General framework for cross-validation of machine learning algorithms using SQL on distributed systems
A general framework for cross-validation of any supervised learning algorithm on a distributed database comprises a multi-layer software architecture that implements training, prediction and metric functions in a C++ layer and iterates processing of different subsets of a data set with a plurality of different models in a Python layer. The best model is determined to be the one with the smallest average prediction error across all database segments.
1. A method of cross-validation of a supervised machine learning algorithm within a distributed database having a plurality of database segments in which data are stored, comprising:
partitioning a data set within said database into a training subset and a validation subset, wherein the partitioning data set comprises partitioning the data set according to randomly sorted data to create two data subsets that are independent and statistically equivalent;
determining coefficients of a first model of said supervised machine learning algorithm using the training subset;
predicting a value of a data element in said validation subset using said first model;
determining a prediction error based at least in part on a difference between said predicted value and the actual value of said data element;
successively repeating said partitioning k times to form k different partitions, wherein at least a subset of the k different partitions have different training and validation subsets;
determining corresponding k prediction errors based at least in part on iteratively determining the coefficients, predicting the value of the data element, and determining the prediction error for each of said k partitions;
evaluating the performance of said first model using said k prediction errors; and
wherein said supervised learning algorithm comprises a target function, a prediction function, and a metric function, the target function establishing coefficient values that are used by said prediction and said metric functions, and wherein said functions are embodied in application programs in a first application program layer within said database, said functions being called by cross-validation functions in a second application layer within said database system.
2. The method of claim 1 , further comprising repeating said method for each of a plurality of other different models, and identifying as the best model the model having the smallest corresponding prediction error.
3. The method of claim 2 , wherein each of said models is defined by a parameter set of one or more parameters, and wherein the method further comprises providing in the database a plurality of such parameter sets for establishing said plurality of models.
4. The method of claim 2 , further comprising performing said method in parallel on each of said database segments, and wherein said identifying comprises identifying the best model using the results of the k partitions on all segments.
5. The method of claim 1 , wherein said partitioning comprises partitioning said data set into a small subset and a large subset, said large subset comprising said training subset, and said small subset comprising said validation subset.
6. The method of claim 1 , wherein said determining coefficients comprises using said training subset to select coefficients of said first model that minimize a target function of said supervised machine learning algorithm.
7. The method of claim 1 , wherein said predicting comprises predicting said value of said data element using a prediction function of said supervised machine learning algorithm, the coefficients of said first model comprising coefficients of said prediction function.
8. The method of claim 1 , wherein said data set comprises table data, and said partitioning comprises running database SQL processing operations to randomly sort said table data set into sorted table data, to attach an index each row of said sorted table data, and to separate using the indices said sorted table data into said training and said validation subsets.
9. The method of claim 1 , wherein said functions in said first application layer have formats which define arguments and parameters of the functions using generic elements, and wherein said cross validation functions dynamically replace said generic elements with particular elements.
10. A computer program product comprising a non-transitory computer readable medium storing executable instructions for controlling the operation of a computer in a distributed database having a plurality of database segments to perform a method of cross-validation of a supervised machine learning algorithm, the method comprising:
partitioning a data set within said database into a training subset and a validation subset, wherein the partitioning data set comprises partitioning the data set according to randomly sorted data to create two data subsets that are independent and statistically equivalent;
determining coefficients of a first model of said supervised machine learning algorithm using the training subset;
predicting a value of a data element in said validation subset using said first model;
determining a prediction error based at least in part on a difference between said predicted value and the actual value of said data element;
wherein at least a subset of the k different partitions have partition having different training and validation subsets;
determining corresponding k prediction errors based at least in part on iteratively determining the coefficients, predicting the value of the data element, and determining the prediction error for each of said k partitions; and
evaluating the performance of said first model using said k prediction errors; and
wherein said supervised learning algorithm comprises a target function, a prediction function, and a metric function, the target function establishing coefficient values that are used by said prediction and said metric functions, and wherein said functions are embodied in application programs in a first application program layer within said database, said functions being called by cross-validation functions in a second application layer within said database system.
11. The computer program product of claim 10 , further comprising instructions for repeating said method for each of a plurality of other different models, and identifying as the best model the model having the smallest corresponding prediction error.
12. The computer program product of claim 11 , wherein each of said models is defined by a parameter set of one or more parameters, and wherein the method further comprises providing in the database a plurality of such parameter sets for establishing said plurality of models.
13. The computer program product of claim 10 further comprising performing said method in parallel on each of said database segments, and wherein said identifying comprises identifying the best model using the results of the k partitions on all segments.
14. The computer program product of claim 10 , wherein said partitioning comprises partitioning said data set into a small subset and a large subset, said large subset comprising said training subset, and said small subset comprising said validation subset.
15. The computer program product of claim 10 , wherein said determining coefficients comprises using said training subset to select coefficients of said first model that minimize a target function of said supervised machine learning algorithm.
16. The computer program product of claim 10 , wherein said predicting comprises predicting said value of said data element using a prediction function of said supervised machine learning algorithm, the coefficients of said first model comprising coefficients of said prediction function.
17. The computer program product of claim 10 , wherein said data set comprises table data, and said partitioning comprises running database SQL processing operations to randomly sort said table data set into sorted table data, to attach an index each row of said sorted table data, and to separate using the indices said sorted table data into said training and said validation subsets.
18. The computer program product of claim 10 , wherein said functions in said first application layer have formats which define arguments and parameters of the functions using generic elements, and wherein said cross validation functions dynamically replace said generic elements with particular elements.