Multiple lib changes
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@@ -1,30 +1,33 @@
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"""This module implements some common validation schemes from pca and pls.
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"""
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from scipy import ones,mean,sqrt,dot,newaxis,zeros,sum,empty,\
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apply_along_axis,eye, kron
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apply_along_axis,eye,kron,array,sort
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from scipy.stats import median
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from scipy.linalg import triu,inv,svd,norm
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from select_generators import w_pls_gen,w_pls_gen_jk,pls_gen,pca_gen,diag_pert
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from engines import w_simpls,pls, bridge,pca
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from pylab import *
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from engines import w_simpls,pls,bridge,pca
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from cx_utils import m_shape
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def w_pls_cv_val(X, Y, amax, n_blocks=None, algo='simpls'):
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"""RMSEP calc for pls with wide X.
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"""Returns and RMSEP for pls tailored for wide X.
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"""
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k, l = Y.shape
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k, l = m_shape(Y)
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PRESS = zeros((l, amax+1), dtype='f')
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# X,Y are centered
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# X,Y are centered0
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if n_blocks==None:
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n_blocks = Y.shape[0]
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V = w_pls_gen(dot(X, X.T), Y, n_blocks=n_blocks, center=True)
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XXt = dot(X, X.T)
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V = w_pls_gen(XXt, Y, n_blocks=n_blocks, center=True)
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for Din, Doi, Yin, Yout in V:
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ym = -sum(Yout, 0)[newaxis]/(1.0*Yin.shape[0])
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Yin = Yin - ym
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PRESS[:,0] = PRESS[:,0] + ((Yout - ym)**2).sum(0)
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if algo=='simpls':
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dat = w_simpls(Din, Yin, amax)
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Q,U,H = dat['Q'], dat['U'], dat['H']
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Q, U, H = dat['Q'], dat['U'], dat['H']
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That = dot(Doi, dot(U, inv(triu(dot(H.T,U))) ))
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else:
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"Other algo-support comming soon"
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raise NotImplementedError
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#Yhat = empty((amax, k, l),dtype='<f8')
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Yhat = []
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@@ -34,13 +37,14 @@ def w_pls_cv_val(X, Y, amax, n_blocks=None, algo='simpls'):
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E = E + sum(E, 0)/Din.shape[0]
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PRESS[j,1:] = PRESS[j,1:] + sum(E**2, 0)
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#Yhat = Y - dot(That,Q.T)
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return sqrt(PRESS/Y.shape[0])
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rmsep = sqrt(PRESS/Y.shape[0])
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aopt = find_aopt_from_sep(rmsep)
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return rmsep, aopt
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def pls_val(X, Y, amax=2, n_blocks=10,algo='pls'):
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""" Validation results of pls model.
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"""
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k, l = Y.shape
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"""
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k, l = m_shape(Y)
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PRESS = zeros((l, amax+1), dtype='<f8')
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EE = zeros((amax, k, l), dtype='<f8')
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Yhat = zeros((amax, k, l), dtype='<f8')
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@@ -50,6 +54,7 @@ def pls_val(X, Y, amax=2, n_blocks=10,algo='pls'):
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ym = -sum(Yout,0)[newaxis]/Yin.shape[0]
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Yin = (Yin - ym)
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PRESS[:,0] = PRESS[:,0] + ((Yout - ym)**2).sum(0)
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if algo=='pls':
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dat = pls(Xin, Yin, amax, mode='normal')
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elif algo=='bridge':
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@@ -62,9 +67,11 @@ def pls_val(X, Y, amax=2, n_blocks=10,algo='pls'):
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EE[a,out,:] = E
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PRESS[:,a+1] = PRESS[:,a+1] + sum(E**2,0)
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return sqrt(PRESS/(k-1.)), EE, Yhat
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rmsep = sqrt(PRESS/(k-1.))
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aopt = find_aopt_from_sep(rmsep)
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return rmsep, aopt
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def pca_alter_val(a, amax, n_sets=10,method='diag'):
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def pca_alter_val(a, amax, n_sets=10, method='diag'):
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"""Pca validation by altering elements in X.
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"""
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# todo: it is just as easy to do jk-estimates her as well
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@@ -79,18 +86,27 @@ def pca_alter_val(a, amax, n_sets=10,method='diag'):
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EE = a_sub - Xhat.ravel().take(ind)
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tot = (a_sub**2).sum()
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sep[i,j] = (EE**2).sum()/tot
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return sqrt(sep.mean(0))
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#return sep
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sep = sqrt(sep)
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aopt = find_aopt_from_sep(sep)
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return sep, aopt
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def pca_cv_val(X, amax, n_sets):
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""" Cross validation of pca using random sets crossval.
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def pca_cv_val(a, amax, n_sets):
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""" Returns PRESS from cross-validated pca using random segments.
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input:
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-- a, data matrix (m x n)
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-- amax, maximum nuber of components used
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-- n_sets, number of segments to calculate
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output:
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-- sep, (amax x m x n), squared error of prediction (press)
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-- aopt, guestimated optimal number of components
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"""
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m, n = X.shape
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xtot = (X**2).sum()
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V = pca_gen(X, n_sets=7, center=True, index_out=True)
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m, n = a.shape
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E = empty((amax, m, n), dtype='f')
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for xi,xout,ind in V:
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dat_i = pca(xi, amax, mode='detailed')
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xtot = (a**2).sum() # this needs centering
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V = pca_gen(a, n_sets=7, center=True, index_out=True)
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for xi, xout, ind in V:
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dat_i = pca(xi, amax, mode='fast')
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Pi = dat_i['P']
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for a in xrange(amax):
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Pia = Pi[:,:a+1]
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@@ -99,7 +115,9 @@ def pca_cv_val(X, amax, n_sets):
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sep = []
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for a in xrange(amax):
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sep.append(E[a].sum()/xtot)
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return sqrt(sep.mean(0))
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sep = array(sep)
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aopt = find_aopt_from_sep(sep)
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return sep, aopt
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def pls_jkW(a, b, amax, n_blocks=None, algo='pls', use_pack=True):
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""" Returns CV-segments of paramter W for wide X.
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@@ -128,7 +146,20 @@ def pls_jkW(a, b, amax, n_blocks=None, algo='pls', use_pack=True):
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return WW
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def pca_jkP(a, aopt, n_blocks=None):
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""" Returns CV-segments of paramter P.
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"""Returns loading from PCA on CV-segments.
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input:
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-- a, data matrix (n x m)
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-- aopt, number of components in model.
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-- nblocks, number of segments
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output:
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-- PP, loadings collected in a three way matrix
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(n_segments, m, aopt)
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comments:
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* The loadings are scaled with the (1/samples)*eigenvalues.
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* Crossvalidation method is currently set to random blocks of samples.
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todo: add support for T
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fixme: more efficient to add this in validation loop
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"""
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@@ -138,8 +169,30 @@ def pca_jkP(a, aopt, n_blocks=None):
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PP = empty((n_blocks, a.shape[1], aopt), dtype='f')
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V = pca_gen(a, n_sets=n_blocks, center=True)
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for nn,(a_in, a_out) in enumerate(V):
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dat = pca(a_in, aopt, mode='fast')
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dat = pca(a_in, aopt, mode='fast', scale='loads')
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P = dat['P']
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PP[nn,:,:] = P
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return PP
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def find_aopt_from_sep(sep, method='75perc'):
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"""Returns an estimate of optimal number of components from rmsecv.
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"""
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if method=='vanilla':
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# min rmsep
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rmsecv = sqrt(sep.mean(0))
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return rmsecv.argmin() + 1
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elif method=='75perc':
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prct = .75 #percentile
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ind = 1.*sep.shape[0]*prct
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med = median(sep)
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prc_75 = []
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for col in sep.T:
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col.sort()
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prc_75.append(col[int(ind)])
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prc_75 = array(prc_75)
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for i in range(1, sep.shape[1], 1):
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if med[i-1]<prc_75[i]:
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return i
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return len(med)
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