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This is Table 1.1 in pattern recognition and machine learning (free)

enter image description here

We can gain some insight into the problem by examining the values of the coefficients $w^*$ obtained from polynomials of various order, as shown in Table 1.1. We see that, as M increases, the magnitude of the coefficients typically gets larger.

what does "the magnitude of the coefficients" mean here, how to compute this quantity based on this table, when M=1 and M=9?

this post seems to be relative, I didn't see a concrete approach (formula) to compute this quantity.

PsychometStats
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fu DL
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1 Answers1

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It simply means their general value. For M=0 you get something that is less than one, as M increase the general (absolute) value of the coefficients increase... For M = 9 most coefficients are over 1000, but there are some exception ($w_0$ = 0.35). The use of 'magnitude' here convey that idea that the general value increase with M without specifying an exact metric (average value, difference between min and max... etc.). The important word in the paragraph you cite is 'typically' meaning that this is a rule of thumbs, not an exact rule over an exact metric.

lcrmorin
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