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Could you be more specific about what kind of math you've been seeing in the papers that you'd like to understand (and/or link some of the papers)? What you ne

Could you be more specific about what kind of math you've been seeing in the papers that you'd like to understand (and/or link some of the papers)? What you need to know is on this list http://www.gatsby.ucl.ac.uk/teaching/courses/ml1-2009/cribsheet.pdf http://www.gatsby.ucl.ac.uk/teaching/courses/ml1-2009/cribsh... for the most part. Because math is layered, once you've got three or four layers of unfamiliar abstraction, it gets very hard to figure out what's going on. The way to get around this initially is by brute force. For example, say you have a matrix function (from matrices to matrices). The formula uses the exponential of a matrix, and you're not sure what that actually looks like. So find the definition, and write it out. Think about what that means, maybe do a couple of examples to get a sense of it. Write out your matrix function with this definition expanded (which probably means you'll write it element-wise), so that you know what each element of the output matrix is as a function of the elements of the input matrix. Work a couple of examples, think about it. Eventually, you get familiar with the exponential of a matrix, and you do the mapping in your head - so your brain has just acquired a new abstraction. The process above applies to basically every mathematical structure you'll run into. Sometimes you'll have to recurse a few levels. It's not about books, it's about process. You can know how to do lots of math problems and still not grok papers - and you can learn to quickly grok papers and be able to implement them / reason about them without being very good at math problems (I'm in the 2nd bunch). In terms of books, you only really need Wikipedia / Wolfram MathWorld, plus maybe one of the standard math references like Kreyszig or Boas. Learning to use Mathematica can make your life much easier as well. One last comment: A book that totally changed my relationship to math is Peter Szekeres' Modern Mathematical Physics: Groups, Hilbert Space, and Differential Geometry. The explanations are uncompromisingly lucid, written in plain english, with minimal symbol walls. The book takes you essentially from zero, and introduces nearly all the math that underpins modern physics. This book really changed my conception of myself - I've lost my fear, when reading papers, that maybe this is the one I'm not smart enough to understand. When that fear goes, the stress goes - and you know it's just a matter of learning the definitions. Then it becomes pleasurable, like a puzzle.

Torn 17y ago
One of the ones that prompted me to post this topic was over here, on the topic of CRF statistical models: http://www.cs.umass.edu/~mccallum/papers/ifcrf-uai2003.pdf http://www.cs.umass.edu/~mccallum/papers/ifcrf-uai2003.pdf From reading it I get most of what it's about, and how they work, but the embedded probability stuff is mostly squiggles to me. I guess my ultimate aim with this is would be able to quickly grok papers on various compsci subjects, and then go around and code implementations to test things out.
- ewjordan 17y ago
  "Quickly grok" to "test things out" - it just isn't going to happen like that, even if you know the math behind it (FWIW, for that paper you're going to need a lot about statistics and Markov chains, but you may be able to get pretty far just by Googling the terms you don't know). Comp sci is notorious for having a huge gap between published work and working implementations. It often takes heroic efforts to put together a working version of the algorithms described, sometimes so much work that nobody has ever done it (Chazelle has some algorithms that have never been implemented in code). Even if it's plausible to do, don't be surprised if it takes weeks to get it working right. The more "on the edge" the algorithms are, the more difficult it tends to be, and it's not really likely that you'll be able to quickly experiment with new methods unless the authors have published code. This happens far less often than it should, because simple possession of a working algorithm is often enough to squeeze several more papers out of a topic, so authors have no particular incentive to share theirs, or even make it easy to create one from scratch. Computer graphics papers are particularly bad on that front, often omitting so much detail that even with significant study and effort you could never reproduce their results without researching the problem on your own anyways. Other people have offered good advice: go through it in excruciating detail, think about every equation as its own sub-problem, and make sure you understand what's happening at each step. These papers are meant for detailed study, not quick reading, even if the reader already knows a lot about the field. Google should help you through most of the math stuff, and try going to book search or the papers search if you're not finding anything online, which will give you good keywords to look for books on.
  - 17y ago

Torn 17y ago

One of the ones that prompted me to post this topic was over here, on the topic of CRF statistical models: http://www.cs.umass.edu/~mccallum/papers/ifcrf-uai2003.pdf http://www.cs.umass.edu/~mccallum/papers/ifcrf-uai2003.pdf From reading it I get most of what it's about, and how they work, but the embedded probability stuff is mostly squiggles to me. I guess my ultimate aim with this is would be able to quickly grok papers on various compsci subjects, and then go around and code implementations to test things out.

ewjordan 17y ago
"Quickly grok" to "test things out" - it just isn't going to happen like that, even if you know the math behind it (FWIW, for that paper you're going to need a lot about statistics and Markov chains, but you may be able to get pretty far just by Googling the terms you don't know). Comp sci is notorious for having a huge gap between published work and working implementations. It often takes heroic efforts to put together a working version of the algorithms described, sometimes so much work that nobody has ever done it (Chazelle has some algorithms that have never been implemented in code). Even if it's plausible to do, don't be surprised if it takes weeks to get it working right. The more "on the edge" the algorithms are, the more difficult it tends to be, and it's not really likely that you'll be able to quickly experiment with new methods unless the authors have published code. This happens far less often than it should, because simple possession of a working algorithm is often enough to squeeze several more papers out of a topic, so authors have no particular incentive to share theirs, or even make it easy to create one from scratch. Computer graphics papers are particularly bad on that front, often omitting so much detail that even with significant study and effort you could never reproduce their results without researching the problem on your own anyways. Other people have offered good advice: go through it in excruciating detail, think about every equation as its own sub-problem, and make sure you understand what's happening at each step. These papers are meant for detailed study, not quick reading, even if the reader already knows a lot about the field. Google should help you through most of the math stuff, and try going to book search or the papers search if you're not finding anything online, which will give you good keywords to look for books on.
- 17y ago