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Daphne’sApproximateGroup ofStudents
Outline
Linear Regression Unregularized L2 Regularized
What is a GP? Prediction with a GP Relationship to SVM Implications
What does this mean?
Linear Regression Predicting Y given X Y = wtx + n
w_ml = argmax y[m+1] = w_mltx[m+1]
L2 Regularized Lin Reg L2 Regularized (Gaussian Prior on w)
Y = wtx + n w ~ N(0,S) w_map = argmax blah + ||w||^2
What is a random process?
It’s a prior over functions
What is a Gaussian Process?
It’s a prior over functions that generalized a Gaussian Random Vector
Prior over Y(x) ~ N(0,I)
Alternate Definition The thing with Euler’s equation
This is weird Not used to thinking of prior over Ys Or are we?
We ARE used to thining about prior over w What prior over y does this induce
Math P(w) -> P(Y) Wow! This became a Gaussian Process!
Prediction with a GP Predict y*[m+1] given y[1]…y[m]
We get a covariance = error bars Wow! This prediction is the same as w_map
but we get error bars!
Generalize that shit - Covariance Functions
Note that we have a thing here that is defined by C(x1,x2) which can be kernelized
Has to be pos semidefinite Is a kernel function
Relationship to SVM
Example
How do we reconcile these views?
Does this change anything?