  This work studies the total variation regularized $\ell_2$ estimator (fused
lasso) in the setting of a change point detection problem. Compared with
existing works that focus on the sum of squared estimation errors, we give
bound on the element-wise estimation error. Our bound is nearly optimal in the
sense that the sum of squared error matches the best existing result, up to a
logarithmic factor. This analysis of the element-wise estimation error allows a
screening method that can approximately detect all the change points. We also
generalize this method to the muitivariate setting, i.e., to the problem of
group fused lasso.
