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Kernel density integral transformation

Project description


The kernel-density integral transformation (McCarter, 2023, TMLR), like min-max scaling and quantile transformation, maps continuous features to the range [0, 1]. It achieves a happy balance between these two transforms, preserving the shape of the input distribution like min-max scaling, while nonlinearly attenuating the effect of outliers like quantile transformation. It can also be used to discretize features, offering a data-driven alternative to univariate clustering or K-bins discretization.

You can tune the interpolation $\alpha$ between 0 (quantile transform) and $\infty$ (min-max transform), but a good default is $\alpha=1$, which is equivalent to using scipy.stats.gaussian_kde(bw_method=1). This is an easy way to improves performance for a lot of supervised learning problems. See this notebook for example usage and the paper for a detailed description of the method.

Accuracy on Iris
rMSE on CA Housing


Installation from PyPI

pip install kditransform

Installation from source

After cloning this repo, install the dependencies on the command-line, then install kditransform:

pip install -r requirements.txt
pip install -e .


kditransform.KDTransformer is a drop-in replacement for sklearn.preprocessing.QuantileTransformer. When alpha (defaults to 1.0) is small, our method behaves like the QuantileTransformer; when alpha is large, it behaves like sklearn.preprocessing.MinMaxScaler.

import numpy as np
from kditransform import KDITransformer
X = np.random.uniform(size=(500, 1))
kdt = KDITransformer(alpha=1.)
Y = kdt.fit_transform(X)

kditransform.KDIDiscretizer offers an API based on sklearn.preprocessing.KBinsDiscretizer. It encodes each feature ordinally, similarly to KBinsDiscretizer(encode='ordinal').

from kditransform import KDIDiscretizer
rng = np.random.default_rng(1)
x1 = rng.normal(1, 0.75, size=int(0.55*N))
x2 = rng.normal(4, 1, size=int(0.3*N))
x3 = rng.uniform(0, 20, size=int(0.15*N))
X = np.sort(np.r_[x1, x2, x3]).reshape(-1, 1)
kdd = KDIDiscretizer()
T = kdd.fit_transform(X)

Initialized as KDIDiscretizer(enable_predict_proba=True), we can also output one-hot encodings and probabilistic one-hot encodings of single-feature input data.

kdd = KDIDiscretizer(enable_predict_proba=True).fit(X)
P = kdd.predict(X)  # one-hot encoding
P = kdd.predict_proba(X)  # probabilistic one-hot encoding

Citing this method

If you use this tool, please cite KDITransform using the following reference to our TMLR paper:

In Bibtex format:

title={The Kernel Density Integral Transformation},
author={Calvin McCarter},
journal={Transactions on Machine Learning Research},

Usage with TabPFN

TabPFN is a meta-learned Transformer model for tabular classification. In the TabPFN paper, features are preprocessed with the concatenation of z-scored & power-transformed features. After simply adding KDITransform'ed features, I observed improvements on the reported benchmarks. In particular, on the 30 test datasets in OpenML-CC18, mean AUC OVO increases from 0.8943 to 0.8950; on the subset of 18 numerical datasets in Table 1 of the TabPFN paper, mean AUC OVO increases from 0.9335 to 0.9344.

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