Generative concept representations have three major advantages over discriminative ones: they can represent uncertainty, they support integration of learning and reasoning, and they are good for unsupervised and semi-supervised learning. We discuss probabilistic and generative deep learning, which generative concept representations are based on, and the use of variational autoencoders and generative adversarial networks for learning generative concept representations, particularly for concepts whose data are sequences, structured data or graphs.
The aim of this chapter is twofold. In the first part we will provide a brief overview of the mathematical and statistical foundations of graphical models, along with their fundamental properties, estimation and basic inference procedures. In particular we will develop Markov networks (also known as Markov random fields) and Bayesian networks, which comprise most past and current literature on graphical models. In the second part we will review some applications of graphical models in systems biology.
Probabilistic models can define relationships between variables and be used to calculate probabilities. For example, fully conditional models may require an enormous amount of data to cover all possible cases, and probabilities may be intractable to calculate in practice. Simplifying assumptions such as the conditional independence of all random variables can be effective, such as in the case of Naive Bayes, although it is a drastically simplifying step. An alternative is to develop a model that preserves known conditional dependence between random variables and conditional independence in all other cases. Bayesian networks are a probabilistic graphical model that explicitly capture the known conditional dependence with directed edges in a graph model.
Machine learning is an exciting topic about designing machines that can learn from examples. The course covers the necessary theory, principles and algorithms for machine learning. The methods are based on statistics and probability-- which have now become essential to designing systems exhibiting artificial intelligence. Reference textbooks for different parts of the course are "Pattern Recognition and Machine Learning" by Chris Bishop (Springer 2006) and "Probabilistic Graphical Models" by Daphne Koller and Nir Friedman (MIT Press 2009) and "Deep Learning" by Goodfellow, Bengio and Courville (MIT Press 2016).