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Machine Learning and Optimization Cheat Sheet (DRAFT) by

Cheat sheet for "Machine Learning and Optimization" course

This is a draft cheat sheet. It is a work in progress and is not finished yet.

Linear Algebra

A+B
has result, only if A and B have same dim
Ax=x_1*a_1+...+x_n*a_n
result is vector
A*B
row of A times column of B, result is matrix
AT
row becomes column and vice versa
Properties of transpose
(1) if A is (m x n) AT is (n x m)
(2) (AT)T=A
(3) (A+B)T=AT+BT
(4) (AB)T = BTAT
(5) (tA)T=tAT
Inverse of Matrix
AA-1=I=A-1A
Properties of invertible matrix
(A-1)-1= A
(AB)-1= B-1A-1
(AT)-1=(A-1)T
Singular value decomp­osition
A = UΣVT
what means that every vector­-ma­tri­x-m­ult­ipl­ication can be viewed as a 3 step process
(1) rotation into space V
(2) scaling by singular value
(3) rotation into new space U
Eigen value decomp­osition
A = QΛQ-1
this is only possible, if A and Q are square matrices
 

Linear regression

Model
y = Xθ*+z
Risk

Ridge regression

 

Logistic Regression

 

Support Vector Machines

 

Neuronal Networks