mblondel

# Mathieu Blondel, October 2010
# License: BSD 3 clause

import numpy as np
from numpy import linalg

def linear_kernel(x1, x2):
    return np.dot(x1, x2)

def polynomial_kernel(x, y, p=3):

mblondel

# Mathieu Blondel, February 2012
# License: BSD 3 clause

# Port to Python of examples in chapter 5 of
# "Introductory Statistics with R" by Peter Dalgaard

import numpy as np
from scipy.stats import ttest_1samp, wilcoxon, ttest_ind, mannwhitneyu

# daily intake of energy in kJ for 11 women

mblondel

from random import random

"""
Find pi by the Monte-Carlo method.

area of a circle = pi r^2
area of a square = (2r)^2 = 4 r^2

Perform random uniform sampling between -1 and 1.
The proportion of points in the unit circle is:

mblondel

# Mathieu Blondel, September 2010
# License: BSD 3 clause

import numpy as np
from numpy import linalg
import cvxopt
import cvxopt.solvers

def linear_kernel(x1, x2):
    return np.dot(x1, x2)

mblondel

# Copyright Mathieu Blondel December 2011
# License: BSD 3 clause

import numpy as np
import pylab as pl

from sklearn.base import BaseEstimator
from sklearn.utils import check_random_state
from sklearn.cluster import MiniBatchKMeans
from sklearn.cluster import KMeans as KMeansGood

mblondel

# Mathieu Blondel, May 2012
# License: BSD 3 clause

import numpy as np

def euclidean_distances(X, Y=None, Y_norm_squared=None, squared=False):
    XX = np.sum(X * X, axis=1)[:, np.newaxis]
    YY = np.sum(Y ** 2, axis=1)[np.newaxis, :]
    distances = np.dot(X, Y.T)
    distances *= -2

mblondel

# Author: Mathieu Blondel
# License: BSD 3 clause

import numpy as np


def projection_simplex(V, z=1, axis=None):
    """
    Projection of x onto the simplex, scaled by z:
        P(x; z) = argmin_{y >= 0, sum(y) = z} ||y - x||^2

mblondel

"""
License: BSD
Author: Mathieu Blondel

Implements three algorithms for projecting a vector onto the simplex: sort, pivot and bisection.

For details and references, see the following paper:

Large-scale Multiclass Support Vector Machine Training via Euclidean Projection onto the Simplex
Mathieu Blondel, Akinori Fujino, and Naonori Ueda.

mblondel

"""
Efficient implementation of FISTA.
"""

# Author: Mathieu Blondel
# License: BSD 3 clause

import numpy as np

mblondel

# (C) Mathieu Blondel, November 2013
# License: BSD 3 clause

import numpy as np


def ranking_precision_score(y_true, y_score, k=10):
    """Precision at rank k

    Parameters