https://github.com/ofai/bayesiannonparametrics.jl
BayesianNonparametrics in julia
https://github.com/ofai/bayesiannonparametrics.jl
bayesian-machine-learning bayesian-methods bayesian-nonparametric-models dirichlet-process-mixtures julia
Last synced: 27 days ago
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BayesianNonparametrics in julia
- Host: GitHub
- URL: https://github.com/ofai/bayesiannonparametrics.jl
- Owner: OFAI
- License: other
- Created: 2016-12-02T15:13:39.000Z (over 8 years ago)
- Default Branch: master
- Last Pushed: 2018-09-06T11:32:22.000Z (over 6 years ago)
- Last Synced: 2025-03-27T10:01:49.650Z (about 1 month ago)
- Topics: bayesian-machine-learning, bayesian-methods, bayesian-nonparametric-models, dirichlet-process-mixtures, julia
- Language: Julia
- Homepage: http://ofai.at
- Size: 284 KB
- Stars: 32
- Watchers: 2
- Forks: 11
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE.md
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README
BayesianNonparametrics.jl
===========
[](https://travis-ci.org/OFAI/BayesianNonparametrics.jl)
[](https://coveralls.io/github/OFAI/BayesianNonparametrics.jl?branch=master)
*BayesianNonparametrics* is a Julia package implementing state-of-the-art Bayesian nonparametric models for medium-sized unsupervised problems. The software package brings Bayesian nonparametrics to non-specialists allowing the widespread use of Bayesian nonparametric models. Emphasis is put on consistency, performance and ease of use allowing easy access to Bayesian nonparametric models inside Julia.
*BayesianNonparametrics* allows you to
- explain discrete or continous data using: Dirichlet Process Mixtures or Hierarchical Dirichlet Process Mixtures
- analyse variable dependencies using: Variable Clustering Model
- fit multivariate or univariate distributions for discrete or continous data with conjugate priors
- compute point estimtates of Dirichlet Process Mixtures posterior samples
#### News
*BayesianNonparametrics* is Julia 0.7 / 1.0 compatible
Installation
------------
You can install the package into your running Julia installation using Julia's package manager, i.e.
```julia
pkg> add BayesianNonparametrics
```
Documentation
-------------
Documentation is available in Markdown:
[documentation](docs/README.md)
Example
-------
The following example illustrates the use of *BayesianNonparametrics* for clustering of continuous observations using a Dirichlet Process Mixture of Gaussians.
After loading the package:
```julia
using BayesianNonparametrics
```
we can generate a 2D synthetic dataset (or use a multivariate continuous dataset of interest)
```julia
(X, Y) = bloobs(randomize = false)
```
and construct the parameters of our base distribution:
```julia
μ0 = vec(mean(X, dims = 1))
κ0 = 5.0
ν0 = 9.0
Σ0 = cov(X)
H = WishartGaussian(μ0, κ0, ν0, Σ0)
```
After defining the base distribution we can specify the model:
```julia
model = DPM(H)
```
which is in this case a Dirichlet Process Mixture. Each model has to be initialised, one possible initialisation approach for Dirichlet Process Mixtures is a k-Means initialisation:
```julia
modelBuffer = init(X, model, KMeansInitialisation(k = 10))
```
The resulting buffer object can now be used to apply posterior inference on the model given `X`. In the following we apply Gibbs sampling for 500 iterations without burn in or thining:
```julia
models = train(modelBuffer, DPMHyperparam(), Gibbs(maxiter = 500))
```
You shoud see the progress of the sampling process in the command line. After applying Gibbs sampling, it is possible explore the posterior based on their posterior densities,
```julia
densities = map(m -> m.energy, models)
```
number of active components
```julia
activeComponents = map(m -> sum(m.weights .> 0), models)
```
or the groupings of the observations:
```julia
assignments = map(m -> m.assignments, models)
```
The following animation illustrates posterior samples obtained by a Dirichlet Process Mixture:
Alternatively, one can compute a point estimate based on the posterior similarity matrix:
```julia
A = reduce(hcat, assignments)
(N, D) = size(X)
PSM = ones(N, N)
M = size(A, 2)
for i in 1:N
for j in 1:i-1
PSM[i, j] = sum(A[i,:] .== A[j,:]) / M
PSM[j, i] = PSM[i, j]
end
end
```
and find the optimal partition which minimizes the lower bound of the variation of information:
```julia
mink = minimum(length(m.weights) for m in models)
maxk = maximum(length(m.weights) for m in models)
(peassignments, _) = pointestimate(PSM, method = :average, mink = mink, maxk = maxk)
```
The grouping wich minimizes the lower bound of the variation of information is illustrated in the following image:
