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Learning Parameters When Some Data is Missing - Sprinkler Example

Answered Learning Parameters When Some Data is Missing - Sprinkler Example

  • venerdì 6 aprile 2012 17:09
     
     
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    Noob question please :) In the sprinkler example packaged with Infer.NET, the 2nd part of the program attempts to learn parameters of the model given data C, S, R, W. What if I cannot observe C, but would still like to infer ProbCloudyPosterior?

    Thanks a lot in advance

     

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  • sabato 7 aprile 2012 10:37
     
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    In LearnParameters you will see the line

      Cloudy.ObservedValue = cloudy;

    If you change this to:  

      Cloudy.ClearObservedValue();

    Then Cloudy will be left unobserved.  See ProbRain for an example of this.

    • Contrassegnato come risposta exx lunedì 9 aprile 2012 16:41
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    • Contrassegnato come risposta exx mercoledì 18 aprile 2012 18:14
    • Contrassegno come risposta annullato exx mercoledì 18 aprile 2012 19:20
    • Contrassegnato come risposta exx mercoledì 18 aprile 2012 19:20
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  • lunedì 9 aprile 2012 16:41
     
     
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    Thanks a lot Tom!
     
  • martedì 17 aprile 2012 22:34
     
     
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    Hi Tom,

    It seems that if I do not provide any observed values to Cloudy (i.e. Cloudy.ClearObservedValue()), the model has a very hard time learning the probabilities. The learned probabilities, even when I generate 10,000 sample data points, are:

        Prob. Cloudy:                                            Ground truth: 0.30, Inferred: 0.50
        Prob. Sprinkler | Cloudy:                            Ground truth: 0.10, Inferred: 0.38
        Prob. Sprinkler | Not Cloudy:                      Ground truth: 0.50, Inferred: 0.38
        Prob. Rain      | Cloudy:                              Ground truth: 0.80, Inferred: 0.38
        Prob. Rain      | Not Cloudy:                        Ground truth: 0.20, Inferred: 0.38
        Prob. Wet Grass | Sprinkler, Rain:               Ground truth: 0.99, Inferred: 0.99
        Prob. Wet Grass | Sprinkler, Not Rain          Ground truth: 0.90, Inferred: 0.89
        Prob. Wet Grass | Not Sprinkler, Rain:         Ground truth: 0.90, Inferred: 0.90
        Prob. Wet Grass | Not Sprinkler, Not Rain:   Ground truth: 0.00, Inferred: 0.00

    (note: I changed the actual prob. cloudy from (0.5, 0.5) in the original code to (0.3, 0.7)).

    Any help is greatly appreciated.


    • Modificato exx martedì 17 aprile 2012 22:35
    • Contrassegnato come risposta exx mercoledì 18 aprile 2012 18:14
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  • mercoledì 18 aprile 2012 10:46
     
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    By the looks of it, the parameters have come out symmetric.  When you don't observe Cloudy, the model effectively becomes a mixture model.  So you have to be careful about breaking symmetry as explained in the Mixture of Gaussians example.


    • Modificato Tom MinkaMicrosoft Employee mercoledì 18 aprile 2012 10:47
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  • mercoledì 18 aprile 2012 18:54
     
     
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    Thanks so much Tom. Did as you suggested, and now, P(S | C) and P(R | C) are better calculated. But it seems P(C) still can't be inferred.

    Prob. Cloudy:                                       Ground truth: 0.30, Inferred: 0.50
    Prob. Sprinkler | Cloudy:                        Ground truth: 0.10, Inferred: 0.16
    Prob. Sprinkler | Not Cloudy:                   Ground truth: 0.50, Inferred: 0.60
    Prob. Rain      | Cloudy:                         Ground truth: 0.80, Inferred: 0.60
    Prob. Rain      | Not Cloudy:                    Ground truth: 0.20, Inferred: 0.16
    Prob. Wet Grass | Sprinkler, Rain:            Ground truth: 0.99, Inferred: 0.99
    Prob. Wet Grass | Sprinkler, Not Rain        Ground truth: 0.90, Inferred: 0.90
    Prob. Wet Grass | Not Sprinkler, Rain:       Ground truth: 0.90, Inferred: 0.90
    Prob. Wet Grass | Not Sprinkler, Not Rain: Ground truth: 0.00, Inferred: 0.00


    • Modificato exx mercoledì 18 aprile 2012 19:20
    • Modificato exx mercoledì 18 aprile 2012 19:26
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  • giovedì 19 aprile 2012 12:47
     
     
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    Yes, it isn't possible to recover the true parameters exactly when cloudy is not observed.  This is because the model has too many parameters.  There is 1 for cloudy, 2 for sprinkler, 2 for rain, totalling 5 for p(sprinkler,rain) alone.  But you only need 3 parameters to describe any joint distribution of (sprinkler,rain).