handson-ml3 icon indicating copy to clipboard operation
handson-ml3 copied to clipboard

fixed "log(X) with X ~ loguniform" plot domain

Open lklaszlokovacs opened this issue 1 year ago • 0 comments

ugly proof:

loguniform pdf: x: [0.001, 1000] pdf = 1/(x*ln(1000/0.001))

loguniform cdf: x: [0.001, 1000] cdf value set: [0, 1] cdf = ln(x)/ln(1000/0.001) - ln(0.001)/ln(1000/0.001)

inv(cdf): x: [0,1] inv(cdf) value set: [0.001, 1000] inv(cdf) = 0.001 * (1000/0.001)^x

ln(inv(cdf)): x: [0, 1] ln(inv(cdf)) value set: [ln(0.001), ln(1000)] ln(inv(cdf)) = ln(0.001 * (1000/0.001)^x)

inv(ln(inv(cdf))): x: [ln(0.001), ln(1000)] inv(ln(inv(cdf))) value set: [0, 1] inv(ln(inv(cdf))) = (3*ln(10) + x) / ln(1000/0.001)

derivative of inv(ln(inv(cdf))): x: [ln(0.001), ln(1000)] derivative of inv(ln(inv(cdf))) = 1/ln(1000/0.001) = 0.07238241365054197127518815315277

(ln(1000) - ln(0.001)) * 0.07238241365054197127518815315277 = 1

lklaszlokovacs avatar Mar 31 '23 09:03 lklaszlokovacs