11.4 Summary
I admit, the fine details of topology, limits, and continuity can feel complex and abstract. However, in my experience, taking the hardest path is the most rewarding, especially when learning technical topics. To sum up, we’ve learned
- what topology is,
- what it has to do with sequences and limits,
- how to take limits of functions,
- and finally, what a continuous function is.
Now that we are familiar with all the above, we are ready to tackle a subject at the heart of machine learning: differentiation. We’ll look at how to analyze functions and what makes a function “behave nicely.”
If you think through what machine learning is really about, you’ll find that it is quite straightforward from a bird’s eye view. In essence, all we want to do is 1. Design parameterized functions to explain the relationships between data and observations and 2. Find the parameters that best fit our data.
To find models that are expressive enough yet easy...
