Question

Let X and Y be real-valued random variables and Y is generated from X as follows: ? ~ N(0, ?^2) Y = aX + ? Here, ? is the independent variable which is drawn from Gaussian Distribution with 0 mean and ? standard deviation. This is a single feature linear regression model, where "a" is the only weight parameter. The conditional probability of Y has distribution p(Y | X, a) ~ N(aX, ?^2), so it can be written as: p(Y | X, a) = 1 / ?(2??) exp( - 1 / (2?^2) (Y - aX)^2 ) Consider, we have a dataset with "n" training example where i = 1...n. Select ALL which correctly represents the maximum likelihood estimation of parameter "a". ? arg max_a ?_i 1/?(2??) exp( - 1/(2?^2) (Y_i - a X_i)^2 ) ? arg max_a ?_i 1/?(2??) exp( - 1/(2?^2) (Y_i - a X_i)^2 ) ? arg max_a 1/2 ?_i (Y_i - a X_i)^2 ? arg min_a 1/2 ?_i (Y_i - a X_i)^2

          Let X and Y be real-valued random variables and Y is generated from X as follows:

? ~ N(0, ?^2)
Y = aX + ?

Here, ? is the independent variable which is drawn from Gaussian Distribution with 0 mean and ? standard deviation. This is a single feature linear regression model, where "a" is the only weight parameter. The conditional probability of Y has distribution p(Y | X, a) ~ N(aX, ?^2), so it can be written as:

p(Y | X, a) = 1 / ?(2??) exp( - 1 / (2?^2) (Y - aX)^2 )

Consider, we have a dataset with "n" training example where i = 1...n. Select ALL which correctly represents the maximum likelihood estimation of parameter "a".

? arg max_a ?_i 1/?(2??) exp( - 1/(2?^2) (Y_i - a X_i)^2 )

? arg max_a ?_i 1/?(2??) exp( - 1/(2?^2) (Y_i - a X_i)^2 )

? arg max_a 1/2 ?_i (Y_i - a X_i)^2

? arg min_a 1/2 ?_i (Y_i - a X_i)^2

Let X and Y be real-valued random variables and Y is generated from X as follows:

? N(0, ?^2)
Y = aX + ?

Here, ? is the independent variable which is drawn from Gaussian Distribution with 0 mean and ? standard deviation. This is a single feature linear regression model, where "a" is the only weight parameter. The conditional probability of Y has distribution p(Y | X, a) N(aX, ?^2), so it can be written as:

p(Y | X, a) = 1 / ?(2??) exp( - 1 / (2?^2) (Y - aX)^2 )

Consider, we have a dataset with "n" training example where i = 1...n. Select ALL which correctly represents the maximum likelihood estimation of parameter "a".

? arg maxa ?i 1/?(2??) exp( - 1/(2?^2) (Yi - a Xi)^2 )

? arg maxa ?i 1/?(2??) exp( - 1/(2?^2) (Yi - a Xi)^2 )

? arg maxa 1/2 ?i (Yi - a Xi)^2

? arg mina 1/2 ?i (Yi - a Xi)^2

Added by Gabriel Y.

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