  Incomplete sky analysis of cosmic microwave background (CMB) polarization
spectra poses a major problem of leakage between $E$- and $B$-modes. We present
a machine learning approach to remove this $E$-to-$B$ leakage using a
convolutional neural network (CNN) in presence of detector noise. The CNN
predicts the full sky $E$- and $B$-modes spectra for multipoles $2 \leq \ell
\leq 384$ from the partial sky spectra for $N_{\rm{side}} = 256$. We use
tensor-to-scalar ratio $r=0.001$ to simulate the CMB polarization maps. We
train our CNN using $10^5$ full sky target spectra and an equal number of noise
contaminated partial sky spectra obtained from the simulated maps. The CNN
works well for two masks covering the sky area of $\sim 80\%$ and $\sim 10\%$
respectively after training separately for each mask. For the assumed
theoretical $E$- and $B$-modes spectra, predicted full sky $E$- and $B$-modes
spectra agree well with the corresponding target spectra and their means agree
with theoretical spectra. The CNN preserves the cosmic variances at each
multipole, effectively removes correlations of the partial sky $E$- and
$B$-modes spectra, and retains the entire statistical properties of the targets
avoiding the problem of so-called $E$-to-$B$ leakage for the chosen theoretical
model.
