A decision-tree based conditional independence test
Project description
.. image:: https://img.shields.io/badge/License-MIT-yellow.svg
:target: https://opensource.org/licenses/MIT
:alt: License
*A Decision Tree (Conditional) Independence Test (DTIT).*
Introduction
-----------
Let *x, y, z* be random variables. Then deciding whether *P(y | x, z) = P(y | z)*
can be difficult, especially if the variables are continuous. This package
implements a simple yet efficient and effective conditional independence test,
described in [link to arXiv when we write it up!]. Important features that differentiate
this test from competition:
* It is fast. Worst-case speed scales as O(n_data * log(n_data) * dim), where dim is max(x_dim + z_dim, y_dim). However, amortized speed is O(n_data * log(n_data) * log(dim)).
* It applies to cases where some of x, y, z are continuous and some are discrete, or categorical (one-hot-encoded).
* It is very simple to understand and modify.
* It can be used for unconditional independence testing with almost no changes to the procedure.
We have applied this test to tens of thousands of samples of thousand-dimensional datapoints in seconds. For smaller dimensionalities and sample sizes, it takes a fraction of a second. The algorithm is described in [arXiv link coming], where we also provide detailed experimental results and comparison with other methods. However for now, you should be able to just look through the code to understand what's going on -- it's only 90 lines of Python, including detailed comments!
Usage
-----
Basic usage is simple, and the default settings should work in most cases. To perform an *unconditional test*, use dtit.test(x, y):
.. code:: python
import numpy as np
from dtit import dtit
x = np.random.rand(1000, 1)
y = np.random.randn(1000, 1)
pval_i = dtit.test(x, y) # p-value should be uniform on [0, 1].
pval_d = dtit.test(x, x + y) # p-value should be very small.
To perform a conditional test, just add the third variable z to the inputs:
.. code:: python
import numpy as np
from dtit import dtit
# Generate some data such that x is indpendent of y given z.
n_samples = 300
z = np.random.dirichlet(alpha=np.ones(2), size=n_samples)
x = np.vstack([np.random.multinomial(20, p) for p in z])
y = np.vstack([np.random.multinomial(20, p) for p in z])
# Run the conditional independence test.
pval = dtit.test(x, y, z)
Note that x.shape = (n_samples, x_dim), y.shape = (n_samples, y_dim), z.shape = (n_samples, z_dim).
Installation
-----------
pip install dtit
Requirements
------------
The usual scientific Python packages:
* numpy >= 1.12
* scikit-learn >= 0.18.1
* scipy >= 0.16.1
.. _pip: http://www.pip-installer.org/en/latest/
:target: https://opensource.org/licenses/MIT
:alt: License
*A Decision Tree (Conditional) Independence Test (DTIT).*
Introduction
-----------
Let *x, y, z* be random variables. Then deciding whether *P(y | x, z) = P(y | z)*
can be difficult, especially if the variables are continuous. This package
implements a simple yet efficient and effective conditional independence test,
described in [link to arXiv when we write it up!]. Important features that differentiate
this test from competition:
* It is fast. Worst-case speed scales as O(n_data * log(n_data) * dim), where dim is max(x_dim + z_dim, y_dim). However, amortized speed is O(n_data * log(n_data) * log(dim)).
* It applies to cases where some of x, y, z are continuous and some are discrete, or categorical (one-hot-encoded).
* It is very simple to understand and modify.
* It can be used for unconditional independence testing with almost no changes to the procedure.
We have applied this test to tens of thousands of samples of thousand-dimensional datapoints in seconds. For smaller dimensionalities and sample sizes, it takes a fraction of a second. The algorithm is described in [arXiv link coming], where we also provide detailed experimental results and comparison with other methods. However for now, you should be able to just look through the code to understand what's going on -- it's only 90 lines of Python, including detailed comments!
Usage
-----
Basic usage is simple, and the default settings should work in most cases. To perform an *unconditional test*, use dtit.test(x, y):
.. code:: python
import numpy as np
from dtit import dtit
x = np.random.rand(1000, 1)
y = np.random.randn(1000, 1)
pval_i = dtit.test(x, y) # p-value should be uniform on [0, 1].
pval_d = dtit.test(x, x + y) # p-value should be very small.
To perform a conditional test, just add the third variable z to the inputs:
.. code:: python
import numpy as np
from dtit import dtit
# Generate some data such that x is indpendent of y given z.
n_samples = 300
z = np.random.dirichlet(alpha=np.ones(2), size=n_samples)
x = np.vstack([np.random.multinomial(20, p) for p in z])
y = np.vstack([np.random.multinomial(20, p) for p in z])
# Run the conditional independence test.
pval = dtit.test(x, y, z)
Note that x.shape = (n_samples, x_dim), y.shape = (n_samples, y_dim), z.shape = (n_samples, z_dim).
Installation
-----------
pip install dtit
Requirements
------------
The usual scientific Python packages:
* numpy >= 1.12
* scikit-learn >= 0.18.1
* scipy >= 0.16.1
.. _pip: http://www.pip-installer.org/en/latest/
Project details
Download files
Download the file for your platform. If you're not sure which to choose, learn more about installing packages.
Source Distribution
dtit-1.1.0.tar.gz
(4.6 kB
view hashes)