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Scanning through some literature, does this method require that the input space be equipped with a probability density function “quantifying the variability of

by tobmlt 7y ago

Scanning through some literature, does this method require that the input space be equipped with a probability density function “quantifying the variability of the inputs”? Seems like that would be the (or a function of the) thing we are after in sensitivity analysis. On the other hand, it appears that I may be able to get away with some naive assumption about this quantity, compute eigenvectors and find the active subspace... and then vary the mode in these directions. Is this for local or global optimization? Part of my stuff was about finding a way to guarantee that a particular set of inputs results in a feasible design. (Edit: maybe active subspace could replace this... or exclude poor regions faster) The other part (the gradient driven part) solves curves and surfaces for shape which conforms to constraints. We really need the fine details to match as the constraints are often of equality type. From there, it seems this active subspace method could really help in searching the design space. (From what I read, this is the purpose) A more efficient method of response surface design. My stuff is agnostic about this. Then again, surely it could be of used in more efficiently optimizing constrained curves and surfaces... I will keep thinking but it seems a secondary use at best, or would you agree?

peterwoerner 7y ago
We should move this conversation to email (as I will check that more frequently and will be more likely to get back to it). See email in my profile. Active subspace comes from the uncertainty quantification community. If you assume all your parameters are Gaussian, then the sensitivity matrix is directly correlated to the probability density functions. I find it easier to think in terms of the sensitivity matrix, but useful to realize the sensitivity matrix to approximate (complex) probability distributions. My though was that if you were optimizing have a huge parameter space theta = [theta1, ... thetam] then you could reduce the parameter space by only looking at theta_reduce = [theta | d loss/d theta > threshold] or you could look at active subspaces and change the parameter space to xi = [xi1, ... xi_m] where x_i = SUM a_j theta_j. xi_i could be given by the largest eigenvectors of the sensitivity matrix S_ij = d^2 loss/dtheta_i dtheta_j Wouldn't it be nice if hacker news supported latex. I haven't done any work here, but I suspect I will be doing some of this towards the end of summer.

by tobmlt 7y ago

peterwoerner 7y ago

We should move this conversation to email (as I will check that more frequently and will be more likely to get back to it). See email in my profile. Active subspace comes from the uncertainty quantification community. If you assume all your parameters are Gaussian, then the sensitivity matrix is directly correlated to the probability density functions. I find it easier to think in terms of the sensitivity matrix, but useful to realize the sensitivity matrix to approximate (complex) probability distributions. My though was that if you were optimizing have a huge parameter space theta = [theta1, ... thetam] then you could reduce the parameter space by only looking at theta_reduce = [theta | d loss/d theta > threshold] or you could look at active subspaces and change the parameter space to xi = [xi1, ... xi_m] where x_i = SUM a_j theta_j. xi_i could be given by the largest eigenvectors of the sensitivity matrix S_ij = d^2 loss/dtheta_i dtheta_j Wouldn't it be nice if hacker news supported latex. I haven't done any work here, but I suspect I will be doing some of this towards the end of summer.