# The Hyperdimensional Transform for Distributional Modelling, Regression and Classification

arXiv: https://arxiv.org/abs/2311.08150 · HTML: https://mlsanity.com/paper/2311.08150/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 70 references that are in the map.
- First posted on arXiv 14 Nov 2023.

## Builds on (most cited first, 23 of 23)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Kernel Mean Embedding of Distributions: A Review and Beyond](https://mlsanity.com/paper/1605.09522/) (2016)
- [Therapeutics Data Commons: Machine Learning Datasets and Tasks for Drug Discovery and Development](https://mlsanity.com/paper/2102.09548/) (2021)
- [A Survey on Hyperdimensional Computing aka Vector Symbolic Architectures, Part I: Models and Data Transformations](https://mlsanity.com/paper/2111.06077/) (2021)
- [A Survey on Hyperdimensional Computing aka Vector Symbolic Architectures, Part II: Applications, Cognitive Models, and Challenges](https://mlsanity.com/paper/2112.15424/) (2021)
- [A comparison of Vector Symbolic Architectures](https://mlsanity.com/paper/2001.11797/) (2020)
- [A Neuro-vector-symbolic Architecture for Solving Raven's Progressive Matrices](https://mlsanity.com/paper/2203.04571/) (2022)
- [Classification using Hyperdimensional Computing: A Review](https://mlsanity.com/paper/2004.11204/) (2020)
- [A Theoretical Perspective on Hyperdimensional Computing](https://mlsanity.com/paper/2010.07426/) (2020)
- [Deep Randomized Neural Networks](https://mlsanity.com/paper/2002.12287/) (2020)
- [Robust High-dimensional Memory-augmented Neural Networks](https://mlsanity.com/paper/2010.01939/) (2020)
- [GraphHD: Efficient graph classification using hyperdimensional computing](https://mlsanity.com/paper/2205.07826/) (2022)
- [Variable Binding for Sparse Distributed Representations: Theory and Applications](https://mlsanity.com/paper/2009.06734/) (2020)
- [High-Dimensional Gaussian Process Inference with Derivatives](https://mlsanity.com/paper/2102.07542/) (2021)
- [Sum-product networks: A survey](https://mlsanity.com/paper/2004.01167/) (2020)
- [An EMG Gesture Recognition System with Flexible High-Density Sensors and Brain-Inspired High-Dimensional Classifier](https://mlsanity.com/paper/1802.10237/) (2018)
- [Physics Informed Deep Kernel Learning](https://mlsanity.com/paper/2006.04976/) (2020)
- [Holographic Graph Neuron: a Bio-Inspired Architecture for Pattern Processing](https://mlsanity.com/paper/1501.03784/) (2015)
- [Less is More: Parameter-Free Text Classification with Gzip](https://mlsanity.com/paper/2212.09410/) (2022)
- [Reservoir Computing and Extreme Learning Machines using Pairs of Cellular Automata Rules](https://mlsanity.com/paper/1703.05807/) (2017)
- [Demeter: A Fast and Energy-Efficient Food Profiler using Hyperdimensional Computing in Memory](https://mlsanity.com/paper/2206.01932/) (2022)
- [Training a HyperDimensional Computing Classifier using a Threshold on its Confidence](https://mlsanity.com/paper/2305.19007/) (2023)
- [The Hyperdimensional Transform: a Holographic Representation of Functions](https://mlsanity.com/paper/2310.16065/) (2023)

## Built on by (most cited first, 2 of 2)

- [Vector-Symbolic Architecture for Event-Based Optical Flow](https://mlsanity.com/paper/2405.08300/) (2024)
- [Hyperdimensional computing: a fast, robust and interpretable paradigm for biological data](https://mlsanity.com/paper/2402.17572/) (2024)

## Abstract (arXiv)

Hyperdimensional computing (HDC) is an increasingly popular computing paradigm with immense potential for future intelligent applications. Although the main ideas already took form in the 1990s, HDC recently gained significant attention, especially in the field of machine learning and data science. Next to efficiency, interoperability and explainability, HDC offers attractive properties for generalization as it can be seen as an attempt to combine connectionist ideas from neural networks with symbolic aspects. In recent work, we introduced the hyperdimensional transform, revealing deep theoretical foundations for representing functions and distributions as high-dimensional holographic vectors. Here, we present the power of the hyperdimensional transform to a broad data science audience. We use the hyperdimensional transform as a theoretical basis and provide insight into state-of-the-art HDC approaches for machine learning. We show how existing algorithms can be modified and how this transform can lead to a novel, well-founded toolbox. Next to the standard regression and classification tasks of machine learning, our discussion includes various aspects of statistical modelling, such as representation, learning and deconvolving distributions, sampling, Bayesian inference, and uncertainty estimation.