… Section 3 provides an overview of the state of the art in probabilistic dimensionality reduction…
probabilistic nature of the generative LVMs to explicitly provide distributions over the metric …

… We generalize the concept of a metric space by associating a cumulative distribution function,
… be an ordinary metric space with the distancefunction d(a, b). We call a probabilistic metric …

This distinctly nonclassical treatment focuses on developing aspects that differ from the
theory of ordinary metric spaces, working directly with probability distribution functions rather …

… metrics has been intractable for complex network geometries. … In summary, the probabilistic
distance models presented in … distribution of network performance metrics, and the explicit …

… We define a notion of a set of metric spaces that probabilistically-approximates another
metric space. We prove that any metric space can be probabilistically-approximated by …

… Probabilistic metric spaces were first introduced by K. Menger in 1942 and reconsidered by
… In concluding this introduction we remark that products of probabilistic metric spaces have …

… Menger, who dealt with probabilistic geometry. The new theory of fundamental probabilistic
… The main influence upon the development of the theory of probabilistic metric spaces is …

… 6), we will return to the question of a synthetic versus metric approach to geometry. The
definition states that in order to prove {S, L,d} is a metric geometry, we need to find for each le L a …

… of probabilistic geometry has been researched in the field of mathematics for well over 50
years. Applying the intrinsic yet unintuitive metrics … distance and discrimination metrics are both …

… , namely failure probability (FP), on the aortic wall using aorta geometries at the systolic and
… probabilistic FP metric had more discriminative power than the deterministic Tsai-Hill metric, …