def linearRegression_2(inputs, outputs):
"""
Computers the least squares estimator (LSE) B_hat that minimises the sum of the
squared errors.
Computes B_hat as B_hat = X^+ . y
with X^+ the pseudoinverse of matrix X.
http://en.wikipedia.org/wiki/Moore-Penrose_pseudoinverse
In:
inputs: Matrix of inputs (X) (nxp matrix)
format: [[observation_1], ..., [observation_n]]
outputs: Column vector (Matrix) of outputs y (nx1 matrix)
format: [[y_1], ... , [y_n]]
Out:
B_hat: Column vector (Matrix) of fitted slopes (px1 matrix)
format: [[b_0], ... , [b_{p-1}]]
"""
X = T.dmatrix('X')
y = T.dcol('y')
# http://deeplearning.net/software/theano/library/sandbox/linalg.html
# MatrixPinv is the class.
# pinv is the method based upon the MatrixPinv class.
# B_hat = X^+ . y
B_hat = T.dot(linOps.pinv(X),y)
lse = function([X, y], B_hat)
b = lse(inputs, outputs)
return b
def test_pseudoinverse_correctness():
rng = numpy.random.RandomState(utt.fetch_seed())
d1 = rng.randint(4) + 2
d2 = rng.randint(4) + 2
r = rng.randn(d1, d2).astype(theano.config.floatX)
x = tensor.matrix()
xi = pinv(x)
ri = function([x], xi)(r)
assert ri.shape[0] == r.shape[1]
assert ri.shape[1] == r.shape[0]
assert ri.dtype == r.dtype
# Note that pseudoinverse can be quite unprecise so I prefer to compare
# the result with what numpy.linalg returns
assert _allclose(ri, numpy.linalg.pinv(r))
def test_pseudoinverse_correctness():
rng = numpy.random.RandomState(utt.fetch_seed())
d1 = rng.randint(4) + 2
d2 = rng.randint(4) + 2
r = rng.randn(d1, d2).astype(theano.config.floatX)
x = tensor.matrix()
xi = pinv(x)
ri = function([x], xi)(r)
assert ri.shape[0] == r.shape[1]
assert ri.shape[1] == r.shape[0]
assert ri.dtype == r.dtype
# Note that pseudoinverse can be quite unprecise so I prefer to compare
# the result with what numpy.linalg returns
assert _allclose(ri, numpy.linalg.pinv(r))
