The random-cluster model has been widely studied as a unifying framework for random graphs, spin systems and electrical networks, but its dynamics have so far largely resisted analysis. In this paper we analyze the Glauber dynamics of the random-cluster model in the canonical case where the underlying graph is an n × n box in the Cartesian lattice Z. Our main result is a O(n log n) upper bound ...

Many machine learning algorithms have hyperparameters flags, values, and other configuration information that guides the algorithm. Sometimes this configuration applies to the space of functions that the learning algorithm searches (e.g. the number of nearest neighbours to use in KNN). Sometimes this configuration applies to the way in which the search is conducted (e.g. the step size in stocha...

I describe the basics of probability theory, statistical signal processing and information theory, and how these disciplines inter-relate to form the foundations of a theory of information processing. Examples are drawn from point-process applications. Johnson Basics of Information Processing 1 Probability theory Random variables can be either discrete or continuous valued. Discrete random vari...