[Work Log] Work Log

January 12, 2015
Project FIRE
Subproject Piecewise Linear Clustering (tests)
Working path projects/​fire/​trunk/​src/​piecewise_linear/​test
SVN Revision unknown (see text)
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Training epipolar prior.

Fixing local prior using parameters learned yesterday. The computing the epipolar and full prior is more computationally intensive, since it involves twice as many dimensions. To mitigate, I eliminated every other point from the data.

Without the epipolar prior, the data likelihood is:

Log-likelihood (baseline) =  -2471.12

Fixing euclidean scale and variance to zero, I trained the epipolar variance:

Log-likelihood =  -2395.05
training_result = 

    epipolar_variance: 4.39

By allowing some euclidean-correlated variance, the iid variance should be able to drop a bit. Fixing euclidean scale to 1/1002, I trained epipolar_variance and euclidean_variance jointly:

Log-likelihood = -2394.88
training_result =

    epipolar_variance: 4.3214
      euclidean_scale: 1.0000e-04
   euclidean_variance: 0.0335

Now training all three:

Log-likelihood = -2394.57
training_result = 

     epipolar_variance: 4.2877
    euclidean_variance: 0.0458
       euclidean_scale: 2.1581e-06

Now training all 10 parameters together:

Log-likelihood = -1294.59
training_result = 

     epipolar_variance: 4.2877
    euclidean_variance: 0.0458
       euclidean_scale: 2.1581e-06
        noise_variance: 0.0821
     geodesic_variance: 193.9141
        geodesic_scale: 0.0031
branch_linear_variance: 0.0800
 branch_const_variance: 6.1725
       linear_variance: 0.1561
        const_variance: 685.7670

...but we actually want noise_variance to be fixed to 1. Repeating previous run with noise_variance=1 results in:

Log-likelihood = -2381.29
training_result = 

     epipolar_variance: 4.2877
    euclidean_variance: 0.0458
       euclidean_scale: 2.1581e-06
        noise_variance: 1
     geodesic_variance: 33.6972
        geodesic_scale: 0.0011
branch_linear_variance: 0.1028
 branch_const_variance: 6.9943
       linear_variance: 0.0737
        const_variance: 1.8641e+03

running for 30 more iterations:

ll = 2376.76
     epipolar_variance: 4.2877
    euclidean_variance: 0.0458
       euclidean_scale: 2.1581e-06
        noise_variance: 1
     geodesic_variance: 160.7604
        geodesic_scale: 5.3712e-04
branch_linear_variance: 0.1028
 branch_const_variance: 6.9943
       linear_variance: 0.0835
        const_variance: 2.1123e+03

The fullly trained model is then:

     epipolar_variance: 4.2877
    euclidean_variance: 0.0458
       euclidean_scale: 2.1581e-06
        noise_variance: 1
     geodesic_variance: 15.9174
        geodesic_scale: 0.0019
branch_linear_variance: 0.0485
 branch_const_variance: 3.7438
       linear_variance: 0.0348
        const_variance: 685.7670

The samples from this prior look very nice:

Motion is restricted to be near the epipolar lines, and the resulting curves remain smooth.

Matlab says only 314 out of 3766 are nonnegligible.

Posted by Kyle Simek
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