T x i 2 Deriving w we get w T 1 T y n by k1 matrix n entries vector k1 entries

T x i 2 deriving w we get w t 1 t y n by k1 matrix n

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T ( x i )) 2 Deriving w we get: w ( T ) 1 T y n by k+1 matrix n entries vector k+1 entries vector This solution is also known as ‘psuedo inverse’
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A probabilistic interpretation Our least squares minimization solution can also be motivated by a probabilistic interpretation of the regression problem: y w T ( x ) The MLE for w in this model is the same as the solution we derived for least squares criteria: w ( T ) 1 T y
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Other types of linear regression Linear regression is a useful model for many problems However, the parameters we learn for this model are global ; they are the same regardless of the value of the input x Extension to linear regression adjust their parameters based on the region of the input we are dealing with
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Splines Instead of fitting one function for the entire region, fit a set of piecewise (usually cubic) polynomials satisfying continuity and smoothness constraints. Results in smooth and flexible functions without too many parameters Need to define the regions in advance (usually uniform) y a x 3 b x 2 c x d 1 1 1 1 y a x 3 b x 2 c x d 2 2 2 2 y a x 3 b x 2 c x d 3 3 3 3
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Credits Yasir Abu Mustafa ,Caltech university, California Barnabas Poczos, Ziv Bar-Joseph School of Computer Science, Carnegie Mellon University Vibhav Gogate The University of Texas at Dallas
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  • Fall '17
  • Mark Isbel

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