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yossi-cohen / preferential-attachment

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Compare the 2D and 1D universal estimator with the theoretical result. #9

Open yossigil opened 3 years ago

yossigil commented 3 years ago

Input: Two (one) dimensional function, that gives the PMF of a univariate distribution. x = f(t1, t2); in Python, this comes as a simple function from Real*Real to Real, case in point, log-normal function.

Algorithm:

  1. Transform the parameter space to unit cube of dimension n=1,2, e.g., (1+ arctan(t))/2 (optional)
  2. Learn the Sigmoid(t1), Sigmoid(t2) (optional: learn t1,t2, not their sigmoid) using the usual statistical method of generating synthetic data.
  3. Compute the variance of the error of learning, it is typically a function of t1, t2, e.g., the error is not the same everywhere.
  4. Compute the fisher information: Log, Derivate, Square (analytically), integrate (numerically) over x, ranging over all reals.
  5. Multiply by n (the number of sample points).
  6. Compute the inverse.
  7. Compare to the actual error from (3)