Getting Started¶

Download¶

Clone the repository available at

$ git clone https://github.com/yassine-laguel/spqr.git
$ cd toolbox/

Installation¶

SPQR requires several packages one can install through conda and provided yaml file spqr_env.yml:

$ conda env create --file spqr_env.yml
$ source activate spqr_env

Simple Case Demo¶

Let X be a numpy ndarray of dimensions \(n \times p\) representing the features and y, is one dimensional array of size \(n\) representing the targets :

import numpy as np
X = np.random.rand(100,2)
w = np.array([1.,2.])
y = np.dot(X,w) + np.random.rand(100)

We propose to minimize the conditional value at risk of \(L_2\)-loss \(\frac{1}{2}\|Y-Xw\|^2\):

def loss(w,x,y):
  return (y - np.dot(x,w))**2
def loss_prime(w,x,y):
  return -2.0 * (y - np.dot(x,w)) * x

For that purpose, a RiskOptimizer object with probability level for CVar \(p=0.8\) is instantiated:

from spqr import RiskOptimizer
optimizer = RiskOptimizer(loss, loss_prime, p=0.8)

One can run selected descent algorithm (by default 'subgradient') with:

optimizer.fit(X,y)
sol = optimizer.solution

A deeper insight of the toolbox is available through https://github.com/yassine-laguel/spqr/blob/master/docs/toolbox_demonstration.ipynb