Markov Chain Monte Carlo Without Jargon
jeremykun.com
Markov Chain Monte Carlo Without Jargon
1–10 of 18 posts
Re: Markov Chain Monte Carlo Without Jargon
#2Ok, instead of reading a Wikipedia page or two, or the most elementary chapter in a probability/statistics textbook and gaining a bunch more skills (among them the tools needed to reason about whether your MCMC is doing anything close to reproducing the original distribution), I can peruse a huge blog post filled with patronizing language and it doesn't even have the Metropolis-Hastings algorithm listed out even in pseudocode. Got it, this is what progress looks like.
Re: Markov Chain Monte Carlo Without Jargon
#3The author draws a distinction between computing expected value of a random variable and computing the volume of a convex set, but from the point of measure theory, both are computations of integrals. So maybe the definition given from the encyclopedia wasn't so bad, given the right prior knowledge.
Re: Markov Chain Monte Carlo Without Jargon
#4The author draws a distinction between computing expected value of a random variable and computing the volume of a convex set, but from the point of measure theory, both are computations of integrals. So maybe the definition given from the encyclopedia wasn't so bad, given the right prior knowledge.
Well, come on. Lots of things are integrals. The Riemann zeta function is an integral. But I don't think MCMC has anything to say about that.
There is no obvious "measure" in the convex set example, so it's not clear how MCMC applies. And, there are not good MCMC convergence results, so even if you apply it, it's not obvious you'd be able to prove anything.
If you think of the set as being defined by an oracle (a function that reports whether its input is inside or out), then it looks like it will require exponentially many probes (in the dimensionality "d" of the space) to get its volume. Basically, a curse of dimensionality argument -- you have to sample independently along each of "d" axes. But it turns out there is an MCMC that is polynomial-time. (Now, granted, IIRC it is like n^17, but...)
Re: Markov Chain Monte Carlo Without Jargon
#5MCMC is waaay more general than metropolis-hastings, which is what all that "bullshit" is about.
Re: Markov Chain Monte Carlo Without Jargon
#6The author draws a distinction between computing expected value of a random variable and computing the volume of a convex set, but from the point of measure theory, both are computations of integrals. So maybe the definition given from the encyclopedia wasn't so bad, given the right prior knowledge.
Well, come on. Lots of things are integrals. The Riemann zeta function is an integral. But I don't think MCMC has anything to say about that. There is no obvious "measure" in the convex set example, so it's not clear how MCMC applies. And, there are not good MCMC convergence results, so even if you apply it, it's not obvious you'd be able to prove anything. If you think of the set as being defined by an oracle (a fun…
The Lebesgue measure could be a candidate for the measure you are asking for. Creating a bounding box around the convex set in question and then scaling, we get a probability measure (measure of the entire set is 1). Some sorts of random walks inside this bounding box will converge to this scaled Lebesgue measure. I think this is the main idea behind the convex volume estimation algorithms.
The oracle you mention is the indicator function of the convex set. Instead of integrating this indicator function directly over Lebesgue measure to get volume, we can use MCMC to get the "expectation" of the oracle.
It's not obvious if we can realize the Riemann zeta function as an integral over a finite measure space, but if we could, I think MCMC could be used to evaluate it.
Re: Markov Chain Monte Carlo Without Jargon
#7Ok, instead of reading a Wikipedia page or two, or the most elementary chapter in a probability/statistics textbook and gaining a bunch more skills (among them the tools needed to reason about whether your MCMC is doing anything close to reproducing the original distribution), I can peruse a huge blog post filled with patronizing language and it doesn't even have the Metropolis-Hastings algorithm listed out even in p…
Sometimes I get the idea that people in CS want to "get all this machine learning/data science stuff" without understanding the principles.
Sure, it's trivially easy to build a classifier in R/Scikit (or even code one up from scratch) so it may seem like it's no big deal. Similarily, it's trivially easy to hack up an inefficient SQL query, without knowledge of relational algebra or normal forms. But I would argue that some basic knowledge is essential in applying these things.
Re: Markov Chain Monte Carlo Without Jargon
#8Ok, instead of reading a Wikipedia page or two, or the most elementary chapter in a probability/statistics textbook and gaining a bunch more skills (among them the tools needed to reason about whether your MCMC is doing anything close to reproducing the original distribution), I can peruse a huge blog post filled with patronizing language and it doesn't even have the Metropolis-Hastings algorithm listed out even in p…
I feel as though your comment comes very close to "gratuitous negativity" of the type mentioned recently on the YC blog.
http://blog.ycombinator.com/new-hacker-news-guideline
Clearly, a blog post primer it is not an alternative to an encyclopedia article or a textbook chapter. Rather it provides something not fulfilled by either: a brief introduction to a technical subject that relies on very little prior knowledge.
I am sure that Jeremy is well aware of the challenges involved in writing in a style that is straight-forward without being "patronizing". Perhaps you don't like the balance that he has found, but is that a good enough reason to outright dismiss his efforts?
Lastly, much of the post is in fact a plain-language explanation of the Metropolis-Hastings algorithm, and he adds: "... if demand is popular enough, I could implement the Metropolis-Hastings algorithm in code"
Re: Markov Chain Monte Carlo Without Jargon
#9Ok, instead of reading a Wikipedia page or two, or the most elementary chapter in a probability/statistics textbook and gaining a bunch more skills (among them the tools needed to reason about whether your MCMC is doing anything close to reproducing the original distribution), I can peruse a huge blog post filled with patronizing language and it doesn't even have the Metropolis-Hastings algorithm listed out even in p…
I feel as though your comment comes very close to "gratuitous negativity" of the type mentioned recently on the YC blog. http://blog.ycombinator.com/new-hacker-news-guideline Clearly, a blog post primer it is not an alternative to an encyclopedia article or a textbook chapter. Rather it provides something not fulfilled by either: a brief introduction to a technical subject that relies on very little prior knowledge.…
I was really surprised to view the comments, and find the attitude expressed in the GP's post #1.
If anything, I read this and thought something along the lines of, "I wish some of the subjects I learned in college were explained this way, at least to start."
Now, I fully appreciate understanding fundamentals, and not black boxing things (see the ongoing framework debate posts), however I didn't read that article looking to be spoon fed a black box for ML or anything...I was just bored and curious. So it made for good reading.
Perhaps I'm generalizing too far, but it reminded me of when I was presented with the classic Lamport paper on "Time, Clocks, and the Ordering of Events in a Distributed System" in undergrad. This would have been around 2004. I had been working (i.e. coding for money) for some time by then, but back then, you could still build a lot with a relatively stock LAMP stack (or similar.) MongoDB, Riak, Redis, Cassandra, DynamoDB, etc. were not all commonplace (much less things you could have a cluster ready to play with by means of a simple 'vagrant up'.) So when I was given the paper, without much context, I had a hard time really "getting it", or how it applied to me. I'm pretty sure I eventually got some commentary on it from the professor in class, while hurriedly going through powerpoint slides, probably anxious to get back to his research. Then a test question or two about it later.
Years later, after working more, and "distributed systems" becoming more of a tangible thing, I re-visited it, and it made more sense. Anyway, my point is that had I gotten some sort of a, "and here's what the paper is talking about, and how it applies to something tangible, in plainspeak", it would have been useful - so we shouldn't groan about an article like this. Someone out there is going to understand the subject much better thanks to that post.
[Note to the reader that's very familiar with the vector clocks paper - I realize it's not written with that much jargon, and DOES do a decent job in the introduction section of using plain language, but the purpose was just lost on me. I mean, it makes reference to ARPA Net, and then goes on to determining event ordering. It just didn't equate to any thing in my world view, and I had done a decent bit of multi-threaded/process programming by then too.]
Re: Markov Chain Monte Carlo Without Jargon
#10Ok, instead of reading a Wikipedia page or two, or the most elementary chapter in a probability/statistics textbook and gaining a bunch more skills (among them the tools needed to reason about whether your MCMC is doing anything close to reproducing the original distribution), I can peruse a huge blog post filled with patronizing language and it doesn't even have the Metropolis-Hastings algorithm listed out even in p…
Sometimes I get the idea that people in CS want to "get all this machine learning/data science stuff" without understanding the principles. Sure, it's trivially easy to build a classifier in R/Scikit (or even code one up from scratch) so it may seem like it's no big deal. Similarily, it's trivially easy to hack up an inefficient SQL query, without knowledge of relational algebra or normal forms. But I would argue tha…
"Sometimes I get the idea that people in CS want to "get all this machine learning/data science stuff" without understanding the principles."
Thought I was the only one.