I’m sorry to say this because I observe that we get these questions somewhat frequently, but I don’t think what you’re asking for - in the format, goals and speed you’d like it - is a thing.
That’s a pretty discouraging statement, so let me try to be more helpful. The mathematics comprising contemporary machine learning and data analysis primarily consists of linear algebra, calculus, mathematical statistics and, at the high end, probability theory. There are boutique efforts to use things like topology but that’s non-standard.
As it stands, your question is underspecified, which is what I repeat for most of these questions. The answers you receive here are going to variously interpret what you’re actually looking for and prescribe based on the author’s interpretation and intuition. It would be more useful if you explained exactly what your goals are. Here’s precisely the problem: you apparently don’t know these mathematics already, but you’re asking for something that “doesn’t necessarily go into depth.” How much depth is too much, and how would you know that exactly given your present unknown unknowns? If you explain what you actually want to achieve, we might be able to
1. Tell you that you don’t actually need that “top level view” to achieve what you’d like,
2. Tell you that such a top level view is not nearly enough for what you’d like to do, or
3. Tell you that a top level view is coherent, and optimize the best materials for you to learn from based on what you want to do.
It would also help us make recommendations if you explained what your current level of mathematical background looks like. Have you taken linear algebra at least once? Exactly how basic do our resources have to be? Different textbooks written for different audiences can variously explain the same concept in two pages or 10 pages, and they can emphasize different things.
I’d like to help, and I probably can, but it would go a long way if you could tell us what your end goal is instead of what you interpret as the next step towards that goal. Then we can provide resources based on your mathematical maturity.
OP here. Thanks for taking time to reply. Really thank you.
Obviously I know very little about these areas and that is why I posted such a question. By posing this question, I didn't mean that I wanted to 'get there' quickly. In fact I am in no hurry and willing to go as deep as possible.
What I actually mean to ask is that I was looking for a kind of syllabus/crash courses so that I can get an idea about what kind of mathematics is involved in these areas. Based on that, I'll be able to start my studies in much more organized way. Also, from there on, I myself be able to figure out how to look for further resources. This is the style of learning I usually follow.
In a nutshell, you take probability distributions and project them onto topological manifolds, such that the distribution consists of points on the manifold. You can find more by searching for key words like "information geometry" or "differential geometry machine learning".
there's also the stuff that ayasdi and carlsson were/are doing but i never really saw the point of that (e.g. just compute connected components instead persistent homology).
That’s a pretty discouraging statement, so let me try to be more helpful. The mathematics comprising contemporary machine learning and data analysis primarily consists of linear algebra, calculus, mathematical statistics and, at the high end, probability theory. There are boutique efforts to use things like topology but that’s non-standard.
As it stands, your question is underspecified, which is what I repeat for most of these questions. The answers you receive here are going to variously interpret what you’re actually looking for and prescribe based on the author’s interpretation and intuition. It would be more useful if you explained exactly what your goals are. Here’s precisely the problem: you apparently don’t know these mathematics already, but you’re asking for something that “doesn’t necessarily go into depth.” How much depth is too much, and how would you know that exactly given your present unknown unknowns? If you explain what you actually want to achieve, we might be able to
1. Tell you that you don’t actually need that “top level view” to achieve what you’d like,
2. Tell you that such a top level view is not nearly enough for what you’d like to do, or
3. Tell you that a top level view is coherent, and optimize the best materials for you to learn from based on what you want to do.
It would also help us make recommendations if you explained what your current level of mathematical background looks like. Have you taken linear algebra at least once? Exactly how basic do our resources have to be? Different textbooks written for different audiences can variously explain the same concept in two pages or 10 pages, and they can emphasize different things.
I’d like to help, and I probably can, but it would go a long way if you could tell us what your end goal is instead of what you interpret as the next step towards that goal. Then we can provide resources based on your mathematical maturity.