What Strategy can I use to apply Machine Learning to Mineral Processing?

Summary

Machine learning (ML) is, in some ways, a new field of application to mineral processing. Yet, it can be argued that machine learning should have been introduced into mineral processing mathematical modelling over 100 years ago.

The author started to write this article as an example of the application of machine learning to comminution.? However, as the article evolved it became apparent that I should first provide a general discussion about machine learning and in a second article provide an example.

What is Machine Learning?

When one tries to identify precisely what ‘machine learning’ is, then they can be understandably confused. Indeed, the definition I use here may not be agreed upon by some readers.? However, in the interests of a working definition, I here define machine learning as:

“A method by which mathematical models of a process are derived by analysing the data, generally with a feedback response”.

Most definitions of ML provide some comment such as: “machine learning is a sub-branch of artificial intelligence”.? I avoid this categorisation, for reasons that will become apparent in this article.

A simple diagram illuminating the machine learning process is shown in Figure 1.

Figure 1 Main conceptual basis of machine learning requiring a feedback loop to improve the mathematical model of the process.

Machine learning was applied long before machine learning was defined.

It is important to recognise that machine learning techniques were developed many years before machine learning was defined.? It would be a bold statement to say when the first machine learning problem was solved.? The first application of Machine Learning is attributed to Samuel, 1949 (see Figure 2).

Figure 2 In 1949, Samuel developed an algorithm which he applied to the game: checkers.? This algorithm is often accredited as the first application of ML.

A milestone step in machine learning was the development of Statistical Mechanics late 1800s. (In turn, Statistical Mechanics led to Quantum Mechanics in the early 1900s.)? The foundation of Statistical Mechanics was probability theory.

Yet these developments occurred long before Machine Learning was coined as a subject area (Samuel,? 1959).? Samuel worked for IBM – and it is clear that his focus of machine learning was ‘computers’ not ‘mathematics’.

Hence machine learning experts are generally recognised as computer experts rather than mathematicians.? The temptation is to apply machine learning via black-box computer algorithms – of which the most popular class of software is neural networks.? Hence machine learning fits in well with the ‘dialogue’ of artificial intelligence.

Is ML a sub-branch of mathematics or computer science?

Yet, as has been explained one can consider ML as a mathematical sub-branch, and indeed fits in well with probability theory (without diminishing the value of other branches of mathematics).

And so we reach an impasse. Many definitions of machine learning are based on software and data.

For example:

“Machine learning is a branch of artificial intelligence that enables algorithms to uncover hidden patterns within datasets. It allows them to predict new, similar data without explicit programming for each task.” (Geek for geeks)

?Such definitions (which I call a purist definition) ignore both: the importance of mathematics, and already available mathematical models.

And so, the ML purist will seem dismissive of mathematics.? Indeed one can give simple ML maths problems to an ML expert with the full expectation that they cannot solve the problem unless they can do repeated experiments and rely on ‘artificial intelligence’.?

One needs to use whatever method is available.? The use of both software and mathematics is complementary.? The dismissal of mathematical approaches displays ignorance.

Prior? to ML

So from a mathematical viewpoint it is worth considering where ML is derived from.? My viewpoint is that one key foundation of ML is ‘Information theory’ (IT), which itself is a form of ‘probability theory’.? Again, I do not wish to bog down on the definition of IT.? Here I use Jaynes’ definition:

“Information theory provides a constructive criterion for setting up probability distributions on the basis of partial knowledge, and leads to a type of statistical inference which is called the maximum-entropy estimate. It is the least biased estimate possible on the given information.”

This sounds a lot like ML doesn’t it!? Hence, I am comfortable in arguing that IT is a foundational approach to ML.

When should have Information Theory been introduced into Mineral Processing?

From ?Jayne’s definition, we see the use of the word ‘probability’; and so it can be argued that IT is only relevant to a subject area if that subject area can be modelled using probabilities.? In the case of mineral processing, all unit operations, and all mathematical analysis methods such as mass balancing can be described as probabilistic systems.? Hence IT is fundamental to mineral processing.? I would tend to argue that the importance of IT to Mineral processing could have realistically been established in the 1960s.

However, such an integration would have occurred only if:

1.?????? ?Mineral processors recognised that most of their unit operations could be described as probabilistic systems.

2.?????? They developed strong collaborative links with probabilitists.

3.?????? Both sides were able to articulate their needs and skills.

4.?????? There would have been opportunity to gain market acceptance of the approach.

This did not occur; and still has not occurred.? Much of the weakness is item 4.? This is fundamentally due to the fact that there is an emphasis on existing methods under the guise of ‘industry standards’.

Available courses

This author offers courses on simulation, unit modelling, information theory and information theory-based machine learning both: directly and via pre-prepared online courses.

However, the two key courses that I want to focus on here are:

1.??? 'Practical Introduction to Information Theory'

2.?????? ‘Information Theory (IT) as a basis for Machine Learning (ML)’

In course 1, I largely expand on what is discussed in this article.? I provide many examples relevant to mineral processing.

In course 2, I focus primarily on some of the techniques to progress from information theory to machine learning (which in the first instance only requires a single feedback).? I primarily use as an example the logic game: Mastermind. ?Market acceptance of this course is poor – so I have added an example of mineral processing.? That example is to be discussed in the next article of this series.

Figure 3? The game Mastermind provides a great example of applying? IT to ML

References

For details on Samuel’s contribution to Machine Learning: https://en.wikipedia.org/wiki/Arthur_Samuel_(computer_scientist)

Jaynes E.T. Information Theory and Statistical Mechanics.? Phys. Rev.?106, 620 –?Published 15 May, 1957. Information Theory and Statistical Mechanics | Phys. Rev.