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LS experiments—3 overlapping processes, 7/15/2004

LS experiments—3 overlapping processes, 7/15/2004. Rank-deficient design matrix. Alternative to OLS: pseudoinverse. In the full-rank matrix case: pseudoinverse = OLS multiplier. Pseudoinverse estimates are visually “better” than the OLS estimates.

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LS experiments—3 overlapping processes, 7/15/2004

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  1. LS experiments—3 overlapping processes, 7/15/2004 • Rank-deficient design matrix. • Alternative to OLS: pseudoinverse. • In the full-rank matrix case: pseudoinverse = OLS multiplier. • Pseudoinverse estimates are visually “better” than the OLS estimates. • The expected data given model for the OLS and the pseudoinverse estimates are the same. • Hard to tell visually whether the estimates converge as the number of trials increases in the case of noise in the data.

  2. OLS learns 3 processes, overlapping in time, 1 voxel, zero noise, start times known, 3 trials

  3. pinv learns 3 processes, overlapping in time, 1 voxel, zero noise, start times known, 3 trials

  4. OLS learns 3 processes, overlapping in time, 1 voxel, zero noise, start times known, 6 trials

  5. pinv learns 3 processes, overlapping in time, 1 voxel, zero noise, start times known, 6 trials

  6. OLS learns 3 processes, overlapping in time, 1 voxel, noise 0.2, start times known, 3 trials

  7. pinv learns 3 processes, overlapping in time, 1 voxel, noise 0.2, start times known, 3 trials

  8. OLS learns 3 processes, overlapping in time, 1 voxel, noise 0.2, start times known, 6 trials

  9. pinv learns 3 processes, overlapping in time, 1 voxel, noise 0.2, start times known, 6 trials

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