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
abalone |
4,177 |
8 |
100% |

cadata |
20,640 |
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.
adult |
32,561 |
123 |
11% |

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.
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:

violence |
1,901 |
18 |
100 |
100% |

bikes |
731 |
2 |
29 |
28% |

naval |
11,934 |
2 |
15 |
100% |