The Hyperdimensional Transform for Distributional Modelling, Regression and Classification
This work provides a foundational framework for hyperdimensional computing, potentially benefiting data science and machine learning by enhancing generalization, interoperability, and explainability, though it appears incremental as it builds on existing HDC ideas.
The paper introduces the hyperdimensional transform as a theoretical foundation for representing functions and distributions as high-dimensional holographic vectors, enabling modifications to existing algorithms and a novel toolbox for tasks like regression, classification, and statistical modeling.
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.