# Hierarchical correlation reconstruction with missing data, for example for biology-inspired neuron

arXiv: https://arxiv.org/abs/1804.06218 · HTML: https://mlsanity.com/paper/1804.06218/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Apr 2018.

## Built on by (most cited first, 6 of 6)

- [Predicting conditional probability distributions of redshifts of Active Galactic Nuclei using Hierarchical Correlation Reconstruction](https://mlsanity.com/paper/2206.06194/) (2022)
- [Time delay multi-feature correlation analysis to extract subtle dependencies from EEG signals](https://mlsanity.com/paper/2305.09478/) (2023)
- [Biology-inspired joint distribution neurons based on Hierarchical Correlation Reconstruction allowing for multidirectional propagation of values and densities](https://mlsanity.com/paper/2405.05097/) (2024)
- [Low cost prediction of probability distributions of molecular properties for early virtual screening](https://mlsanity.com/paper/2207.11174/) (2022)
- [Extracting individual variable information for their decoupling, direct mutual information and multi-feature Granger causality](https://mlsanity.com/paper/2311.13431/) (2023)
- [Improving KAN with CDF normalization to quantiles](https://mlsanity.com/paper/2507.13393/) (2025)

## Abstract (arXiv)

Machine learning often needs to model density from a multidimensional data sample, including correlations between coordinates. Additionally, we often have missing data case: that data points can miss values for some of coordinates. This article adapts rapid parametric density estimation approach for this purpose: modelling density as a linear combination of orthonormal functions, for which L2 optimization says that (independently) estimated coefficient for a given function is just average over the sample of value of this function. Hierarchical correlation reconstruction first models probability density for each separate coordinate using all its appearances in data sample, then adds corrections from independently modelled pairwise correlations using all samples having both coordinates, and so on independently adding correlations for growing numbers of variables using often decreasing evidence in data sample. A basic application of such modelled multidimensional density can be imputation of missing coordinates: by inserting known coordinates to the density, and taking expected values for the missing coordinates, or even their entire joint probability distribution. Presented method can be compared with cascade correlations approach, offering several advantages in flexibility and accuracy. It can be also used as artificial neuron: maximizing prediction capabilities for only local behavior - modelling and predicting local connections.