A lot of this is done in discrete math. You know, the actual probability is defined by this integral, but there is no closed form solution to the integral, so we do sums to find the approximate answer. Anyone can understand sums. And, it's probabilities, so the sums must equal one. Not that hard, right ;)

It sure helps to understand the integral equations, especially if you want to read the original literature. But realistically you are going to need to understand summing, normalizing, algorithms for clustering, and so on. You probably don't want to write your own numerical code anyway; someone else did it, and they handled all the edge cases that a naive implementation misses.

You can find PDFs of the James, Witten, Hastie, Tibshirani book "An Introduction to Statistical Learning" [1]. Scroll on through - there is nothing intimidating math wise. All the heavy lifting is left to R.

Jump in, the water is fine!

[1] http://web.stanford.edu/~hastie/pub.htm

Like most fields, it depends on your definition of "studied." If you want to push the envelope in theoretical non-applied research, you're going to want to learn analysis & measure theoretic probability theory. If you want to apply existing techniques, read (well-written) papers and code up the algorithms you find there, you can get away with undergraduate-level linear algebra & probability knowledge - Bayes' rule, expectations, independence, the general ability to think about random variables (and matrices thereof) as values that can be transformed and combined. And of course, you can fire up a classifier in SciPy without knowing any of this at all. But that's stretching the definition of "studied" quite a bit!

I personally went into a graduate-level probabilistic machine learning course with probability knowledge consisting of an undergraduate course that followed Ross http://www.amazon.com/Introduction-Probability-Models-Tenth-... - so there's certainly no need to have been a math major. But if you've never dealt with random variables whatsoever, you'll hit a wall following research from the last 20 years.

There is applied machine learning (using machine learning to solve business problems) and theoretical machine learning (Optimization bounds, proofs, algorithm design).

With applied machine learning it is certainly possible to quickly get a working knowledge without too much reliance on statistics or difficult theory. You can compare this a bit with using a sorting function without knowing exactly how it works (but you know how fast it is and when to use it).

If you have an engineering background, take a look at the wide array of high-quality ML code and tools. Study trendy and powerful tools like XGBoost.

What do you mean, grad level math analysis? Much of probability theory can be learned with basic multivariate calculus. (Perhaps there's a terminology misunderstanding here - when I see "grad level" I think "grad school," ie masters/phd). Certainly basic probability theory is a plus.

I think, you can get away without mathematical analysis (however, it's not that complex). However, basic probability theory is a must have.

Elementary (ie: math-speak for "undergrad-level") probability theory is quite accessible to someone with only a computer scientist's math classes. You really don't need real analysis until you start reading research papers on probability and they drop down into measure theory for this-and-that.

i would say you can can certainly get away with applying machine learning techniques without knowledge of probability theory, but if you want to do stuff like compare models, compare results, determine accuracy of your model, etc., you are going to quickly have to dive into basic statistics (bayes + frequentist)

This is the 2013 course. The original post is for the spring 2015 machine learning course

The videos don't seem to work.

For linear algebra, I like the "No BS guide to linear algebra" (https://gumroad.com/l/noBSLA) which also includes a high school math refresher for people who need it (I did).

For probability, "Probability Demystified" is a good basic intro.

For statistics, I would really recommend Allen Downey's Think Stats (http://greenteapress.com/thinkstats2/index.html), especially if you're coming from a programming background. Most introductions to statistics focus heavily on the mathematics needed to enable certain analytical approximations to difficult probabilistic calculations (e.g. the t-test), whereas Think Stats just bites that bullet and focuses on simulation / brute force so you can spend more time on the actual fundamental theory behind statistics.

Brian Blais' "Statistical Inference for Everyone" (http://web.bryant.edu/~bblais/statistical-inference-for-ever...) also looks really good, but haven't had a chance to review it in depth.

Depends on how basic you're imagining. Khan Academy [0] is a fairly well-regarded free resource for high-school and undergraduate level mathematics video lectures. They have probability and statistics as well as linear algebra courses.

If you prefer textbooks, I have heard good things about "Linear Algebra Done Right," [1] but I would not recommend it unless you are "math literate" at an undergraduate level already.

[0] https://www.khanacademy.org/math/probability

[1] http://www.amazon.com/dp/3319110799

I think this is a good resource to start: http://betterexplained.com/articles/linear-algebra-guide/

For linear algebra check out Prof. Gilbert Strand's course on MIT OCW. He's great at explaining the material and the course resources are comprehensive.

http://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-...

The videos on computervisiontalks.com are exactly the same as videos on youtube because the site is pulling these videos from youtube. The post points to the spring 2015 lectures. You are pointing to earlier lectures in 2014,2013

The lectures on computervisiontalks are directly being taken from youtube (but tags, navigation, bookmarking and in-video search capability is added). The lecture 1.3 (for spring 2015 class) is exactly of the same length. However on youtube, the lectures for machine learning class 2013 (also by Alex Smola) are available which are of a different length.