Class 04 - Positive Definite Functions and Feature Maps

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Lorenzo Rosasco, MIT, University of Genoa, IIT

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I am repeating the calculations and it seems to me that the definitions of inner products up to minute 35 are slightly wrong.

For the spaces defined by a finite integral with a weighting factor in the measure, it is the factor itself (and not its inverse) that should appear in the associated inner product - this works fine by Cauchy-Schwarz.

Furthermore, since even the Fourier transforms of real functions can be complex, your inner product needs to be sesquilinear - you need to add a complex conjugate to the second entry in the integrals.

Finally - he discloses it - there is an overall disregard for constants when calculating Fourier transforms here, so take every expression with a grain of salt .

alemorita

The example of the RKHS of bandlimited functions, has an error in the definition. The sinc function, which is the kernel is not in L1(R), whereas it needs to be in the Hilbert space H. The L1(R) constraint needs to be replaced by continuity and appropriately interpreted.

GauravSharma

Hello MIT. Thank you for the great content !! Any chance the problem sets and/or the lecture notes could be made public ?

apoorvreddy

Class 04 - Positive Definite Functions and Feature Maps

Class 04 - Positive Definite Functions and Feature Maps

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