This vignette contains benchmarks of sgdnet against other similar packages. The data has been precomputed from scripts that are available at https://github.com/jolars/sgdnet/data-raw/.

The benchmarks were generated as follows:

• We fit with ($$\alpha = 1$$) and ridge ($$\alpha = 0$$) penalties.
• The regularization strength, $$\lambda$$, was set to $$\frac1n$$ for each fit.
• A log-spaced sequence of tolerance thresholds were generated, which were selected after trial-and-error to ensure that the packages ran over approximately the same time frame.
• The run times were recorded using system.time().
• The range of run times were clipped to remove “trailing” times to make sure that each the range of times for each package were constrained around the same values.
• Both loss and run times were normalized and the latter were cut into intervals of 20 slices within which the run times were averaged.

The benchmarks were run on a dedicated Amazon EC2 m4.large instance.

Note that some of the data sets below are not strictly 100% dense, despite the specifications below. They are, however, stored in dense matrix form (the regular matrix class in R), which makes the packages ignore any sparsity.

## Gaussian least squares ordinary regression

Benchmarking data sets for the gaussian model
Name Observations Features Density
abalone 4,177 8 100%
mushroooms 8,124 12 100%

## Binomial logistic regression

In this section, we are going to look at the following datasets:

Benchmarking data sets for the binomial model.
Name Observations Features Density
icjnn1 49,990 22 100%
mushroooms 8,124 112 19%

All of these have been collected from the libsvm binary dataset collection.

## Multinomial logistic regression

For the multinomial model, we have these data sets:

Benchmarking data sets for the multinomial model.
Name Observations Classes Features Density
vehicle 846 4 18 100%
dna 2,000 3 180 25%
poker 25,010 10 22 100%

## Multivariate gaussian regression

For the multivariate gaussian case, we have these data:

Name Observations Responses Features Density
violence 1,901 18 100 100%
bikes 731 2 29 28%
naval 11,934 2 15 100%