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mblondel / projection_simplex.py
Last active May 16, 2025 04:21
Projection onto the simplex
"""
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
mblondel / projection_simplex_vectorized.py
Last active April 5, 2025 00:43
Vectorized projection onto the simplex
# 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
mblondel / check_convex.py
Last active January 3, 2025 12:42
A small script to get numerical evidence that a function is convex
# Authors: Mathieu Blondel, Vlad Niculae
# License: BSD 3 clause
import numpy as np
def _gen_pairs(gen, max_iter, max_inner, random_state, verbose):
rng = np.random.RandomState(random_state)
# if tuple, interpret as randn
@mblondel
mblondel / second_order_ode.py
Created July 23, 2010 08:51
Solve second order differential equation using the Euler and the Runge-Kutta methods
#!/usr/bin/env python
"""
Find the solution for the second order differential equation
u'' = -u
with u(0) = 10 and u'(0) = -5
using the Euler and the Runge-Kutta methods.
@mblondel
mblondel / letor_metrics.py
Last active September 19, 2024 06:13
Learning to rank metrics.
# (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
@mblondel
mblondel / svm.py
Last active September 10, 2024 08:11
Support Vector Machines
# 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
mblondel / hmm.tex
Created July 12, 2010 14:42
Good-looking HMM and Lattice diagrams using TikZ
% (C) Mathieu Blondel, July 2010
\documentclass[a4paper,10pt]{article}
\usepackage[english]{babel}
\usepackage[T1]{fontenc}
\usepackage[ansinew]{inputenc}
\usepackage{lmodern}
\usepackage{amsmath}
@mblondel
mblondel / statistical_tests.py
Last active May 9, 2024 00:46
t-test and wilcoxon-test examples in Python
# 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
mblondel / perceptron.py
Last active April 21, 2024 13:42
Kernel Perceptron
# 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
mblondel / mc_pi.py
Created July 25, 2010 02:39
Compute pi by MCMC
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: