Dear fellow researchers,
I plan to try to use the code example in this 4-D GMM “tutorial” (that uses a toy dataset of 90 points)
to fit the same GMM to a similar toy-dataset of 10.000-100.000 samples.
Will the large sample size be a deal-breaker in doing that ?
I had a very quick look at https://arxiv.org/pdf/1701.02434.pdf to get an answer for this question, and to me it seems, after a very quick look, that the computational complexity scales linearly with the number of data-points - is that correct ? On the other hand it seems to scale cubicly with the number of parameters (due to the need to take the inverse of a matrix that has the size of the number of parameters).
Am I reading that paper correctly ? ( I am a bit new to Stan / MCMC for Bayesian inference - but have theoretical solid state / statistical physics background and I also did a lot of - large scale - computer simulations (MC and MD) for modelling amorphous semiconductors and crystal growth - so the topic - i.e. HMC sampling - looks extremely familiar - but I only spent 20 min on skimming through that paper, trying to answer the question what “equation” describes - the asymptotic computational complexity of HMC Bayesian inference) and it seems that it is - in the first approximation - O(P^3*N), where : P is the number of parameters, N is the number of samples
So if the above tutorial code example takes 10 seconds to get a fit for 100 data-points then it will take 1.000.000 seconds for 10.000 data points. Is that correct ? Do I get this right ?