# take sum log of probability matrix

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Jay Hanuman le 10 Nov 2016
I have data
m= 1 8 3 3 3 8 4 1 8 4 1 6 7 10 10 8 6 8 6 8 6 3 3 8 3 9......2000
with sequence length 2000. with this data I made transition probability matrix p
1 2 3 4 5 6 7 8 9 10
1 0.0781 0.1317 0.0489 0.0652 0.1222 0.0713 0.1371 0.2077 0.0339 0.1039
2 0.0681 0.1482 0.1012 0.0669 0.0319 0.0783 0.0892 0.1163 0.1398 0.1602
3 0.0421 0.1672 0.1125 0.0798 0.0679 0.0805 0.0773 0.1898 0.0974 0.0855
4 0.1421 0.1099 0.0465 0.0661 0.0357 0.0420 0.1528 0.1698 0.1939 0.0411
5 0.1809 0.1485 0.0477 0.0486 0.0837 0.0594 0.1206 0.1773 0.0774 0.0558
6 0.0545 0.0881 0.1186 0.0401 0.1154 0.1202 0.2588 0.0777 0.0897 0.0369
7 0.1935 0.0494 0.0445 0.1698 0.0327 0.1044 0.0661 0.1079 0.0445 0.1872
8 0.0612 0.0564 0.1830 0.0858 0.0828 0.2106 0.0390 0.0318 0.0828 0.1668
9 0.2055 0.0522 0.3804 0.0449 0.0353 0.0449 0.0955 0.0385 0.0425 0.0602
10 0.0781 0.2253 0.0525 0.1133 0.1824 0.0456 0.0394 0.0871 0.0961 0.0802
and initial probability matrix r
1 2 3 4 5 6 7 8 9 10
0.1052 0.1186 0.1136 0.0799 0.0794 0.0892 0.1026 0.1191 0.0890 0.1034
now I want to select data with window size 10, so 10 elements of m i.e. 1 8 3 3 3 8 4 1 8 4 are selected. I want to take sum of log of transition probability and initial probability of corresponding selected elements of m. i.e. 1 8 3 3 3 8 4 1 8 4 are selected so
log(r1)+log(r3)+log(r4)+log(r8)+log(p11)+log(p13)+log(14)+log(18)+log(31)+log(33)+log(34)+log(38)+log(41)+log(43)+log(44)+log(48)+log(81)+log(83)+log(84)+log(88)
in above r1,r3,r4,r8 are initial probability and p11,p13... are transition probability. so above result would be one single value, now same above thing I want to do with sliding window by 1 position to next i.e. skipping previous element and adding next element so selected elements of m will be 8 3 3 3 8 4 1 8 4 1. how to do this for sliding window upto end. each window operation give one value so window operation value should be accumulate in one variable. how to do this.
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### Réponses (1)

Guillaume le 10 Nov 2016
This function will calculate the probability for a window:
function lp = logprobability(window, p, r)
uv = unique(window); %get unique values in window
[row, col] = ndgrid(uv); %generate all combinations of unique values
lp = sum(log(r(uv))) + sum(log(p(sub2ind(size(p), row(:), col(:)))));
end
To apply that to consecutive windows of size 10 of m:
windowsize = 10;
assert(mod(numel(m) / windowsize), 1) == 0, 'number of elements of m not a multiple of window size')
lps = cellfun(@(w) logprobability(w, p, r), mat2cell(m, 1, ones(1, numel(m)/windowsize) * windowsize));
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