https://github.com/ngiann/fastparzenwindows.jl

Fast Parzen Windows: a kernel-based method for non-parametric probability density function.
https://github.com/ngiann/fastparzenwindows.jl

julia kernel-density-estimation statistics

Last synced: 20 days ago
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Fast Parzen Windows: a kernel-based method for non-parametric probability density function.

• Host: GitHub
• URL: https://github.com/ngiann/fastparzenwindows.jl
• Owner: ngiann
• License: mit
• Created: 2022-01-19T20:33:13.000Z (almost 3 years ago)
• Default Branch: main
• Last Pushed: 2024-01-18T11:34:31.000Z (10 months ago)
• Last Synced: 2024-10-03T05:06:01.444Z (about 1 month ago)
• Topics: julia, kernel-density-estimation, statistics
• Language: Julia
• Homepage:
• Size: 139 KB
• Stars: 0
• Watchers: 1
• Forks: 0
• Open Issues: 1
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

        
# FastParzenWindows.jl

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![GitHub](https://img.shields.io/github/license/ngiann/FastParzenWindows.jl)

## ℹ What is this?

This is a Julia implementation of the **Fast Parzen Window Density Estimator** described in 

*X. Wang, P. Tino, M. A. Fardal, S. Raychaudhury and A. Babul, "Fast parzen window density estimator," 2009 International Joint Conference on Neural Networks, 2009, pp. 3267-3274.*

This is a technique for estimating a probability density from an observed set of data points. The data space is partitioned in hyper-discs of fixed radii `r` and each partition is modelled with a Gaussian density.  The final model is a mixture of Gaussians with each Gaussian fitted locally to a partition.

The algorithm presented in the paper has two versions called 'hard' and 'soft'.  This repository provides an implementation of the 'soft' version.

## 💾 How to install

Apart from cloning, an easy way of using the package is to switch into "package mode" with ```]``` in the Julia REPL and use `add FastParzenWindows`.

## ▶ How to use

There are two functions of interest: `fpw` and `cvfpw`.

- `fpw` takes two arguments, a N×D data matrix `X` and a scalar `r` which expresses the radius of the hyper-discs in which the data space is partitioned. The output is an object of the type `Distributions.MixtureModel`.

- `cvfpw` takes two arguments, a N×D data matrix `X` and a range of candidate radii of the hyper-discs. It performs cross-validation for each candidate `r` and returns a matrix of out-of-sample log-likelihoods of dimensions (number of `r` candidates)×(number of folds).

## ▶ Example

We use a dataset taken from the paper. We generate 300 data points using:

```

using FastParzenWindows

using PyPlot # must be independently installed, needed only for plotting present example

using Statistics

X = spiraldata(300)

plot(X[:,1], X[:,2], "bo", label="dataset")

```

We want to find out which `r` works well for this dataset:

```

# define range of 100 candidate radii

r_range = LinRange(0.01, 2.0, 100)

# perform cross-validation

cvresults = cvfpw(X, r_range)

# which is the best r?

r_perf = mean(cvresults, dims=2)

best_index = argmax(r_perf)

r_best = r_range[best_index]

```

Estimate final model:

```

mix = fpw(X, r_best)

# generate observations and plot them

x = rand(mix, 1000)'

plot(x[:,1], x[:,2], "r.", label="generated")

legend()

```

![Spiral example](spiral.png)