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In your polynomial regression example, I can't follow what you mean by p_i = \xi \rightarrow \xi^{i-1} when you're setting up the model.
by soVeryTired 10y ago
In your polynomial regression example, I can't follow what you mean by p_i = \xi \rightarrow \xi^{i-1} when you're setting up the model.
- gabrielgoh 10y agoI just mean p_i(\xi) = \xi^{i-1}. The notation is a little cumbersome here, but it pays of in the second equation
- soVeryTired 10y agoSorry, got it. The fact that you introduce the data as \xi_i a line earlier might throw the reader a little.
- soVeryTired 10y agoMore polynomial regression questions :) Are you using the optimal step size you derived in the previous section? If so, why don't the first and last eigendirections converge at once? If not, doesn't it suggest that there's a trade-off between speed of convergence and the ability to stop early? In general, this is a nicely written article, though. Good work!
- gabrielgoh 10y agoGood question! The parameter has been set to a touch below the optimum. Your observation is accurate, there is indeed such a tradeoff, though it is less than you might think. The qualitative behavior of the system is very sensitive to changes at that point, and the tiny bit of extra convergence you get by getting the step-size exactly right of offset dramatically by the chances of diverging.
- deleted 10y ago[deleted]