ASU CSE 575 Statistical ML - Midterm Exam Cheat Sheet
Trace of a matrix M: tr(M ) = di=1 mii
P
Eigenvector x, eigenvalues λi : M x = λx ⇐⇒ (M − λI)x = 0
tr(M ) = di=1 λi , det(M ) = |M | = di=1 λi where d=diagonal
P Q
∂M x ∂y t x ∂xt M x
∂x
= M t, ∂x
= y, ∂x
= (M + M t )x
P (Hj )P (B|Hj )
Bayes Rule: P (Hj |B) = P∞ P (H )P (B|H ) , where prior prob.=P (Hj ) & posterior=P (Hj |B)
i i i
A, B = independent events ⇒P(AB)=P(A)P(B)
Probability Mass Fct.(PMF) to represent {p1 , p2 , ...pm }, P (X) =prob{X = x} tak-
P
ing m values from v = v1 , ...vm , P (X) ⩾
P0, x∈v P (x) = 1
expected value = mean = µ =PE[x] = x∈v xP (x), E[f (x)] = f (x)P (x), E=linear op-
2 2
erator, V ar[x] = E[(x −
Pµ) ] = (x − µ) P (x)
Covariance matrix = (symmetric) =E[(x-µ)(x−µ)t ], σxy = Cov(x, y) = E[(x−µx )(y−
µy )]
P (x,y) P (x)P (y/x)
Marginal distribution for x : Px (x) = y P (x, y), P (x|y)= P (y) = P P (x)P (y|x)
P
R∞ x
Continuous random variable PDF , p(x) ⩾ 0, −∞ p(x) dx=1
Rx
Cumulative distribution fct. CDF: F (X) = −∞ p(t) dt
....
Continues on the next page of this pdf document
Trace of a matrix M: tr(M ) = di=1 mii
P
Eigenvector x, eigenvalues λi : M x = λx ⇐⇒ (M − λI)x = 0
tr(M ) = di=1 λi , det(M ) = |M | = di=1 λi where d=diagonal
P Q
∂M x ∂y t x ∂xt M x
∂x
= M t, ∂x
= y, ∂x
= (M + M t )x
P (Hj )P (B|Hj )
Bayes Rule: P (Hj |B) = P∞ P (H )P (B|H ) , where prior prob.=P (Hj ) & posterior=P (Hj |B)
i i i
A, B = independent events ⇒P(AB)=P(A)P(B)
Probability Mass Fct.(PMF) to represent {p1 , p2 , ...pm }, P (X) =prob{X = x} tak-
P
ing m values from v = v1 , ...vm , P (X) ⩾
P0, x∈v P (x) = 1
expected value = mean = µ =PE[x] = x∈v xP (x), E[f (x)] = f (x)P (x), E=linear op-
2 2
erator, V ar[x] = E[(x −
Pµ) ] = (x − µ) P (x)
Covariance matrix = (symmetric) =E[(x-µ)(x−µ)t ], σxy = Cov(x, y) = E[(x−µx )(y−
µy )]
P (x,y) P (x)P (y/x)
Marginal distribution for x : Px (x) = y P (x, y), P (x|y)= P (y) = P P (x)P (y|x)
P
R∞ x
Continuous random variable PDF , p(x) ⩾ 0, −∞ p(x) dx=1
Rx
Cumulative distribution fct. CDF: F (X) = −∞ p(t) dt
....
Continues on the next page of this pdf document
