Covariance Estimation for High Dimensional Data Vectors Using the Sparse Matrix Transform (W65)
Guangzhi Cao and Charles A. Bouman Purdue University, School of Electrical and Computer Engineering
Problem:

Covariance estimation for "large p, small n" problems

Approach:

Model eigenvectors as a Sparse Matrix Transform (SMT)
1

E = E1 E2
0 y1
W80 W80 -1 W80 -1 W80 -1 W80 W82

...E

k

w h e r e Ek =
1 y0 y2 y3 y4 y5 y6 y7 y

cos

-sin

0

0

sin

cos
1

are Givens rotations
y0 y1 y2 y3 y4 y5 y6 y7
1 y0 y2
1

y2 y3 y4 y5 y6 y7 y

-1 -1 -1 W80 W81 W82 -1 W8
3

y3 y4
E6 E9

-1 -1 -1 -1

E2

E4 E7 E5

E8

y5

y6
E8 E 10

y7

FFT

-1

E

E3

y

SMT

Compute the ML estimate of Sparse Matrix Transform of order k  plog p
Advantage:

Fast - SMT is a fast transform Accurate - models covariance accurately for physical data