs). To …

In Penny et al.[Penny, W., Ghahramani, Z., Friston, KJ 2005. Bilinear dynamical systems.
Philos. Trans. R. Soc. Lond. B Biol. Sci. 360 (1457) 983–993], a particular case of the Linear …