This tutorial will cover the area of mobile robot localisation and mapping. Beginning with the simple cases of Bayesian localisation and feature based mapping, the tutorial will progress to consider the full Simultaneous Localisation and Mapping (SLAM) problem. This is in many ways a cornerstone of current and future autonomous mobile systems and has been a subject of intense research over the last five years. If we want to send machines into a-priori unknown settings we need robust, embedded SLAM - something that still eludes us. Both Kalman and sample based approaches will be covered. The tutorial will also give time to some major outstanding issues in the area--in particular the loop closing problem (the task of deciding if the current local workspace intesects with an already mapped region) and recent work on appearance based methods.

Bayesian methods provide a sound statistical framework for modelling and decision making. However, most simple parametric models are not realistic for modelling real-world data. Non-parametric models are much more flexible and therefore are much more likely to capture our beliefs about the data. They also often result in better predictive performance.

I will give a survey/tutorial of the field of non-parametric Bayesian statistics from the perspective of machine learning (a slightly revised version of my tutorial at the 2005 UAI Conference). Topics will include:

• The need for non-parametric models
• A very brief review of Gaussian processes
• Chinese restaurant processes, different constructions, Pitman-Yor processes
• Dirichlet processes, Dirichlet process mixtures
• Polya trees
• Dirichlet diffusion trees
• Time permitting, some new work on Indian buffet processes

Dirichlet processes (DPs) are the most widely used class of Bayesian nonparametric models. DPs are most commonly used for mixture modelling where the nonparametric nature of DPs provide an elegant alternative to model selection of finite mixtures. Hierarchical Dirichlet processes (HDPs) are an extension of DPs to mixture modelling of grouped data, where mixture components can be shared across different groups. I shall give an in depth tutorial into both DPs and HDPs. In particular I shall cover the different representations of DPs and HDPs and applications of DPs and HDPs in a variety of fields. If time permits I shall touch upon generalizations of these models and inference schemes.

In this talk I will present a Bayesian approach to ranking a set of objects based on the possibly partial or noisy rankings of small subsets of objects. Rankings are represented by assigning a latent real-valued variable (skill, urgency, value) to each object and sorting the objects according to the magnitude of the latent variables. The system maintains a Gaussian belief about the value of each object in terms of mean and variance. I will discuss approximate message passing in factor graphs as the computational technique to address the problem of inference.

After presenting theoretical and algorithmic aspects of the system, I will outline two applications:

• TrueSkill -- Ranking of players: The system is used to provide matchmaking and leaderboard functionality based on the estimated skills of players. An implementation of the system is currently at the heart of ranking and matchmaking in the online gaming service Xbox Live, used by 1 million players playing approximately 500,000 ranked matches every 24 hours.
• Liberty -- Ranking of potential moves in Computer Go: The system is used to learn the values of local patterns based on the moves played in a given position. The “winner” is determined by observing which one of the legal moves in a given position has been played by an expert player. The result is a probability distribution over moves for a given position. It can serve, for example, as fast stand-alone Go engine of respectable playing strength. The current system plays at 10-15 kyu and correctly predicts expert moves in 34% of the cases.