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So this is all very well and good, I've had about 5 intros to Bayesian Statistics. But those are a fair bit away from actually applying that knowledge in practi
by pmjordan 14y ago
So this is all very well and good, I've had about 5 intros to Bayesian Statistics. But those are a fair bit away from actually applying that knowledge in practice in software.
Let's say we have N different kinds of events with unknown probabilities and unknown dependence or independence between them. The naive approach to gathering data on the probability of event n occurring following an occurrence of event m would require O(N²) in space. Let's say N ~ 10⁹~10¹⁰. Storing that much data as a raw matrix isn't practical in most cases, so we have to find a more efficient data structure - in terms of both space and the operations we need to perform. (and taking into account characteristics of the storage medium, i.e. memory or disk or a combination) What happens if the probabilistic properties of the system change over time?
Are there any introductory books or other resources on modeling this kind of problem? Clearly this has been tackled before, but I'm having a hard time making the leap from theory to practice - and I don't mean import the data into R or SPSS or whatever and let that grind out a solution, but coming up with approximations when you have runtime and space constraints that make that approach impractical.
- trhtrsh 14y agoI think the general approach is dimensionality reduction: start measuring, and round down to 0 for the low-correlation pairs of events. Do you actually have a stream of more than N^2 observations to process? If not, then most of your correlations are in fact 0, and sparse-matrix techniques apply.
- hessenwolf 14y agoSounds like you need a Bayesian network - the junction tree algorithm. You can send the cheque in the mail. ;)