s2 = 0.05 # noise variance y = Phip.dot(b) + np.random.normal(0, s2, N) # cubic B-spline basis (used for regression) p = 3 # order of spline (3 = cubic) nknots = 5 # number of knots (endpoints only counted once) knots = np.linspace(0, 10, nknots) k = splinelab.augknt(knots, p) # pad the knot vector B = bspline.Bspline(k, p) Phi = np.array([B(i) for i in X]) Phis = np.array([B(i) for i in Xs]) hyp0 = np.zeros(2) #hyp0 = np.zeros(4) # use ARD B = BLR(hyp0, Phi, y) hyp = B.estimate(hyp0, Phi, y, optimizer='powell') yhat, s2 = B.predict(hyp, Phi, y, Phis) plt.fill_between(Xs, yhat - 1.96 * np.sqrt(s2), yhat + 1.96 * np.sqrt(s2), alpha=0.2) plt.scatter(X, y) plt.plot(Xs, yhat) plt.show() print(B.nlZ) print(1 / hyp) print(B.m) print('demonstrate likelihood warping ...')
def main(filename, maskfile, outdir, basis, ard=False): """ :outputs: * yhat - predictive mean * ys2 - predictive variance * trendcoeff - coefficients from the trend surface model * negloglik - Negative log marginal likelihood * hyp - hyperparameters * explainedvar - explained variance * rmse - standardised mean squared error * trendcoeffvar - marginal variances """ from bayesreg import BLR np.seterr(invalid='ignore') # load data print("Processing data in", filename) Y, X, maskIndices = load_data(filename, maskfile) Y = np.round( 10000 * Y) / 10000 # truncate precision to avoid numerical probs if len(Y.shape) == 1: Y = Y[:, np.newaxis] N = Y.shape[1] # standardize responses and covariates mY = np.mean(Y, axis=0) sY = np.std(Y, axis=0) Yz = (Y - mY) / sY mX = np.mean(X, axis=0) sX = np.std(X, axis=0) Xz = (X - mX) / sX # create basis set and set starting hyperparamters Phi = create_basis(Xz, basis) if ard is True: hyp0 = np.zeros(Phi.shape[1] + 1) else: hyp0 = np.zeros(2) # estimate the models yhat = np.zeros_like(Yz) ys2 = np.zeros_like(Yz) nlZ = np.zeros(N) hyp = np.zeros((N, len(hyp0))) rmse = np.zeros(N) ev = np.zeros(N) m = np.zeros((N, Phi.shape[1])) bs2 = np.zeros((N, Phi.shape[1])) for i in range(0, N): # print("Estimating model ",i+1,"of",N) breg = BLR() hyp[i, :] = breg.estimate(hyp0, Phi, Yz[:, i], 'powell') m[i, :] = breg.m nlZ[i] = breg.nlZ # compute marginal variances bs2[i] = np.sqrt(np.diag(np.linalg.inv(breg.A))) # compute predictions and errors yhat[:, i], ys2[:, i] = breg.predict(hyp[i, :], Phi, Yz[:, i], Phi) yhat[:, i] = yhat[:, i] * sY[i] + mY[i] rmse[i] = np.sqrt(np.mean((Y[:, i] - yhat[:, i])**2)) ev[i] = 100 * (1 - (np.var(Y[:, i] - yhat[:, i]) / np.var(Y[:, i]))) # print("Variance explained =",ev[i],"% RMSE =",rmse[i]) print("Mean (std) variance explained =", ev.mean(), "(", ev.std(), ")") print("Mean (std) RMSE =", rmse.mean(), "(", rmse.std(), ")") # Write output print("Writing output ...") out_base_name = outdir + "/" + filename.split('/')[-1].split('.nii')[0] np.savetxt(out_base_name + ".tsm.trendcoeff.txt", m, delimiter='\t', fmt='%5.8f') np.savetxt(out_base_name + ".tsm.negloglik.txt", nlZ, delimiter='\t', fmt='%5.8f') np.savetxt(out_base_name + ".tsm.hyp.txt", hyp, delimiter='\t', fmt='%5.8f') np.savetxt(out_base_name + ".tsm.explainedvar.txt", ev, delimiter='\t', fmt='%5.8f') np.savetxt(out_base_name + ".tsm.rmse.txt", rmse, delimiter='\t', fmt='%5.8f') np.savetxt(out_base_name + ".tsm.trendcoeffvar.txt", bs2, delimiter='\t', fmt='%5.8f') save_nifti(yhat, out_base_name + '.tsm.yhat.nii.gz', filename, maskIndices) save_nifti(ys2, out_base_name + '.tsm.ys2.nii.gz', filename, maskIndices)
# estimate the models yhat = np.zeros_like(Yz) ys2 = np.zeros_like(Yz) nlZ = np.zeros(N) hyp = np.zeros((N, len(hyp0))) rmse = np.zeros(N) ev = np.zeros(N) m = np.zeros((N, Phi.shape[1])) bs2 = np.zeros((N, Phi.shape[1])) #for i in range(0, N): i = 0 print("Estimating model ", i + 1, "of", N) breg = BLR() hyp[i, :] = breg.estimate(hyp0, Phi, Yz[:, i], 'powell') m[i, :] = breg.m nlZ[i] = breg.nlZ # compute marginal variances bs2[i] = np.sqrt(np.diag(np.linalg.inv(breg.A))) # compute predictions and errors yhat[:, i], ys2[:, i] = breg.predict(hyp[i, :], Phi, Yz[:, i], Phi) yhat[:, i] = yhat[:, i] * sY[i] + mY[i] rmse[i] = np.sqrt(np.mean((Y[:, i] - yhat[:, i])**2)) ev[i] = 100 * (1 - (np.var(Y[:, i] - yhat[:, i]) / np.var(Y[:, i]))) print("Variance explained =", ev[i], "% RMSE =", rmse[i]) print("Mean (std) variance explained =", ev.mean(), "(", ev.std(), ")")
def estimate(filename, maskfile, basis): """ Estimate a trend surface model This will estimate a trend surface model, independently for each subject. This is currently fit using a polynomial model of a specified degree. The models are estimated on the basis of data stored on disk in ascii or neuroimaging data formats (currently nifti only). Ascii data should be in tab or space delimited format with the number of voxels in rows and the number of subjects in columns. Neuroimaging data will be reshaped into the appropriate format Basic usage:: estimate(filename, maskfile, basis) where the variables are defined below. Note that either the cfolds parameter or (testcov, testresp) should be specified, but not both. :param filename: 4-d nifti file containing the images to be estimated :param maskfile: nifti mask used to apply to the data :param basis: model order for the interpolating polynomial All outputs are written to disk in the same format as the input. These are: :outputs: * yhat - predictive mean * ys2 - predictive variance * trendcoeff - coefficients from the trend surface model * negloglik - Negative log marginal likelihood * hyp - hyperparameters * explainedvar - explained variance * rmse - standardised mean squared error """ # load data print("Processing data in", filename) Y, X, mask = load_data(filename, maskfile) Y = np.round( 10000 * Y) / 10000 # truncate precision to avoid numerical probs if len(Y.shape) == 1: Y = Y[:, np.newaxis] N = Y.shape[1] # standardize responses and covariates mY = np.mean(Y, axis=0) sY = np.std(Y, axis=0) Yz = (Y - mY) / sY mX = np.mean(X, axis=0) sX = np.std(X, axis=0) Xz = (X - mX) / sX # create basis set and set starting hyperparamters Phi = create_basis(Xz, basis) hyp0 = np.zeros(2) # estimate the models for all subjects yhat = np.zeros_like(Yz) ys2 = np.zeros_like(Yz) nlZ = np.zeros(N) hyp = np.zeros((N, len(hyp0))) rmse = np.zeros(N) ev = np.zeros(N) m = np.zeros((N, Phi.shape[1])) for i in range(0, N): print("Estimating model ", i + 1, "of", N) breg = BLR() hyp[i, :] = breg.estimate(hyp0, Phi, Yz[:, i]) m[i, :] = breg.m nlZ[i] = breg.nlZ # compute predictions and errors yhat[:, i], ys2[:, i] = breg.predict(hyp[i, :], Phi, Yz[:, i], Phi) yhat[:, i] = yhat[:, i] * sY[i] + mY[i] rmse[i] = np.sqrt(np.mean((Y[:, i] - yhat[:, i])**2)) ev[i] = 100 * (1 - (np.var(yhat[:, i] - Y[:, i]) / np.var(Y[:, i]))) print("Variance explained =", ev[i], "% RMSE =", rmse[i]) print("Mean (std) variance explained =", ev.mean(), "(", ev.std(), ")") print("Mean (std) RMSE =", rmse.mean(), "(", rmse.std(), ")") # Write output print("Writing output ...") np.savetxt("trendcoeff.txt", m, delimiter='\t', fmt='%5.8f') np.savetxt("negloglik.txt", nlZ, delimiter='\t', fmt='%5.8f') np.savetxt("hyp.txt", hyp, delimiter='\t', fmt='%5.8f') np.savetxt("explainedvar.txt", ev, delimiter='\t', fmt='%5.8f') np.savetxt("rmse.txt", rmse, delimiter='\t', fmt='%5.8f') fileio.save_nifti(yhat, 'yhat.nii.gz', filename, mask) fileio.save_nifti(ys2, 'ys2.nii.gz', filename, mask)
b = [0.5, -0.1, 0.005] # true regression coefficients s2 = 0.05 # noise variance y = Phi.dot(b) + np.random.normal(0, s2, N) yid = range(0, N, 1) hyp0 = np.zeros(2) hyp0 = np.zeros(4) B = BLR(hyp0, Phi[yid, :], y[yid]) #B = BLR() #B.post(hyp0,Phi[yid,:],y[yid]) B.loglik(hyp0, Phi[yid, :], y[yid]) B.dloglik(hyp0, Phi[yid, :], y[yid]) hyp = B.estimate(hyp0, Phi[yid, :], y[yid]) yhat, s2 = B.predict(hyp, Phi[yid, :], y[yid], Phi) plt.plot(X, y) plt.plot(X, yhat) plt.show() ## test GPR #y = y-y.mean() #hyp0 = np.zeros(3) #G = GPR(hyp0, covSqExp, Phi[yid,:], y[yid]) #G.loglik(hyp0, covSqExp, Phi[yid,:], y[yid]) #G.dloglik(hyp0, covSqExp, Phi[yid,:], y[yid]) #hyp = G.estimate(hyp0,covSqExp, Phi[yid,:], y[yid]) #