估计Python中的关节分布并采样给定的响应变量

Question

I have a sequence of samples from a function Y = f(X) for which there are d random variables, X_1 , X_2 ... X_d and a response variable Y with settings for X as x_1 , x_2 , ... x_d and finally for Y as y (Y is real valued). I store these samples in a matrix of dimension (nxd) , and the responses in a vector (dx 1) .

I want to calculate the joint distribution in Python in such a way that upon receiving new samples I can update the distribution painlessly.

Most importantly, I want to be able to sample X settings from my own calculated distribution conditioned on Y , that is -- pick a desired value Y = y and choose from a conditioned, weighted joint distribution a likely set of settings for X given that choice of Y = y .

Some variables are categorical and some ordinal, but I am fine with discretizing them to integers (ie, X_i in set of {'red', 'blue', 'green'} => {1, 2, 3}) if needed.

Doing it is easy enough for small d , but higher up gets more difficult. What solutions or frameworks if any exist for this workflow in Python? Maybe making my own with numpy isn't so bad? Example code? My knowledge of statistics is very, very little, but I'm quite solid at Python.

Answer 1

In general this kind of problem belongs to the field of machine learning , a nice python package you might want to check out is scikit-learn . But if all you need is that sampling, simpler structures would do:

1. keep a list of all (x,y)-pairs, ordered by y. rbtree is quite handy here.

2. When you need a sampling of (x,y)-pairs at some value y=y0, search that list for that value y0, and return a selection of pairs from around that position.