Learning in Function Spaces: An Unified Functional Analytic View of Supervised and Unsupervised Learning
Many machine learning algorithms can be interpreted as procedures for estimating functions defined on the data distribution. In this paper we present a conceptual framework that formulates a wide range of learning problems as variational optimization over function spaces induced by the data distribution. Within this framework the data distribution defines operators that capture structural properties of the data, such as similarity relations or statistical dependencies. Learning algorithms can then be viewed as estimating functions expressed in bases determined by these operators. This perspective provides a unified way to interpret several learning paradigms. In supervised learning the ob...
| Authors | K. Lakshmanan |
|---|---|
| Primary category | cs.LG |
| Published | 15 March 2026 |
| Last updated at source | 15 March 2026 |
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