The Hyperdimensional Transform for Distributional Modelling, Regression
  and Classification
Pieter Dewulf Bernard De Baets Michiel Stock
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.