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.

翻译：超维计算（HDC）是一种日益流行的计算范式，在未来的智能应用领域具有巨大潜力。尽管其主要思想在20世纪90年代已具雏形，但HDC近期才获得显著关注，尤其是在机器学习与数据科学领域。除了高效性、互操作性与可解释性之外，HDC还提供了极具吸引力的泛化特性，可视为神经网络中的联结主义思想与符号主义元素的结合尝试。在近期工作中，我们提出了超维变换，揭示了将函数与分布表征为高维全息向量的深层理论基础。本文向广大的数据科学受众展示了超维变换的强大能力。我们以超维变换为理论基础，深入阐释了用于机器学习的先进HDC方法，展示了如何改进现有算法，以及该变换如何催生一套新颖且基础扎实的工具箱。除机器学习标准的回归与分类任务外，我们的讨论还涵盖统计建模的多个方面，包括分布的表示、学习与反卷积、采样、贝叶斯推断以及不确定性估计。