This work is about directed statistical graphical models, also known as Bayesian networks, and their applications in the fields of molecular biology, computer graphics and computer vision. In particular, it is about algorithms to learn a Bayesian network and to make efficient inference on it. First, we propose algorithms to learn a Bayesian network capable of simulating a process that is only known through independent samples taken from it. To learn a Bayesian network means to learn both the graph that encodes the relationships among the variables in the network, and the parameters of their conditional distributions. Second, we suggest efficient algorithms to perform inference on a class of Bayesian networks of importance in computer vision.

These algorithms are applied in the area of molecular biology to represent ensembles of proteins, leading to novel tools to compare structures and create new ones. Methodologies similar to those that proved useful in this context, were applied to the problem of texture analysis, synthesis and classification, yielding state of the art results. Next we study the application of directed graphical models to represent the distribution of mass in 3D space, and postulate laws that might be used to project these distributions to the 2D image plane. These models suggest a principled framework to make inferences about the 3D world from 2D images of it.