Hey everyone
I'm dealing with a ML problem right now which I'd like to discuss with you and get an oppinion on as I've conversed with several of my coworkers which all have different opinions.
I'm working with time series observations $T_i$ , i=1,...,N which i do feature extraction on to generate an input matrix X. In a more mathematical definition: I have a feature extractor F which maps an aribtrary time series T_i to a feature vector f_i:
F: T_i -> f_i then X = [f_0, f_1, ..., f_N]T
The problem I'm dealing with lies within the handling and the format of the feature vector f. My feature extractor (which does regression analysis) finds a least squares estimator (b) of some parameters but additionally generate a covariance matrix (S) of this estimator so my question is, how would you structure the output the feature vector?
1) You could simply ignore the observed covariance matrix and say:
f_i = b
2) You could concatenate the LS estimator with the variance estimate by vectorizing the observed covariance matrix:
f_i = [b , vec(S)]
3) You could do some sort of whitening of the observed features then f_i ~ N(f_i,I):
f_i = bS-1/2
I'll probably use the data to train a linear classifier, but is it possible to argue for which output to chose independent of the classification method? Which of these do you think is appropriate and why, or do you suggest something different?
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