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Effect of Noise on OLS and Pseudoinverse Estimates in Learning Overlapping Processes

This experiment explores the impact of noise on Ordinary Least Squares (OLS) and Pseudoinverse estimates when learning three overlapping processes in time with one voxel. Results show how noise affects convergence visually. The OLS and Pseudoinverse estimates are visually compared to determine convergence with varying numbers of trials.

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Effect of Noise on OLS and Pseudoinverse Estimates in Learning Overlapping Processes

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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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