Gaussian Process Regression Algorithm

[gkronber]

r8323: initial import of Gaussian process regression algorithm

[gkronber]

r8324:

• fixed build (be ready for the obligatory round of beers at the archery meeting)
• set copy-local to false for new references

[gkronber]

r8325: changed return value type for parameter properties

[gkronber]

r8366 added linear mean and covariance function

[gkronber]

r8368: fixed cloning of linear mean function

[gkronber]

r8371: worked on Gaussian Process algorithm

[gkronber]

r8372: removed unnecessary plugin references.

[gkronber]

r8375: implemented Gaussian process regression operators and analyzers

[gkronber]

r8396: implemented LM-BFGS algorithm and improved GPR

[gkronber]

r8397: added random seed parameters for LM-BFGS

[gkronber]

r8399: fixed plugin dependencies

[gkronber]

r8403: introduced upper limit for scale of SEard covariance function

[gkronber]

r8416: worked on sum and product covariance functions and fixed a few bugs.

[gkronber]

r8417: added periodic covariance function

[gkronber]

r8419: changed initialization of hyperparameter vector for GPR using a PRNG

[gkronber]

r8421: fixed default mean and covariance function for GPR

[gkronber]

r8455: changed calculation of gradients for covariance functions to reduce allocations of arrays

[gkronber]

r8439:

• implemented unit tests for mean and covariance functions.
• implemented sum and product mean function.
• fixed incorrect gradient calculation in CovarianceProd

[gkronber]

r8463: improved GPR implementation:

• implemented additional unit tests
• fixed bugs uncovered by unit tests
• improved performance
• added views for sum and product mean functions

[gkronber]

r8464: added const and noise covariance functions.

[gkronber]

r8473

• added line chart
• made parameters of mean and covariance functions readable
• removed target variable scaling
• moved noise hyperparameter for likelihood function to the end of the parameter list
• added methods to calculate the predicted variance
• removed limits for scale of covariance functions and introduced exception handling to catch non-spd or singular cov matrixes
• implemented rational quadratic covariance function
• added unit test case from GBML book - however, it does not work as the book seemingly uses a noise-less likelihood function

[gkronber]

r8475: fixed bug in calculation of variance in GPR model

[gkronber]

r8484:

• changed interface for covariance functions to improve readability
• fixed several bugs in the covariance functions
• fixed bugs in the line chart for Gaussian process models

[gkronber]

r8489: removed caches in product and sum covariance functions and fixed bug in SE-ARD covariance function

[gkronber]

r8491: fixed test cases, improved performance

[abeham]

I tested GPR on my dataset and found that CovarianceProd, CovarianceSum, and CovariancePeriodic throw an exception in the GaussianProcessRegressionSolutionCreator. Is there anything I need to take care of in these covariance functions?

[gkronber]

r8494:

• changed mean and covariance function parameters to simple value parameters instead of constrained value parameters
• changed the solution creator so that it doesn't throw an exception if no model could be found.

[abeham]

I would prefer constrained value parameters. Otherwise you can't use them in the create experiment dialog. What's the motivation for moving to a value parameter?

[gkronber]

Replying to abeham:

I tested GPR on my dataset and found that CovarianceProd, CovarianceSum, and CovariancePeriodic throw an exception in the GaussianProcessRegressionSolutionCreator. Is there anything I need to take care of in these covariance functions?

The sum and product covariance functions need must be configured to have at least one child. The periodic covariance function only works for the 1d case (one input variable). With r8494 I changed the parameters so that it becomes more obvious that the sum and product covariance function need to be configured correctly. I also changed the solution creator so that it doesn't throw an exception.

[gkronber]

Sum and product covariance function cannot be used in the create experiment dialog anyway.

[gkronber]

r8562: implemented LinearARD and MaternIso covariance functions.

[gkronber]

r8565: implemented RQard covariance function.

[gkronber]

r8580: fixed coloring in line chart for GPR

[gkronber]

r8582:

• implemented a few covariance functions as parameterized named items.
• Implemented rudimentary view for Gaussian process models.

[gkronber]

r8583: fixed build fail.

[gkronber]

r8592: added default ctor for HyperParameter

[gkronber]

r8612: implemented all mean and covariance functions with parameters as ParameterizedNamedItems

[gkronber]

r8614: removed unused file

[gkronber]

r8615: renamed covariance functions

[gkronber]

r8620: renamed more files. implemented scale covariance function.

[gkronber]

r8623: implemented LS Gaussian Process classification

[gkronber]

r8678: added masking covariance function and made necessary changes to interface and utility class.

[gkronber]

r8679:

• changed DiscriminantFunctionClassificationModel and DiscriminantFunctionClassificationSolution to non-abstract.
• Classification based on GPR uses these classes to create a classification solution from a GaussianProcessRegressionModel.
• Also added view classes for DiscriminantFunctionClassificationModel

[abeham]

I noticed that the solution in the run object is only a result collection, but not a DiscriminantFunctionClassificationSolution anymore.

[gkronber]

r8682:

• fixed bug in cloning constructor of CovarianceMask
• removed throwing Exceptions in CovariancePeriodic (the behaviour of the periodic covariance function now matches the GPML implementation again.

[gkronber]

Replying to abeham:

I noticed that the solution in the run object is only a result collection, but not a DiscriminantFunctionClassificationSolution anymore.

Thanks for the hint! The cloning method override is missing.

[gkronber]

r8683: added missing cloning method override in DiscriminantFunctionClassificationSolution

[gkronber]

r8684: fixed a bug related to the virtual call to RecalculateResults in the constructor of DiscriminantFunctionClassificationSolution

[gkronber]

r8732:

• added caching for variances of GaussianProcessRegressionSolution.
• changed hyperparameter initializers to generate initial values for hyperparameters in a larger range.

[gkronber]

r8733: added a unit test to create and run a GPR sample

[gkronber]

r8740: removed assertion for test R² in GPR unit test as we are testing on a benchmark problem where the test set is randomly created.

[gkronber]

r8771: fixed a bug in the noise covariance function

[gkronber]

To do: check range of all input variables and deactivate if necessary.

[gkronber]

r8827: fixed bugs concerning masking covariance function

[gkronber]

r8829: fixed an issue that occurs in scaling if a variable is effectively constant in the training partition

[mkommend]

Reviewing comments:

• Use folders for covariance and mean functions.
• Util.AttachValueChangeHandler is quite ugly
• The HyperParameter class relies heavily on which method SetValue or Value.Set is called and determines according to this whether the fixed flag applies or not.
• Util.SqrDist: Is the scale array always exactly as large as the number of column indixes?.
• Covariance functions expose methods with column indexes which are not always forwarded to the concrete util functions (e.g., CovarianceLinear.GetCrossCovariance).

I have also tested the implementation on sample problem instances for regression and classification and did not find any bugs. However, I must admit that I didn't completely understand how the implementation works as I am lacking the basics of GP.

[gkronber]

Replying to mkommend:

Reviewing comments:

• Util.AttachValueChangeHandler is quite ugly

Please specify the problem in more detail. Do you mean that they should not be located in the Util class?

[mkommend]

Replying to gkronber:

Replying to mkommend:

Reviewing comments:

• Util.AttachValueChangeHandler is quite ugly

Please specify the problem in more detail. Do you mean that they should not be located in the Util class?

The "problem" is that this event registration is implemented in quite a different way as the remaining parts of HL, which makes it harder to grasp what is going on (when is the local parameter cache updated, what happens on a value change, where is the new event registered, ...).

[gkronber]

Replying to mkommend:

Replying to gkronber:

Replying to mkommend:

Reviewing comments:

• Util.AttachValueChangeHandler is quite ugly

Please specify the problem in more detail. Do you mean that they should not be located in the Util class?

The "problem" is that this event registration is implemented in quite a different way as the remaining parts of HL, which makes it harder to grasp what is going on

Yes it is different to the remaining parts of HL and harder to grasp.

AttachValueChangeHandler takes a ValueParameter and registers a handler that executes the action which is specified as second parameter. Because both the value of a parameter, as well as the value of the value of the parameter can change, we have to attach to both events- In case the value of the parameter is changed we have to attach the event handler to the new value.

(when is the local parameter cache updated, what happens on a value change, where is the new event registered).

AttachValueChangeHandler does not have a local parameter cache. Thus, I believe the real issue here is the caching of parameters and values in all covariance and mean functions and not the implementation of AttachValueChangeHandler.

[gkronber]

• r8929: moved covariance and mean functions to folders
• r8931: fixed incorrect handling of dimension masking in CovarianceLinear (and checked all other covariance functions)
• r8932:8933: corrected handling of length-parameter arrays in ARD functions and prevented stacking of mask covariance functions to make sure that the length-parameter and the enumerable of selected column indexes are equally long.

[gkronber]

I thought about possible changes to remove the caching of parameter values in covariance functions and came up with a possible solution returning functions with the cached value in the closure. This would remove the necessity for event registration. It also allows us to remove the SetParameters method. What do you think about this idea?

public Func<double[,], int, int, double> GetCovarianceFunction(IEnumerable<int> columnIndices) {
      var inverseLength = inverseLengthParameter.Value.Value;
      var sf2 = scaleParameter.Value.Value;
      return (x, i, j) => {
        double d = i == j
                     ? 0.0
                     : Util.SqrDist(x, i, j, inverseLength, columnIndices);
        return sf2 * Math.Exp(-d / 2.0);
      };
    }

[mkommend]

Is the proposed solution really working as intended? The inverseLength and scaleParameter could change its value over time, as they are optimized during the runtime. Now I have to know at which time I have to call GetCovarianceFunction to create a new closure containing the updated parameter value, if I am even aware of this issue.

Due to this difficulties, I think the event registration fits the purpose better.

[gkronber]

r8982:

• removed class HyperParameter
• removed the parameter value caching and event handlers for parameter caching in the implemented covariance and mean functions
• the instances of mean and covariance functions configured in the GUI are now actually templates where the structure and fixed parameters of the functions can be specified. In the templates the optimized parameters are null.
• Templates are used in the GaussianProcessModel to create the actual covariance and mean functions as Func objects with specified parameter values (which are optimized using LM-BFGS).

[mkommend]

Reviewed new changesets r8929, r8931, r8932, r8933 and r8982. The refactored way of configuring covariance and mean functions is much cleaner, although I had doubts before I saw the first implementation.

[gkronber]

r9104: fixed a bug occurring when the masking covariance function is used.

[gkronber]

r9106: fixed a bug in ARD covariance functions that would occur when a parameter prior to the inverse length parameter would be fixed.

[gkronber]

The gradients are not returned in the same order of the parameters! This should be checked for all covariance functions.

[gkronber]

r9108: fixed bugs in ARD covariance functions (checked if parameter and gradient order matches for all functions)

[gkronber]

r9111: fixed a calculation bug in the RQiso covariance function

[gkronber]

GP should be a problem. Hyper-parameters are optimized, likelihood should be maximized.

[abeham]

I think I should do the same with NCA which can also be thought of as an optimization problem.

[gkronber]

r9211: reformulated calculation of periodic covariance function

[gkronber]

r9357:9358: minor code improvements: removed commented code, always supply non-null columnIndizes.

[gkronber]

r9360: implemented neural network covariance function plus test case (comparison with GPML) for Gaussian processes