Model 2
/I- A Model 1
tA~
2 ......... ..................................
Figure 2-2 Segmentation example with instantaneous error: black is signal to be
predicted, red and blue are two models, the dotted line below is segmentation.
The criterion used is the instantaneous mean squared error E (n), computed with a
recursive estimate on the instantaneous squared error e (n), using a gamma delay (2.8).
The parameter Yep is the inverse of the memory depth of the filter in samples [13], and
taking the expected values on both sides of (2.8) shows that E[] = E[e2], or p is an
unbiased estimate of estimate of the MSE.
EP(n)= ye 2(n)+(1 Yp)E (n- ) 0< <1 (2.8)
Now yp, is another parameter to set, effectively controlling the "window" over
which the MSE is calculated. If the memory depth of e (n) is too short, it is not really an
average anymore, and some spurious switching might appear; if it is too long, the error is
integrated over too much data, and the change detection might not be as sharp. In fact, the
E (n) has the regretful property of building up when the instantaneous error is high
(when the expert is not a winner), and often the decrease in criterion of the expert that