Machines and Metaphors

I quite enjoy discussions. However, talking just to people within my friend circle can sometimes become boring. After all, I tend to attract similar perspectives, and to occasionally challenge my own outlook, and see things from another vantage point is something I'd like to do. Events with discussion groups are a great place to do this. But one thing that tends to be a challenge with such events, is who to allocate which group to. Let's say there are 5 discussion groups, and the Google Form you have created allows a prospective participant to select their First-Choice and Second-Choice. How do you decide which groups to allocate to each participant? And this is a more general problem than the obscure idea of a discussion event: it could apply in a virtual conference of educational seminars, or even in class allocations.  The most interesting part about AI, is its ability to express and solve seemingly subjective problems. Yes, I do mean that Simulated Annealing can solve this ...

I've written all the instructions and code into a Python Notebook . This is a viewer to see the notebook. Then, you can click Open with Google Colab, Login to your Google Account, and you will be able to edit your own copy of the notebook. If you are doing this, ignore the request in the notebook to make a copy before editing.

Here's a cat - I didn't get a chance to work them into the post. In the previous post, we were discussing Gradient Descent and why it has so many connections to Phase Spaces (check that out over here , if you haven't yet). There, I had dropped a hint about another Optimization Method we could use. Did you catch it? When we discussed some of the calculus involved, I mentioned that the derivative or slope of a function at local minima or maxima is equal to 0. As it turns out, you can simply set the derivative to be equal to 0, and solve for the parameters required. This is sometimes referred to as the Normal Equation Method.  I will talk about a case-specific simplification here.  This method is called Least Squares and it minimizes the following error function, often known as Mean Squared Error, for reasons that will be apparent in a moment: This formula may seem complicated, but don't worry, it is actually quite simple. Before we understand it, though, it is important t...

I'm going to start from where we left off in the last part of this series. If you haven't read that yet, check that out first if you want a more detailed understanding: We explored what a Phase Space is, why it's useful, what it has to do with Machine Learning, and more!  I'm assuming you've read the previous article, or you know what I talked about there: so let's get to it. At the end of the last article, we discovered that it was the power of mathematics that would help us find the best values of the parameters for the lowest cost function. Before we get into what the Math does, however, we'll need to define some things in the math. If you've done Calculus, and in particular, partial derivatives, you can skip this section, but otherwise I would suggest at least a cursory glance. I don't go into too much detail on the subject, but that's only because you won't need it.  Calculus Interlude: Derivatives- The slope of a graph is a concept you...

Phase Spaces One of the least heard of, and most interesting techniques of the sciences, that you rarely realize you’ve used before. Phase spaces are symbolic representations of a particular problem, which you can then use to solve it. Let’s start with a simple problem - in physics maybe. Let’s say we have a car, as all good physics problems do. You’re driving at a set initial speed, and a set acceleration. At what time would you have travelled exactly 15 ft? Let’s look at it in terms of "a phase space". I have a velocity-time graph down here:                                                                                                                                ...