fabianp

"""
Partial Correlation in Python (clone of Matlab's partialcorr)

This uses the linear regression approach to compute the partial 
correlation (might be slow for a huge number of variables). The 
algorithm is detailed here:

    http://en.wikipedia.org/wiki/Partial_correlation#Using_linear_regression

Taking X and Y two variables of interest and Z the matrix with all the variable minus {X, Y},

fabianp

import numpy as np

def isotonic_regression(w, y, x_min=None, x_max=None):
    """
    Solve the isotonic regression model:

        min Sum w_i (y_i - x_i) ** 2

        subject to x_min = x_1 <= x_2 ... <= x_n = x_max

fabianp

import numpy as np
from scipy import sparse

# .. for plotting ..
import pylab as plt
# .. to generate a synthetic dataset ..
from sklearn import datasets

n_samples, n_features = 1000, 10000
A, b = datasets.make_regression(n_samples, n_features)

fabianp

# -*- coding: utf-8 -*-
"""
===================================
Swiss Roll reduction with LLE
===================================

An illustration of Swiss Roll reduction
with locally linear embedding

"""

fabianp

"""
Implementation of pairwise ranking using scikit-learn LinearSVC

Reference: 

    "Large Margin Rank Boundaries for Ordinal Regression", R. Herbrich,
    T. Graepel, K. Obermayer 1999

    "Learning to rank from medical imaging data." Pedregosa, Fabian, et al., 
    Machine Learning in Medical Imaging 2012.

fabianp

fabianp

import numpy as np
from scipy import linalg, optimize

MAX_ITER = 100


def group_lasso(X, y, alpha, groups, max_iter=MAX_ITER, rtol=1e-6,
             verbose=False):
    """
    Linear least-squares with l2/l1 regularization solver.

fabianp

# Copyright 2021 Google LLC
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     https://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,

fabianp

# Copyright 2021 Google LLC
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     https://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,

fabianp

"""
Low rank approximation for the lena image
"""
import numpy as np
import scipy as sp
from scipy import linalg
import pylab as pl

X = sp.lena().astype(np.float)
pl.gray()