Matlab implementation of numerical experiments from the paper
Dmitrii M. Ostrovskii, Francis Bach. Finite-sample analysis of M-estimators using self-concordance
To run the experiments, clone or download the repository and launch the following MATLAB commands:
run_exp_gauss
run_exp_hazan
The data for the curves will appear in data/<...>, where <...> corresponds to the experiment: Gauss-logistic, Gauss-probit and Hazan-always-1.
Plots will appear in similar subfolders in figs/<...>.
The experiments that reproduce the curves reported in the paper take a few days to run. To obtain (less accurate) results faster,
change the number of Monte-Carlo trials: parameter T in run_exp_gauss.m and run_exp_hazan.m.
One may also explore additional scenarios (not reported in the paper due to space limitations) by changing xKey and yKey variables in generate_data_class.m.
They control the scenario for the design and conditional distribution of the label and take the following values:
xKey: 'Gauss', 'Hazan' or 'Rademacher';
yKey: 'always-1', '0-1', 'logistic', 'ill-spec' or 'probit'.
Here, Rademacher stands for the design with i.i.d. fair Bernoulli entries.
yKey specifies the conditional distribution of
given
:
'0-1': ;
'logistic': ;
'ill-spec': ;
'probit': , where
is the standard Gaussian c.d.f.
The generated data and plots will appear in data/<xKey>-<yKey> and figs/<xKey>-<yKey> correspondingly.