PrologMethods/Misc.-other/kde.md

+# Kernel Density Estimation
+
+An implementation of kernel density estimation with dual-tree algorithms. Given a set of reference points and query points and a kernel function, this can estimate the density function at the location of each query point using trees.
+
+# Available Predicates
+
+* [initAndBuildModel/14](https://gitlab.cs.uni-duesseldorf.de/stups/abschlussarbeiten/prolog-mlpack-libary/-/wikis/PrologMethods/Misc.-other/kde#initandbuildmodel14)
+* [evaluateWithQuery/5](https://gitlab.cs.uni-duesseldorf.de/stups/abschlussarbeiten/prolog-mlpack-libary/-/wikis/PrologMethods/Misc.-other/kde#evaluatewithquery5)
+* [evaluateNoQuery/2](https://gitlab.cs.uni-duesseldorf.de/stups/abschlussarbeiten/prolog-mlpack-libary/-/wikis/PrologMethods/Misc.-other/kde#evaluatenoquery2)
+
+---
+
+[links/resources](https://gitlab.cs.uni-duesseldorf.de/stups/abschlussarbeiten/prolog-mlpack-libary/-/wikis/PrologMethods/Misc.-other/kde#connected-linksresources)
+
+## **_initAndBuildModel/14_**
+
+Build the KDE model with the given parameters and then trains it with the given reference data.
+
+```prolog
+%% part of the predicate definition
+initAndBuildModel( +float32, +float32, +float32, 
+                    +string, +string, +string, 
+                    +integer, 
+                    +float32, +integer, +float32, +float32, 
+                    +pointer(float_array), +integer, +integer).
+```
+
+### Parameters
+| Name | Type | Description | Default |
+|------|------|-------------|---------|
+| bandwidth | +float | Bandwidth of the kernel. | 1.0 |
+| relError | +float | Relative error tolerance for the prediction. | 0.05 |
+| absError | +float | Absolute error tolerance for the prediction. | 0.0 |
+| kernelType | +string | Kernel to use for the prediction.(‘gaussian’, ‘epanechnikov’, ‘laplacian’, ‘spherical’, ‘triangular’). | gaussian |
+| treeType | +string | Tree to use for the prediction.(‘kd-tree’, ‘ball-tree’, ‘cover-tree’, ‘octree’, ‘r-tree’). | kd-tree |
+| algorithm | +string | Algorithm to use for the prediction.(‘dual-tree’, ‘single-tree’). | dual-tree |
+| monteCarlo | +integer(bool) | Whether to use Monte Carlo estimations when possible. | (0)false |
+| mcProb | +float | Probability of the estimation being bounded by relative error when using Monte Carlo estimations. | 0.95 |
+| initialSampleSize | +integer |  | 100 |
+| mcEntryCoef | +float | Controls how much larger does the amount of node descendants has to be compared to the initial sample size in order to be a candidate for Monte Carlo estimations. | 3.0 |
+| mcBreakCoef | +float | Controls what fraction of the amount of node’s descendants is the limit for the sample size before it recurses. | 0.4 |
+| referenceSet | +matrix | Input reference dataset use for KDE. | - |
+
+---
+
+## **_evaluateWithQuery/5_**
+
+Perform kernel density estimation on the given query set.
+
+**_initAndBuildModel/14_** has to be called before.
+
+```prolog
+%% part of the predicate definition
+evaluateWithQuery(  +pointer(float_array), +integer, +integer, 
+                    -pointer(float_array), -integer).
+```
+
+### Parameters
+| Name | Type | Description | Default |
+|------|------|-------------|---------|
+| querySet | +matrix | Query dataset to KDE on. | - |
+| estimations | -vector | Vector to store density predictions. | - |
+
+---
+
+## **_evaluateNoQuery/2_**
+
+Perform kernel density estimation on the reference set.
+
+If possible, it returns normalized estimations.
+
+**_initAndBuildModel/14_** has to be called before.
+
+```prolog
+%% part of the predicate definition
+evaluateNoQuery(  -pointer(float_array), -integer).
+```
+
+### Parameters
+| Name | Type | Description | Default |
+|------|------|-------------|---------|
+| estimations | -vector | Vector to store density predictions. | - |
+
+---
+
+# Connected Links/Resources
+
+If you want a more detailed explanation, then go to the python documentation. There is most of the time a good explanation on how the methods work and what the parameters do.
+
+* [MLpack::kde_C++\_documentation](https://www.mlpack.org/doc/stable/doxygen/classmlpack_1_1kde_1_1KDE.html)
+* [MLpack::kde_Python_documentation](https://www.mlpack.org/doc/stable/python_documentation.html#kde)
+
+added some of the links from the python documentation
+
+* knn
+* [Kernel density estimation on Wikipedia](https://en.wikipedia.org/wiki/Kernel_density_estimation)
+* [Tree-Independent Dual-Tree Algorithms (pdf)](https://arxiv.org/pdf/1304.4327.pdf)
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