NNDensity 0.0.2

Nearest Neighbor Density Estimation

Nearest Neighbor Density Estimation (NNDensity)

The package implements six nearest neighbor based density estimation method and provides efficient tools for density estimation research. See paper/paper.md for more descriptions and details in methodology and literature.

Contents

• Installation
• Basic Usage
  • Data Generation
  • Density Estimation
  • Visualization
• Reference

Installation

Since NNDensity is based on Cython, installation requires c/c++ compiler. Users can check by

gcc -v
g++ -v

to see their version. For Linux, users can install gcc/g++ by apt. For macOS, refer to Xcode. For Windows, refer to Microsoft c++ building tools.

Via PypI

pip install NNDensity

Via GitHub

pip install git+https://github.com/Karlmyh/NNDensity.git

Mannul Install

git clone [e-mail]:Karlmyh/NNDensity.git
cd NNDensity 
python setup.py install

Basic Usage

Data Generation

Density generation tools. Below is a show case using a mixture distribution.

from NNDensity import MultivariateNormalDistribution, MixedDistribution, ExponentialDistribution
# setup
dim=2
density1 = ExponentialDistribution(lamda = np.ones(dim)*0.5) 
density2 = MultivariateNormalDistribution(mean = np.zeros(dim)-1.5, cov = np.diag(np.ones(dim)*0.3)) 
density_seq = [density1, density2]
prob_seq = [0.4, 0.6]
densitymix = MixedDistribution(density_seq, prob_seq)

# generate 10 samples and return their pdf
samples, samples_pdf = densitymix.generate(10)
samples

# evaluate pdf at given samples
densitymix.density(samples)

# compare with true pdf
(samples_pdf == samples).all()

Out[1]:  array([[-2.23087816, -1.08521314],
       [-1.03424594, -1.24327987],
       [-2.02698363, -1.63201056],
       [ 1.43021832,  1.51448518],
       [ 1.58820377,  1.8541296 ],
       [-0.88802267, -2.398429  ],
       [-1.26067249, -2.12988644],
       [-1.92476226, -2.0167295 ],
       [-2.0035588 , -1.35662414],
       [-1.46406062, -1.9693262 ]])
Out[2]: True

Density Estimation

Adopt AWNN model to estimate the density.

###### using AWNN to estimate density
from NNDensity import AWNN

# generate samples
X_train, pdf_X_train =densitymix.generate(1000)
X_test, pdf_X_test =densitymix.generate(1000)

# choose parameter C=0.1
model_AWNN=AWNN(C=.1).fit(X_train)
# output is log scaled
est_AWNN=np.exp(model_AWNN.predict(X_test))
# compute the mean absolute error
np.abs(est_AWNN-pdf_X_test).mean()

Out[3]:  0.09148487940943466

Automatically select parameter using GridSearchCV to improve result.

from sklearn.model_selection import GridSearchCV

# generate samples
X_train, pdf_X_train =densitymix.generate(1000)
X_test, pdf_X_test =densitymix.generate(1000)

# select parameter grid
parameters={"k":[int(i*1000) for i in [0.01,0.02,0.05,0.1,0.2,0.5]]}
# use all available cpu, use 10 fold cross validation
cv_model_KNN=GridSearchCV(estimator=KNN(),param_grid=parameters,n_jobs=-1,cv=10)
_=cv_model_KNN.fit(X_train)
model_KNN=cv_model_KNN.best_estimator_
    
# output is log scaled
est_KNN=np.exp(model_KNN.predict(X_test))
# compute the mean absolute error
np.abs(est_KNN-pdf_X_test).mean()

Out[4]:  0.055937476261628344

Visualization

Frequently used visualization plots for density estimation research.

###### 3d prediction surface using WKNN
from NNDensity import contour3d

# generate samples
dim=2
density1 = MultivariateNormalDistribution(mean = np.zeros(dim)+1.5, cov = np.diag(np.ones(dim)*0.4)) 
density2 = MultivariateNormalDistribution(mean = np.zeros(dim)-1.5, cov = np.diag(np.ones(dim)*0.7)) 
density_seq = [density1, density2]
prob_seq = [0.4, 0.6]
densitymix = MixedDistribution(density_seq, prob_seq)
X_train, pdf_X_train =densitymix.generate(1000)

model_plot=contour3d(X_train,method="WKNN",k=100)
model_plot.estimation()
fig=model_plot.make_plot()

###### 2d prediction contour using BKNN

from NNDensity import contour2d
from sklearn.model_selection import GridSearchCV

# generate samples
X_train, pdf_X_train =densitymix.generate(1000)

model_plot=contour2d(X_train,method="BKNN",C=10)
model_plot.estimation()
fig=model_plot.make_plot()

###### prediction curve plot

# generate samples
X_train, pdf_X_train =densitymix.generate(1000)


kargs_seq= [{"k":100},{"k":100},{"k":100} ]
model_plot=lineplot(X_train,method_seq=["KNN", "WKNN", "TKNN"],true_density_obj=densitymix,kargs_seq=kargs_seq)
fig=model_plot.plot()

kargs_seq= [{"C":0.9},{"C":1},{"C":1} ]
model_plot=lineplot(X_train,method_seq=["AKNN", "BKNN", "AWNN"],true_density_obj=densitymix,kargs_seq=kargs_seq)
fig=model_plot.plot()

Reference

NNDensity utilizes tools from numpy, matplotlib, scipy, jupyter notebooks, scikit-learn, cython and numba. Also, large part of KD tree implementation was borrowed from scikit-learn. For specific citations, see papers/paper.md.