Less Mathematical Approaches to Machine Learning?

Question

Out of curiosity, I've been reading up a bit on the field of Machine Learning, and I'm surprised at the amount of computation and mathematics involved. One book I'm reading through uses advanced concepts such as Ring Theory and PDEs (note: the only thing I know about PDEs is that they use that funny looking character). This strikes me as odd considering that mathematics itself is a hard thing to "learn."

Are there any branches of Machine Learning that use different approaches?

I would think that a approaches relying more on logic, memory, construction of unfounded assumptions, and over-generalizations would be a better way to go, since that seems more like the way animals think. Animals don't (explicitly) calculate probabilities and statistics; at least as far as I know.

Answer 1

The behaviour of the neurons in our brains is very complex, and requires some heavy duty math to model. So, yes we do calculate extremely complex math, but it's done in a way that we don't perceive.

I don't know whether the math you typically find in A.I. research is entirely due to the complexity of the natural neural systems being modelled. It may also be due, in part, to heuristic techniques that don't even attempt to model the mind (e.g., using convolution filters to recognise shapes).

Answer 2

If you want to avoid the math but do AI like stuff, you can always stick to simpler models. In 90% of the time, the simpler models will be good enough for real world problems.

I don't know of a track of AI that is completely decoupled from math though. Probability theory is the tool for handling uncertainty which plays a major role in AI. So even if there was not-so-mathematical subfield, math techniques would most be a way to improve on those methods. And thus the mathematics would be back in game. Even simple techniques like the naive Bayes and decision trees can be used without a lot of math, but the real understanding comes only through it.

Machine learning is very math heavy. It is sometimes said to be close to "computational statistics", with a little more focus on the computational side. You might want to check out "Collective Intelligence" by O'Reilly, though. I hear they have a good collection of ML techniques without math too hard.

Answer 3

You might find evolutionary computing approaches to machine learning a little less front-loaded with heavy-duty maths, approaches such as ant-colony optimisation or swarm intelligence.

I think you should put to one side, if you hold it as your question kind of suggests you do, the view that machine learning is trying to simulate what goes on in the brains of animals (including Homo Sapiens). A lot of the maths in modern machine learning arises from its basis in pattern recognition and matching; some of it comes from attempts to represent what is learnt as quasi-mathematical statements; some of it comes from the need to use statistical methods to compare different algorithms and approaches. And some of it comes because some of the leading practitioners come from scientific and mathematical backgrounds rather than computer science backgrounds, and they bring their toolset with them when they come.

And I'm very surprised that you are suprised that machine learning involves a lot of computation since the long history of AI has proven that it is extremely difficult to build machines which (seem to) think.

Answer 4

I attended a course in machine-learning last semester. The cognitive science chair at our university is very interested in symbolic machine learning (That's the stuff without mathematics or statistics ;o)). I can recommend two outstanding textbooks:

• Machine Learning (Thomas Mitchell)
• Artificial Intelligence: A Modern Approach (Russel and Norvig)

The first one is more focused on machine learning, but its very compact has got a very gentle learning curve. The second one is a very interesting read with many historical informations.

These two titles should give you a good overview (All aspects of machine learning not just symbolic approaches), so that you can decide for yourself which aspect you want to focus on.

Basically there is always mathematics involved but I find symbolic machine learning easier to start with because the ideas behind most approaches are often amazingly simple.

Answer 5

I've been thinking about this kind of stuff a lot lately.

Unfortunately, most engineer/mathematician types are so tied to their own familiar mathematical/computational worlds, they often forget to consider other paradigms.

Artists, for example, often think of the world in a very fluid way, usually untethered by mathematical models. Much of what happens in art is archetypal or symbolic, and often doesn't follow any seemingly conventional logical arrangement. There are, of course, very strong exceptions to this. Music, for instance, especially in music theory, often requires strong left brained processes and so forth. In truth, I would argue that even the most right brained activities are not devoid of left logic, but rather are more complex mathematical paradigms, like chaos theory is to the beauty of fractals. So the cross-over from left to right and back again is not a schism, but a symbiotic coupling. Humans utilize both sides of the brain.

Lately I've been thinking about a more artful representational approach to math and machine language -- even in a banal world of ones and zeroes. The world has been thinking about machine language in terms of familiar mathematical, numeric, and alphabetic conventions for a fairly long time now, and it's not exactly easy to realign the cosmos. Yet in a way, it happens naturally. Wikis, wysisygs, drafting tools, photo and sound editors, blogging tools, and so forth, all these tools do the heavy mathematical and machine code lifting behind the scenes to make for a more artful end experience for the user.

But we rarely think of doing the same lifting for coders themselves. To be sure, code is symbolic, by its very nature, lingual. But I think it is possible to turn the whole thing on its head, and adopt a visual approach. What this would look like is anyone's guess, but in a way we see it everywhere as the whole world of machine learning is abstracted more and more over time. As machines become more and more complex and can do more and more sophisticated things, there is a basic necessity to abstract and simplify those very processes, for ease of use, design, architecture, development, and...you name it.

That all said, I do not believe machines will ever learn anything on their own without human input. But that is another debate, as to the character of religion, God, science, and the universe.

Answer 6

Mathematics is simply a tool in machine learning. Knowing the maths enables one to efficiently approach the modelled problems at hand. Of course it might be possible to brute force one's way through, but usually this would come with the expense of lessened understanding of the basic principles involved.

So, pick up a maths book, study the topics until it you're familiar with the concepts. No mechanical engineer is going to design a bridge without understanding the basic maths behind the system behaviour; why should this be any different in the area of machine learning?

Answer 7

There is a lot of stuff in Machine Learning, outside just the math..

You can build the most amazing probabilistic model using a ton of math, but fail because you aren't extracting the right features from the data (which might often require domain insight) or are having trouble figuring out what your model is failing on a particular dataset (which requires you to have a high-level understanding of what the data is giving, and what the model needs).

Without the math, you cannot build new complicated ML models by yourself, but you sure can play with existing tried-and-tested ones to analyze information and do cool things.
You still need some math knowledge to interpret the results the model gives you, but this is usually a lot easier than having to build these models on your own.

Try playing with http://www.cs.waikato.ac.nz/ml/weka/ and http://mallet.cs.umass.edu/ .. The former comes with all the standard ML algorithms along with a lot of amazing features that enable you to visualize your data and pre/post-process it to get good results.

Answer 8

Yes, machine learning research is now dominated by researchers trying to solve the classification problem: given positive/negative examples in an n-dimensional space, what is the best n-dimensional shape that captures the positive ones.

Another approach is taken by case-based reasoning (or case-based learning) where deduction is used alongside induction. The idea is that your program starts with a lot of knowledge about the world (say, it understands Newtonian physics) and then you show it some positive examples of the desired behavior (say, here is how the robot should kick the ball under these circumstances) then the program uses these together to extrapolate the desired behavior to all circumstances. Sort of...