Regression on manifolds: Estimation of the exterior derivative
By Anil Jayanti Aswani, Peter J. Bickel, Claire Jennifer Tomlin. 2011
77 citations recorded by the source corpus.
Collinearity and near-collinearity of predictors cause difficulties when doing regression. In these cases, variable selection becomes untenable because of mathematical issues concerning the existence and numerical stability of the regression coefficients, and interpretation of the coefficients is ambiguous because gradients are not defined. Using a differential geometric interpretation, in which the regression coefficients are interpreted as estimates of the exterior derivative of a function, we develop a new method to do regression in the presence of collinearities. Our regularization scheme can improve estimation error, and it can be easily modified to include lasso-type regularization. These estimators also have simple extensions to the "large $p$, small $n$" context.
Subfields: Geometry and Topology, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/e90cd32b4548aa0be3a2b2711899e925424477bf
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In Geometry and Topology
In Statistics and Probability
Citations in the corpus
- The topology of probability distributions on manifolds (2013, background): “The motivating principle behind manifold learning is using low dimensional geometric summaries of the data for statistical inference [4, 10, 21, 31, 50].”
- Provably safe and robust learning-based model predictive control (2011, unknown): “Though designing a controller that ensures SE can be difficult, checking a posteriori whether a system has SE is straightforward [46,7,8].”