@hal-r.bsky.social

@hal-r.bsky.social

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This perturbation rank framing is interesting... it's reminding me of something that might be relevant, or might not, which I want your opinion on. As part of the same project that has me considering these ideas, I was playing around with a model where I was trying to classify the input to a noisy dynamical system from the system's outputs, and I was comparing using QDA (allowing for different covariances in the system for each input) and linear classifiers. I tended to find that QDA only improved over the linear case when the dimensionality of the input was high -- or more specifically: the input was set up as discrete points in some N-dimensional space, 2 per dimension (I think kinda like a hypercube, then), and I was trying to classify between all of those points. So I was both increasing the dimensionality of the input, and the number of points I was trying to decode between at the same time (at a rate of 2^N, duh), and I'm not 100% sure which of those was relevant (though some experiments with more points in a lower dimensional space suggested it was the dimension). Anyway, QDA did better with higher dimensional inputs (sometimes, depending on how the dynamical system itself was setup, which is what I was interested in but isn't super relevant here I think). So the covariance mattered more in that case, and I feel like that could be conceptually related (even caused by?) the perturbation rank induced by the inputs (might be misusing the word here) being higher there, in a way that changing covariances could pick up on better than changing means. What do you think? Could have been some weird fluke depending on the details of the dynamical system too, or anything else too I suppose