Multi-Task Optimal Experiment Design
summary
Shows that pooling samples with the maximum likelihood / least-squares estimator gives zero improvement at epoch-2 design points unless the subspaces overlap: mean-squared error at those points is identical to using only epoch-2 data, even as epoch-1 samples → ∞. Proof uses operator-norm distance between orthogonal projections, PSD partial-order and pseudo-inverse order, and an orthogonality under the induced inner product argument. Concludes g-optimal design useless for this estimator and points to alternative estimators that can exploit cross-task samples.
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chapters (10)
- 0:00Intro
- 1:12Multi-task setting (II)
- 7:00Distance between subspaces
- 8:31Various interesting questions
- 11:50Naive estimator
- 16:33Optimal experiment design
- 18:43Simple example
- 21:40No improvement in G-optimal design
- 24:29Another example
- 26:06Proposition
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