We use anisotropic diffusion processes to generalize normal distributions to manifolds and to construct a framework for likelihood estimation of template and covariance structure from manifold valued data. The procedure avoids the linearization that arise when first estimating a mean or template before performing PCA in the tangent space of the mean. We derive flow equations for the most probab...

Probabilistic logic programs have primarily studied the problem of entailment of probabilistic atoms. However, there are some interesting applications where we are interested in finding a possible world that is most probable. Our first result shows that the problem of computing such ”maximally probable worlds” (MPW) is intractable. We subsequently show that we can often greatly reduce the size ...

We introduce the M-Modes problem for graphical models: predicting the M label configurations of highest probability that are at the same time local maxima of the probability landscape. M-Modes have multiple possible applications: because they are intrinsically diverse, they provide a principled alternative to non-maximum suppression techniques for structured prediction, they can act as codebook...

In addition to computing the posterior distributions for hidden variables in Bayesian networks, one other important inference task is to find the most probable explanation (MPE). MPE provides the most likely configurations to explain away the evidence and helps to manage hypotheses for decision making. In recent years, researchers have proposed a few methods to find the MPE for discrete Bayesia...

Uncertainty is inevitable at every stage of the life cycle development of a product. To make use of probabilistic information and to make reliable decisions by incorporating decision maker’s risk attitude under uncertainty, methods for propagating the effect of uncertainty are therefore needed. When designing complex systems, the efficiency of methods for uncertainty analysis becomes critical. ...

The eeective action provides an appropriate cost function to determine most probable (or optimal) histories for nonlinear dynamics with strong noise. In such strong-coupling problems, a nonperturbative technique is required to calculate the eeective action. We have proposed a Rayleigh-Ritz variational approximation, which employs simple moment-closures or intuitive guesses of the statistics to ...

Multidimensional Bayesian network classifiers have gained popularity over the last few years due to their expressive power and their intuitive graphical representation. A drawback of this approach is that their use to perform multidimensional classification, a generalization of multi-label classification, can be very computationally demanding when there are a large number of class variables. Th...