text: Review for Deformation of Bregman divergence and its application Summary:This paper considers parameter estimation for discrete probability models. The authors propose an estimator that is computed by minimizing a deformed Bregman divergence. The authors prove that the proposed estimator is more computationally efficient and more robust than the maximal likelihood estimator (MLE), both in theory and simulation. Major Comments:1. After the definition 1, the likelihood $L(\theta)$ is defined to be the sum of $\log \bar{q}_{\theta}(x_i). $ Why the gradient of $L(\theta)$ is a related to $\tilde{p}$. 2. After the equation (4), when the authors say $f=(U’)^{-1}$ the authors assume that the first order derivative of $U$ should be a strictly increasing function (otherwise the inverse function is not well defined, at least in classic notations). I would like to know whether we only need assume the convexity of $U$. Are there other assumptions? 3. In Proposition 1, I think the “Fisher consistent” means that (6) holds for any reasonable $U$ and $f$ just as the authors said before Proposition 1. It is better to add this in the statement of Proposition 1 too. 4. The “Proof 1” is better to be replaced with “Proof of Proposition 1” (same issues for “Proof 2”, “Proof 3”, etc). 5. In the statement of Theorem 1, do the authors have any constraint for $U$? 6. $\xi_{U,f}$ appears in Theorem 2 without a clear definition. Even if it seems to be defined in (17), it is better to be defined again. 7. Why Theorem 2 indicates that “the estimator (5) is not influenced so much by the outlier”? 8. How to solve (5)? Is it trivial? I expect to see something like “We use … algorithm or toolbox to solve (5)“. Minor Comments:1. In Example 2, I suggest use some more beautiful symbol like $\top$ to denote the transpose instead of $T$. 2. The length of the equations should not exceed the line-width (e.g., (4) and (7)). 3. In page 5, “We find some examples satisfying 25 in Theorem 2”. The “25” should be “(25)”.