Archive for July, 2017

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Lectures: Learning with Graphical Models

July 15, 2017

 

 

I’m giving a series of lectures this semester combining graphical models and some elements of nonparametric statistics.  The intent is to build up to the theory of discrete matrix factorisation and its many variations. The lectures start on 27th July and are mostly given weekly.  Weekly details are given in the calendar too.  The slides are on the Monash share drive under “Wray’s Slides” so if you are at Monash, do a search on Google drive to find them.  If you cannot find them, email me for access.

Motivating Probability and Decision Models, Lecture 1, 27/07/17, Wray Buntine
This is an introduction to motivation for using Bayesian methods, these days called “full probability modelling” by the cognoscenti, to avoid prior cultish associations and implications. We will look at modelling, causality, probability as frequency, and axiomatic underpinnings for reasoning, decisions, and belief . The importance of priors and computation form the basis of this.

No lectures 03/08 (writing for ACML) and 10/08 (attending ICML).

Information and working with Independence, Lecture 2, 17/08/17, Wray Buntine
This will continue with information (entropy) left over from the previous lecture.  Then we will look at the definition of independence and the some independence models, including its relationship with causality.  Basic directed and undirected models will be introduced.  Some example problems will be presented (simply) to tie these together:  simple bucket search, bandits, graph colouring and causal reasoning.

Directed and Undirected Independence Models, Lecture 3, 31/08/17, Wray Buntine
We will develop the basic properties and results for directed and undirected graphical models.  This includes testing for independence, developing the corresponding functional form, and understanding probability operations such as marginalising and conditioning.  To complete this section, we will also investigate operations on clique trees, to illustrate the principles.  We will not do full graphical model inference.

Basic Distributions and Poisson Processes, Lecture 4, 07/09/17, Wray Buntine
We review the standard discrete distributions, relationships, properties and conjugate distributions.  This includes deriving the Poisson distribution as an infinitely divisible distribution on natural numbers with a fixed rate.  Then we introduce Poisson point processes as a model of stochastic processes.  We show how they behave in both the discrete and continuous case, and how they have both constructive and axiomatic definitions.  The same definitions can be extended to any infinitely divisible distributions, so we use this to introduce the gamma process.  We illustrate Bayesian operations for the gamma process:  data likelihoods, conditioning on discrete evidence and marginalising.

No lectures the following two weeks, 14th and 21st September, as I will be on travel.

 

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