Lin, W.-Y., Liu, S., Ren, C., Cheung, N.-M., Li, H., &amp;amp; Matsushita, Y. (2021). Shell Theory: A Statistical Model of Reality. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1–1. doi:10.1109/tpami.2021.3084598
The foundational assumption of machine learning is that the data under consideration is separable into classes; while intuitively reasonable, separability constraints have proven remarkably difficult to formulate mathematically. We believe this problem is rooted in the mismatch between existing statistical techniques and commonly encountered data; object representations are typically high dimensional but statistical techniques tend to treat high dimensions a degenerate case. To address this problem, we develop a dedicated statistical framework for machine learning in high dimensions. The framework derives from the observation that object relations form a natural hierarchy; this leads us to model objects as instances of a high dimensional, hierarchal generative processes. Using a distance based statistical technique, also developed in this paper, we show that in such generative processes, instances of each process in the hierarchy, are almost-always encapsulated by a distinctive-shell that excludes almost-all other instances. The result is shell theory, a statistical machine learning framework in which separability constraints (distinctive-shells) are formally derived from the assumed generative process.
This research is supported by core funding from: Institute for Infocomm Research
Grant Reference no. : SC20/19-128610-CORE
This research / project is supported by the Ministry of Education - Academic Research Fund (AcRF) Tier 1
Grant Reference no. : N.A