A library of scalable Bayesian generalised linear models with fancy features
Project description
A library of scalable Bayesian generalised linear models with fancy features
This library implements various Bayesian linear models (Bayesian linear regression) and generalised linear models. A few features of this library are:
A fancy basis functions/feature composition framework for combining basis functions like radial basis function, sigmoidal basis functions, polynomial basis functions etc.
Basis functions that can be used to approximate Gaussian processes with shift invariant covariance functions (e.g. square exponential) when used with linear models [1], [2], [3].
Non-Gaussian likelihoods with Bayesian generalised linear models using a modified version of the nonparametric variational inference algorithm presented in [4].
Large scale learning using stochastic gradient descent (ADADELTA).
Quickstart
To install, simply run setup.py:
$ python setup.py installor install with pip:
$ pip install git+https://github.com/nicta/revrand.git@releaseRefer to docs/installation.rst for advanced installation instructions.
Have a look at some of the demos, e.g.:
$ python demos/demo_regression.pyOr,
$ python demos/demo_glm.pyBayesian Linear Regression Example
Here is a very quick example of how to use Bayesian linear regression with SGD optimisation of the likelihood noise, regulariser and basis function parameters. Assuming we already have training noisy targets y, inputs X, and some query inputs Xs (as well as the true noiseless function f):
import matplotlib.pyplot as pl
import numpy as np
from revrand.basis_functions import LinearBasis, RandomRBF
from revrand.regression import learn_sgd, predict
...
# Concatenate a linear basis and a Random radial basis (GP approx)
basis = LinearBasis(onescol=True) + RandomRBF(nbases=300, Xdim=X.shape[1])
init_lenscale = 1.0
# Learn regression parameters and predict
params = learn_sgd(X, y, basis, [init_lenscale])
Eys, Vfs, Vys = predict(Xs, basis, *params)
# Training/Truth
pl.plot(X, y, 'k.', label='Training')
pl.plot(Xs, f, 'k-', label='Truth')
# SGD Regressor
Sys = np.sqrt(Vys)
pl.plot(Xs, Eys, 'r-', label='SGD Bayes linear reg.')
pl.fill_between(Xs, Eys - 2 * Sys, Eys + 2 * Sys, facecolor='none',
edgecolor='r', linestyle='--', label=None)
pl.legend()
pl.grid(True)
pl.title('Regression demo')
pl.ylabel('y')
pl.xlabel('x')
pl.show()This script will output something like the following,
Bayesian Generalised Linear Model Example
This example is very similar to that above, but now let’s assume our targets y are drawn from a Poisson likelihood, or observation, distribution which is a function of the inputs, X. The task here is to predict the mean of the Poisson distribution for query inputs Xs, as well as the uncertainty associated with the prediction.
import matplotlib.pyplot as pl
import numpy as np
from revrand.basis_functions import RandomRBF
from revrand.glm import learn, predict_meanvar, predict_interval
...
# Random radial basis (GP approx)
basis = RandomRBF(nbases=100, Xdim=X.shape[1])
init_lenscale = 1.0
# Set up the likelihood of the GLM
llhood = likelihoods.Poisson(tranfcn='exp') # log link
# Learn regression parameters and predict
params = learn(X, y, llhood, [], basis, [init_lenscale])
Eys, _, _, _ = predict_meanvar(Xs, llhood, basis, *params)
y95n, y95x = predict_interval(0.95, Xs, llhood, basis, *params)
# Training/Truth
pl.plot(X, y, 'k.', label='Training')
pl.plot(Xs, f, 'k-', label='Truth')
# GLM SGD Regressor
pl.plot(Xs, Eys, 'b-', label='GLM mean.')
pl.fill_between(Xs, y95n, y95x, facecolor='none',
edgecolor='b', linestyle='--', label=None)
pl.legend()
pl.grid(True)
pl.title('Regression demo')
pl.ylabel('y')
pl.xlabel('x')
pl.show()This script will output something like the following,
Useful Links
- Home Page
- Documentation
- Issue tracking
Bugs & Feedback
For bugs, questions and discussions, please use Github Issues.
References
Copyright & License
Copyright 2015 National ICT Australia.
Licensed under the Apache License, Version 2.0 (the “License”); you may not use this file except in compliance with the License. You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an “AS IS” BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License.
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