/usr/share/pyshared/mdp/nodes/regression_nodes.py is in python-mdp 3.3-1.
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from mdp import numx, numx_linalg, utils, Node, NodeException, TrainingException
from mdp.utils import mult
# ??? For the future: add an optional second phase to compute
# residuals, significance of the slope.
class LinearRegressionNode(Node):
"""Compute least-square, multivariate linear regression on the input
data, i.e., learn coefficients ``b_j`` so that::
y_i = b_0 + b_1 x_1 + ... b_N x_N ,
for ``i = 1 ... M``, minimizes the square error given the training ``x``'s
and ``y``'s.
This is a supervised learning node, and requires input data ``x`` and
target data ``y`` to be supplied during training (see ``train``
docstring).
**Internal variables of interest**
``self.beta``
The coefficients of the linear regression
"""
def __init__(self, with_bias=True, use_pinv=False,
input_dim=None, output_dim=None, dtype=None):
"""
:Arguments:
with_bias
If true, the linear model includes a constant term
- True: y_i = b_0 + b_1 x_1 + ... b_N x_N
- False: y_i = b_1 x_1 + ... b_N x_N
If present, the constant term is stored in the first
column of ``self.beta``.
use_pinv
If true, uses the pseudo-inverse function to compute
the linear regression coefficients, which is more robust
in some cases
"""
super(LinearRegressionNode, self).__init__(input_dim, output_dim, dtype)
self.with_bias = with_bias
self.use_pinv = use_pinv
# for the linear regression estimator we need two terms
# the first one is X^T X
self._xTx = None
# the second one is X^T Y
self._xTy = None
# keep track of how many data points have been sent
self._tlen = 0
# final regression coefficients
# if with_bias=True, beta includes the bias term in the first column
self.beta = None
@staticmethod
def is_invertible():
return False
def _check_train_args(self, x, y):
# set output_dim if necessary
if self._output_dim is None:
self._set_output_dim(y.shape[1])
# check output dimensionality
self._check_output(y)
if y.shape[0] != x.shape[0]:
msg = ("The number of output points should be equal to the "
"number of datapoints (%d != %d)" % (y.shape[0], x.shape[0]))
raise TrainingException(msg)
def _train(self, x, y):
"""
**Additional input arguments**
y
array of size (x.shape[0], output_dim) that contains the observed
output to the input x's.
"""
# initialize internal vars if necessary
if self._xTx is None:
if self.with_bias:
x_size = self._input_dim + 1
else:
x_size = self._input_dim
self._xTx = numx.zeros((x_size, x_size), self._dtype)
self._xTy = numx.zeros((x_size, self._output_dim), self._dtype)
if self.with_bias:
x = self._add_constant(x)
# update internal variables
self._xTx += mult(x.T, x)
self._xTy += mult(x.T, y)
self._tlen += x.shape[0]
def _stop_training(self):
try:
if self.use_pinv:
invfun = utils.pinv
else:
invfun = utils.inv
inv_xTx = invfun(self._xTx)
except numx_linalg.LinAlgError, exception:
errstr = (str(exception) +
"\n Input data may be redundant (i.e., some of the " +
"variables may be linearly dependent).")
raise NodeException(errstr)
self.beta = mult(inv_xTx, self._xTy)
# remove junk
del self._xTx
del self._xTy
def _execute(self, x):
if self.with_bias:
x = self._add_constant(x)
return mult(x, self.beta)
def _add_constant(self, x):
"""Add a constant term to the vector 'x'.
x -> [1 x]
"""
return numx.concatenate((numx.ones((x.shape[0], 1),
dtype=self.dtype), x), axis=1)
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