  In binary classification framework, we are interested in making cost
sensitive label predictions in the presence of uniform/symmetric label noise.
We first observe that $0$-$1$ Bayes classifiers are not (uniform) noise robust
in cost sensitive setting. To circumvent this impossibility result, we present
two schemes; unlike the existing methods, our schemes do not require noise
rate. The first one uses $\alpha$-weighted $\gamma$-uneven margin squared loss
function, $l_{\alpha, usq}$, which can handle cost sensitivity arising due to
domain requirement (using user given $\alpha$) or class imbalance (by tuning
$\gamma$) or both. However, we observe that $l_{\alpha, usq}$ Bayes classifiers
are also not cost sensitive and noise robust. We show that regularized ERM of
this loss function over the class of linear classifiers yields a cost sensitive
uniform noise robust classifier as a solution of a system of linear equations.
We also provide a performance bound for this classifier. The second scheme that
we propose is a re-sampling based scheme that exploits the special structure of
the uniform noise models and uses in-class probability $\eta$ estimates. Our
computational experiments on some UCI datasets with class imbalance show that
classifiers of our two schemes are on par with the existing methods and in fact
better in some cases w.r.t. Accuracy and Arithmetic Mean, without using/tuning
noise rate. We also consider other cost sensitive performance measures viz., F
measure and Weighted Cost for evaluation. As our re-sampling scheme requires
estimates of $\eta$, we provide a detailed comparative study of various $\eta$
estimation methods on synthetic datasets, w.r.t. half a dozen evaluation
criterion. Also, we provide understanding on the interpretation of cost
parameters $\alpha$ and $\gamma$ using different synthetic data experiments.
