CS计算机代考程序代写 Analytical Regression

Analytical Regression
RMIT Classification: Trusted

RMIT Classification: Trusted
Solving for Weights
The minimum of the the loss function occurs at the point where the partial derivatives are zero Thus % can be solved for analytically using normal equations
Solve for &
/ & % =⋯=0(foreveryj)
&% =(%&+*%++
,&% =⋯=0 ,%
1″
&%’,%(,…,%) =23h, 5* −7(*)
&
/,#
Simultaneously solve for %’, %(, … , %)
*+(
COSC2673 | COSC2793 Week 2: Regression 33

RMIT Classification: Trusted
Solving for Weights
Caveats:
This analytical approach effectively gives an matrix equation:
7 = 8&
• Vectorofoutputsfromtrainingexamples:,={.(%)+⋯+.(-)}
• Matrixofinputsfromtrainingexamples:$
To solve requires inverting: & = 8<&7 • Maynothaveasolution • Butcanbeapproximated,throughothertechniques,notdiscussedinthiscourse COSC2673 | COSC2793 Week 2: Regression 34 RMIT Classification: Trusted Solving for Weights Approximated with the analytical “equivalent” of the gradient descent loss function: Quadratic Minimisation problem23/||7 − 8&||' $ • Findvaluesof&whichminimisestheabove Has a unique solution: If the attributes are independent &= 8=8<&8=7 COSC2673 | COSC2793 Week 2: Regression 35