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https://github.com/JuliaRobotics/KernelDensityEstimate.jl

Kernel Density Estimate with product approximation using multiscale Gibbs sampling
https://github.com/JuliaRobotics/KernelDensityEstimate.jl

bayesian gadfly inference julialang multiscale-gibbs-sampling probabilistic-programming

Last synced: 3 months ago
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Kernel Density Estimate with product approximation using multiscale Gibbs sampling

Host: GitHub
URL: https://github.com/JuliaRobotics/KernelDensityEstimate.jl
Owner: JuliaRobotics
License: lgpl-2.1
Created: 2016-04-07T13:00:34.000Z (over 8 years ago)
Default Branch: master
Last Pushed: 2024-01-22T11:40:59.000Z (10 months ago)
Last Synced: 2024-07-21T07:04:46.110Z (4 months ago)
Topics: bayesian, gadfly, inference, julialang, multiscale-gibbs-sampling, probabilistic-programming
Language: Julia
Size: 640 KB
Stars: 23
Watchers: 4
Forks: 7
Open Issues: 12
Metadata Files:
- Readme: README.md
- License: LICENSE

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awesome-sciml - JuliaRobotics/KernelDensityEstimate.jl: Kernel Density Estimate with product approximation using multiscale Gibbs sampling

README

        # KernelDensityEstimate.jl

[![CI](https://github.com/JuliaRobotics/KernelDensityEstimate.jl/actions/workflows/ci.yml/badge.svg)](https://github.com/JuliaRobotics/KernelDensityEstimate.jl/actions/workflows/ci.yml)

[![codecov.io](https://codecov.io/github/JuliaRobotics/KernelDensityEstimate.jl/coverage.svg?branch=master)](https://codecov.io/github/JuliaRobotics/KernelDensityEstimate.jl?branch=master)

Kernel Density Estimation **with product approximation using multiscale Gibbs sampling**.

All code is implemented in native Julia, including plotting. The main focus of this module is the ability to take the product between multiple KDEs, and makes this module unique from other KDE implementations. This package also supports n-dimensional KDEs. Please see examples below for details. The implementation is already fairly optimized from a symbolic standpoint and is based on work by:

    Sudderth, Erik B.; Ihler, Alexander, et al. "Nonparametric belief propagation." Communications of the ACM 53.10 (2010): 95-103.

## Installation

In Julia 1.0 and above:

```julia

] add KernelDensityEstimate

```

## Plotting Functions

The plotting functions for this library have been separated into [KernelDensityEstimatePlotting.jl](http://www.github.com/JuliaRobotics/KernelDensityEstimatePlotting.jl).  Plotting functionality uses [Gadfly](https://github.com/GiovineItalia/Gadfly.jl).  Comments welcome.

# Examples

Bring the module into the workspace

```julia

using KernelDensityEstimate

# Basic one dimensional examples

# using leave-one-out likelihood cross validation for bandwidth estimation

p100 = kde!([randn(50);10.0.+2*randn(50)])

p2 = kde!([0.0;10.0],[1.0]) # multibandwidth still to be added

p75 = resample(p2,75)

# bring in the plotting functions

using KernelDensityEstimatePlotting

plot([p100;p2;p75],c=["red";"green";"blue"]) # using Gadfly under the hood

```

![alt tag](https://raw.githubusercontent.com/JuliaRobotics/KernelDensityEstimate.jl/master/test/FirstExamplePlot.png)

Multidimensional example

```julia

pd2 = kde!(randn(3,100));

@time pd2 = kde!(randn(3,100)); # defaults to loocv

pm12 = marginal(pd2,[1;2]);

pm2 = marginal(pm12,[2]);

plot(pm2);

```

Multiscale Gibbs product approximation example

```julia

p = kde!(randn(2,100))

q = kde!(2.0.+randn(2,100))

dummy = kde!(rand(2,100),[1.0]);

mcmciters = 5

pGM, = prodAppxMSGibbsS(dummy, [p;q], nothing, nothing, Niter=mcmciters)

pq = kde!(pGM)

pq1 = marginal(pq,[1])

Pl1 = plot([marginal(p,[1]);marginal(q,[1]);marginal(pq,[1])],c=["red";"green";"black"])

```

Direct histogram of points from the product

```julia

using Gadfly

Pl2 = Gadfly.plot(x=pGM[1,:],y=pGM[2,:],Geom.histogram2d);

draw(PDF("product.pdf",15cm,8cm),hstack(Pl1,Pl2))

```

![alt tag](https://raw.githubusercontent.com/JuliaRobotics/KernelDensityEstimate.jl/master/test/product.png)

KDE product between non-gaussian distributions

```julia

using Distributions

p = kde!(rand(Beta(1.0,0.45),300));

q = kde!(rand(Rayleigh(0.5),100).-0.5);

dummy = kde!(rand(1,100),[1.0]);

pGM, = prodAppxMSGibbsS(dummy, [p;q], nothing, nothing, Niter=5)

pq = kde!(pGM)

plot([p;q;pq],c=["red";"green";"black"])

```

![alt tag](https://raw.githubusercontent.com/JuliaRobotics/KernelDensityEstimate.jl/master/test/RayleighBetaProduct.png)

Draw multidimensional distributions as marginalized 2D contour plots

```julia

axis=[[-5.0;5]';[-2.0;2.0]';[-10.0;10]';[-5.0;5]']

draw(PDF("test.pdf",30cm,20cm),

 plot( kde!(randn(4,200)) ) )

N=200;

pts = [2*randn(1,N).+3;

 [2*randn(1,round(Int,N/2))'.+3.0;2*randn(1,round(Int,N/2))'.-3.0]';

 2*randn(2,N).+3];

p, q = kde!(randn(4,100)), kde!(pts);

draw(PNG("MultidimPlot.png",15cm,10cm),

 plot( [p*q;p;q],c=["red";"black";"blue"], axis=axis, dims=2:4,dimLbls=["w";"x";"y";"z"], levels=4) )

```

![alt tag](https://raw.githubusercontent.com/JuliaRobotics/KernelDensityEstimate.jl/master/test/MultidimPlot.png)

```julia

# or draw product natively

draw(PNG("MultidimPlotProd.png",10cm,7cm),

 plot( p*q, axis=axis, dims=[2;4],dimLbls=["w";"x";"y";"z"]) )

```

![alt tag](https://raw.githubusercontent.com/JuliaRobotics/KernelDensityEstimate.jl/master/test/MultidimPlotProd.png)

# Contributors

The original C++ kde package was written by Alex Ihler and Mike Mandel in 2003, and has be rewritten in Julia and continuously modified by Dehann Fourie since.  

Thank you to contributors and users alike, comments and improvements welcome according to JuliaLang and JuliaRobotics standards.