build an ensemble with a number of data points (ensemble members) greater than or equal to the number of polynomials

[ghost]

for an L2 (smoothness) constraint, build an ensemble with D members, where

D ~= 10 * (((N + P)! / (N! * P!)) - 1)

or, in Python:

import math

def num_polynomials(dimensions: int, order: int) -> int:
    return int(math.factorial(dimensions + order) / (math.factorial(dimensions) * math.factorial(order))) - 1

members = 10 * num_polynomials(4, 3)

[ghost]

number of ensemble members recommended by this rule of thumb under an L2 regularization scheme:

variables / order	2	3	4	5	6
2	50	90	140	200	270
3	90	190	340	550	830
4	140	340	690	1250	2090
5	200	550	1250	2510	4610
6	270	830	2090	4610	9230

[WPringle]

Cool, do you have numbers for L1 regularization scheme?

[ghost]

Cool, do you have numbers for L1 regularization scheme?

I'm not sure about the rest of L1, but Khachik said that Lasso would be able to handle factors of 2 or 3, so I guess for Lasso you would multiply these ensemble sizes by 0.25

[WPringle]

I see so 2,3 (((N + P)! / (N! P!)) - 1) ?

[ghost]

yes exactly

[WPringle]

Then the numbers seem pretty good