Model-based machine learning

Abstract

Several decades of research in the field of machine learning have resulted in a multitude of different algorithms for solving a broad range of problems. To tackle a new application, a researcher typically tries to map their problem onto one of these existing methods, often influenced by their familiarity with specific algorithms and by the availability of corresponding software implementations. In this study, we describe an alternative methodology for applying machine learning, in which a bespoke solution is formulated for each new application. The solution is expressed through a compact modelling language, and the corresponding custom machine learning code is then generated automatically. This model-based approach offers several major advantages, including the opportunity to create highly tailored models for specific scenarios, as well as rapid prototyping and comparison of a range of alternative models. Furthermore, newcomers to the field of machine learning do not have to learn about the huge range of traditional methods, but instead can focus their attention on understanding a single modelling environment. In this study, we show how probabilistic graphical models, coupled with efficient inference algorithms, provide a very flexible foundation for model-based machine learning, and we outline a large-scale commercial application of this framework involving tens of millions of users. We also describe the concept of probabilistic programming as a powerful software environment for model-based machine learning, and we discuss a specific probabilistic programming language called Infer.NET, which has been widely used in practical applications.

Figure 1.

A neural network with two layers of adjustable parameters, in which each parameter corresponds to one of the links in the network. (Online version in colour.)

Figure 2.

A directed graphical model representing the joint probability distribution over three variables a, b and c, corresponding to the decomposition on the right-hand side of (4.2). (Online version in colour.)

Figure 3.

A directed acyclic graph over seven variables. This graph expresses a decomposition of the joint distribution given by (4.3). (Online version in colour.)

Figure 4.

Graphical model representation of a hidden Markov model. This same graph also represents a linear dynamical system. Here, the shaded nodes represent observed variables, i.e. ones whose values are fixed by the dataset. (Online version in colour.)

Figure 5.

An extension of the model in figure 4 to include auto-regressive dependencies. (Online version in colour.)

Figure 6.

An extension of the model in figure 4 to include input variables as well as outputs. (Online version in colour.)

Figure 7.

An extension of the model in figure 4 for multiple hidden Markov processes. (Online version in colour.)

Figure 8.

A simple Markov chain of variables. (Online version in colour.)

Figure 9.

Directed graph showing the TrueSkill model for a single game between two players. See the text for details. (Online version in colour.)

Figure 10.

Graph of skill levels for two players in an online game, showing the much faster convergence obtained using TrueSkill compared to the traditional Elo algorithm. (Online version in colour.)

Figure 11.

Modified skill rating graph showing the inclusion of three teams A, B and C, in which team B has two players. (Online version in colour.)

Figure 12.

Csoft code for the TrueSkill model.

Figure 13.

Flow diagram showing the operation of Infer.NET. (Online version in colour.)