[Numpy-discussion] Multiple Regression
Thu Nov 12 19:20:35 CST 2009
On Thu, Nov 12, 2009 at 6:44 PM, Robert Kern <firstname.lastname@example.org> wrote:
> On Thu, Nov 12, 2009 at 17:38, Alexey Tigarev <email@example.com> wrote:
>> Hi All!
>> I have implemented multiple regression in a following way:
>> def multipleRegression(x, y):
>> """ Perform linear regression using least squares method.
>> X - matrix containing inputs for observations,
>> y - vector containing one of outputs for every observation """
>> mulregLogger.debug("multipleRegression(x=%s, y=%s)" % (x, y))
>> xt = transpose(x)
>> a = dot(xt, x) # A = xt * x
>> b = dot(xt, y) # B = xt * y
>> return linalg.solve(a, b)
> Never, ever use the normal equations. :-)
> Use linalg.lstsq(x, y) instead.
>> except linalg.LinAlgError, lae:
>> mulregLogger.warn("Singular matrix:\n%s" % (a))
>> mulregLogger.warn("Determinant: %f" % (linalg.det(a)))
>> raise lae
>> Can you suggest me something to optimize it?
>> I am using it on large number of observations so it is common to have
>> "x" matrix of about 5000x20 and "y" vector of length 5000, and more.
>> I also have to run that multiple times for different "y" vectors and
>> same "x" matrix.
> Just make a matrix "y" such that each column vector is a different
> output vector (e.g. y.shape == (5000, number_of_different_y_vectors))
or if you want to do it sequentially, this should work
xpinv = linalg.pinv(x)
for y in all_ys:
beta = np.dot(xpinv, y)
but this works for singular problems without warning
> Robert Kern
> "I have come to believe that the whole world is an enigma, a harmless
> enigma that is made terrible by our own mad attempt to interpret it as
> though it had an underlying truth."
> -- Umberto Eco
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