/usr/share/pyshared/mlpy/_lars.py is in python-mlpy 2.2.0~dfsg1-2.1.
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## This code is written by Davide Albanese, <albanese@fbk.eu>.
## (C) 2010 Fondazione Bruno Kessler - Via Santa Croce 77, 38100 Trento, ITALY.
## This program is free software: you can redistribute it and/or modify
## it under the terms of the GNU General Public License as published by
## the Free Software Foundation, either version 3 of the License, or
## (at your option) any later version.
## This program is distributed in the hope that it will be useful,
## but WITHOUT ANY WARRANTY; without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
## GNU General Public License for more details.
## You should have received a copy of the GNU General Public License
## along with this program. If not, see <http://www.gnu.org/licenses/>.
__all__ = ["Lar", "Lasso", "LarExt", "LassoExt"]
import numpy as np
def lars(x, y, m, method="lar"):
"""
lar -> m <= x.shape[1]
lasso -> m can be > x.shape[1]
"""
mu = np.zeros(x.shape[0])
active = []
inactive = range(x.shape[1])
beta = np.zeros(x.shape[1])
for i in range(m):
if len(inactive) == 0:
break
# equation 2.8
c = np.dot(x.T, (y - mu))
# equation 2.9
ct = c.copy()
ct[active] = 0.0 # avoid re-selections
ct_abs = np.abs(ct)
j = np.argmax(ct_abs)
if np.any(np.isnan(ct_abs)): # saturation
break
C = ct_abs[j]
active.append(j)
inactive.remove(j)
# equation 2.10
s = np.sign(c[active])
# equation 2.4
xa = x[:, active] * s
# equation 2.5
G = np.dot(xa.T, xa)
try:
Gi = np.linalg.inv(G)
except np.linalg.LinAlgError:
Gi = np.linalg.pinv(G)
A = np.sum(Gi)**(-0.5)
# equation 2.6
w = np.sum(A * Gi, axis=1)
u = np.dot(xa, w)
# equation 2.11
a = np.dot(x.T, u)
# equation 2.13
g1 = (C - c[inactive]) / (A - a[inactive])
g2 = (C + c[inactive]) / (A + a[inactive])
g = np.concatenate((g1, g2))
g = g[g > 0.0]
if g.shape[0] == 0:
gammahat = C / A # equation 2.21
else:
gammahat = np.min(g)
if method == "lasso":
rm = False
g = - beta # equation 3.4
g[active] /= w # equation 3.4
gp = g[g > 0.0] # equation 3.5
if gp.shape[0] == 0:
gammatilde = gammahat
else:
gammatilde = np.min(gp) # equation 3.5
# equation 3.6
if gammatilde < gammahat:
gammahat = gammatilde
idx = np.where(gammahat == g)[0]
rm = True
beta[active] = beta[active] + gammahat * w
mu = mu + (gammahat * u) # equation 2.12 and 3.6 (lasso)
if method == "lasso" and rm:
beta[idx] = 0.0
for k in idx:
active.remove(k)
inactive.append(k)
beta[active] = beta[active] * s
return active, beta, i+1
class Lar(object):
"""LAR.
"""
def __init__(self, m=None):
"""Initialization.
:Parameters:
m : int (> 0)
max number of steps (= number of features selected).
If m=None -> m=x.shape[1] in .learn(x, y)
"""
self.__m = m # max number of steps
self.__beta = None
self.__selected = None
self.__steps = None
def learn(self, x, y):
"""Compute the regression coefficients.
:Parameters:
x : numpy 2d array (nxp)
matrix of regressors
y : numpy 1d array (n)
response
"""
if not isinstance(x, np.ndarray):
raise ValueError("x must be an numpy 2d array")
if not isinstance(y, np.ndarray):
raise ValueError("y must be an numpy 1d array")
if x.ndim > 2:
raise ValueError("x must be an 2d array")
if x.shape[0] != y.shape[0]:
raise ValueError("x and y are not aligned")
if self.__m > x.shape[1] or self.__m == None:
m = x.shape[1]
else:
m = self.__m
self.__selected, self.__beta, self.__steps = \
lars(x, y, m, "lar")
def pred(self, x):
"""Compute the predicted response.
:Parameters:
x : numpy 2d array (nxp)
matrix of regressors
:Returns:
yp : 1d ndarray
predicted response
"""
if not isinstance(x, np.ndarray):
raise ValueError("x must be an numpy 2d array")
if x.ndim > 2:
raise ValueError("x must be an 2d array")
if x.shape[1] != self.__beta.shape[0]:
raise ValueError("x and beta are not aligned")
return np.dot(x, self.__beta)
def selected(self):
"""Returns the regressors ranking.
"""
return self.__selected
def beta(self):
"""Return b_1, ..., b_p.
"""
return self.__beta
def steps(self):
"""Return the number of steps really performed.
"""
return self.__steps
class Lasso(object):
"""LASSO computed with LARS algoritm.
"""
def __init__(self, m):
"""Initialization.
:Parameters:
m : int (> 0)
max number of steps.
"""
self.__m = m # max number of steps
self.__beta = None
self.__selected = None
self.__steps = None
def learn(self, x, y):
"""Compute the regression coefficients.
:Parameters:
x : numpy 2d array (nxp)
matrix of regressors
y : numpy 1d array (n)
response
"""
if not isinstance(x, np.ndarray):
raise ValueError("x must be an numpy 2d array")
if not isinstance(y, np.ndarray):
raise ValueError("y must be an numpy 1d array")
if x.ndim > 2:
raise ValueError("x must be an 2d array")
if x.shape[0] != y.shape[0]:
raise ValueError("x and y are not aligned")
self.__selected, self.__beta, self.__steps = \
lars(x, y, self.__m, "lasso")
def pred(self, x):
"""Compute the predicted response.
:Parameters:
x : numpy 2d array (nxp)
matrix of regressors
:Returns:
yp : 1d ndarray
predicted response
"""
if not isinstance(x, np.ndarray):
raise ValueError("x must be an numpy 2d array")
if x.ndim > 2:
raise ValueError("x must be an 2d array")
if x.shape[1] != self.__beta.shape[0]:
raise ValueError("x and beta are not aligned")
return np.dot(x, self.__beta)
def selected(self):
"""Returns the regressors ranking.
"""
return self.__selected
def beta(self):
"""Return b_1, ..., b_p.
"""
return self.__beta
def steps(self):
"""Return the number of steps really performed.
"""
return self.__steps
class LarExt(object):
def __init__(self, m=None):
self.__m = m # max number of steps
self.__selected = None
def learn(self, x, y):
if x.ndim == 1:
xx = x.copy()
xx.shape = (-1, 1)
if x.ndim == 2:
xx = x
if x.ndim > 2:
raise ValueError("x must be an 1-D or 2-D array")
if x.shape[0] != y.shape[0]:
raise ValueError("x and y are not aligned")
if self.__m > xx.shape[1] or self.__m == None:
m = xx.shape[1]
else:
m = self.__m
# compute number of LAR steps
runs = m / x.shape[0]
ms = ([xx.shape[0]] * runs) + \
[m - (xx.shape[0] * runs)]
active = []
remaining = np.arange(xx.shape[1])
for i in ms:
lars = Lar(m=i)
lars.learn(xx[:, remaining], y)
sel = lars.selected()
active.extend(remaining[sel].tolist())
remaining = np.setdiff1d(remaining, remaining[sel])
self.__selected = np.array(active)
def selected(self):
return self.__selected
class LassoExt(object):
def __init__(self, m):
self.__m = m # max number of steps
self.__selected = None
def learn(self, x, y):
if x.ndim == 1:
xx = x.copy()
xx.shape = (-1, 1)
if x.ndim == 2:
xx = x
if x.ndim > 2:
raise ValueError("x must be an 1-D or 2-D array")
if x.shape[0] != y.shape[0]:
raise ValueError("x and y are not aligned")
m = self.__m
# compute number of LASSO steps
runs = xx.shape[1] / xx.shape[0]
ms = ([xx.shape[0]] * runs) + \
[xx.shape[1] - (xx.shape[0] * runs)]
active = []
remaining = np.arange(xx.shape[1])
while len(remaining) != 0:
lasso = Lasso(m=m)
lasso.learn(xx[:, remaining], y)
sel = lasso.selected()
active.extend(remaining[sel].tolist())
remaining = np.setdiff1d(remaining, remaining[sel])
self.__selected = np.array(active)
def selected(self):
return self.__selected
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