*K*in case of K-fold cross-validation). These jobs could run in parallel in Aster with little help from R. This post will illustrate how to run

**linear regression models**

*K***in parallel**in Aster as part of the

*K*-fold cross-validation procedure.

### The Problem

Cross-validation is important technique in machine learning that receives its own chapters in the textbooks (e.g. see Chapter 7 here). In our examples we implement a

Further more, the examples will be concerned only with the step in

To simplify examples we will also use R package

which results in:

This problem is not beyond R memory limits but our goal is to execute linear regression in Aster. We enlist

Lastly, we need to define the folds (partitions) on the table to build linear regression model on each of them. Usually, this step performs equal and random division into partitions. Doing this with R and Aster is actually not extremely difficult but will take us beyond the scope of the main topic. For this reason alone we propose

Again, do not replicate this method in real cross-validation task but use it as a template or a prototype only.

To make each fold's compliment (used to train 12 models later) we simply exclude each month's data, e.g. selecting the compliment to the fold 6 in its entirety (in SQL):

This results in the list

Next, we replace the

*K*-fold cross-validation method to demonstrate how to run parallel jobs in Aster with R. The implementation of K-fold cross-validation that will be given is neither exhaustive nor exemplary as it introduces certain bias (based on month of the year) into the models. But this approach could definitely lead to a general solution for cross-validation and other problems involving execution of many similar but independent tasks on Aster platform.*K*-fold cross-validation that creates*models on overlapping but different partitions of the training dataset. We will show how to construct***K****independent linear regression models in parallel on Aster, each for one of the***K***partitions of the table (not the same as table partitioning in Aster).***K*### Data and R Packages

We will use Dallas Open Data data set available from here (including Aster load scripts).To simplify examples we will also use R package

**toaster**for Aster and several other packages - all available from CRAN:### Data set, Model and K Folds

Dallas Open Data has information on building permits across city of
Dallas for the period between January 2012 through May 2014 stored in
the table dallasbuildingpermits. We can quickly analyze this table from R with toaster and see its numerical columns:

which results in:

[1] "area" "value" "lon" "lat"These 4 fields will make up our simple linear model to determine the value of construction using its area and location. And now the same in R terms:

This problem is not beyond R memory limits but our goal is to execute linear regression in Aster. We enlist

**toaster**'s*computeLm*function that returns R*lm*object:Lastly, we need to define the folds (partitions) on the table to build linear regression model on each of them. Usually, this step performs equal and random division into partitions. Doing this with R and Aster is actually not extremely difficult but will take us beyond the scope of the main topic. For this reason alone we propose

**quick and dirty**method of dividing building permits into 12 partitions (**) using issue date's month value (in SQL):***K=12*Again, do not replicate this method in real cross-validation task but use it as a template or a prototype only.

To make each fold's compliment (used to train 12 models later) we simply exclude each month's data, e.g. selecting the compliment to the fold 6 in its entirety (in SQL):

### Computing Cross-Validation Models in Aster with R

Before we get to parallel execution with R we show how to script in R
Aster cross-validation of linear regression. To begin we use standard R

*loop and***for***computeLm*with the argument*that limits data to the required fold just like in SQL example above:***where**This results in the list

*that contains 12 linear regression models for each fold respectively.***fit.folds**Next, we replace the

*loop with the specialized***for***foreach*function designed for parallel execution in R. There is no parallel execution yet but all necessary structure for transition to parallel processing:*foreach*performs the same iterations from 1 to 12 as*loop and combines results into list by default.***for**### Parallel Computing in Aster with R

Finally, we are ready to enable parallel execution in R. For more details on using package

**doParallel**see here, but the following suffices to enable a parallel backend in R on Windows:
After that

*foreach*with operator*%dopar%*automatically recognizes parallel backend**and runs its iterations in parallel:***cl*
Comparing with

*foreach**%do%*earlier notice extra handling for ODBC connection inside*foreach %dopar%*. This is necessary due to inability of sharing the same database connection between parallel processes (or threads, depending on the backend implementation). Effectively, with each loop we reconnect to Aster with a brand new connection by reusing original connection's configuration in function*odbcReConnect*.### Elaspsed Time

Lastly, let's see if the whole thing was worth the effort. Chart below
contains elapsed times (in seconds) for all 3 types of loops:

*loop in R,***for***foreach %do%*(sequential), and*foreach %dopar%*(parallel):