The Hyperdimensional Transform for Distributional Modelling, Regression and Classification

TL;DR

This paper introduces the hyperdimensional transform, a theoretical foundation for representing functions and distributions as high-dimensional vectors, enhancing machine learning methods with improved generalization, interpretability, and a new toolbox for distributional modeling.

Contribution

It presents the hyperdimensional transform as a novel theoretical basis for distributional modeling, regression, and classification in hyperdimensional computing, connecting neural and symbolic approaches.

Findings

The hyperdimensional transform enables new algorithms for distributional representation.

It improves existing HDC methods for regression and classification.

The approach facilitates statistical modeling, Bayesian inference, and uncertainty estimation.

Abstract

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.