Weighted Empirical Risk Minimization: Transfer Learning based on Importance Sampling
We consider statistical learning problems, when the distribution of the training observations differs from the distribution involved in the risk one seeks to minimize (referred to as the 	extit{test distribution}) but is still defined on the same measurable space as and dominates it. In the unrealistic case where the likelihood ratio is known, one may straightforwardly extends the Empirical Risk Minimization (ERM) approach to this specific 	extit{transfer learning} setup using the same idea as that behind Importance Sampling, by minimizing a weighted version of the empirical risk functional computed from the *biased* training data with weights . Although the 	extit{importance function} is generally unknown in practice, we show that, in various situations frequently encountered in practice, it takes a simple form and can be directly estimated from the *s and some auxiliary information on the statistical population . By means of linearization techniques, we then prove that the generalization capacity of the approach aforementioned is preserved when plugging the resulting estimates of the *s into the weighted empirical risk. Beyond these theoretical guarantees, numerical results provide strong empirical evidence of the relevance of the approach promoted in this article.
The authors consider the problem of a mismatch between the distribution of the training observations and the test distribution (a transfer learning setup). The paper seems technically sound but it is not easy to read. Even Section 2 it is difficult to read. - Main drawback: Please define the weights w_i of Eq. (5) in Section 2. - I have a question: is it possible to extend your work considering Multiple Importance Sampling and Generalized Multiple Importance Sampling schemes? please discuss.
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
Weighted Empirical Risk Minimization: Transfer Learning based on Importance Sampling
We consider statistical learning problems, when the distribution of the training observations differs from the distribution involved in the risk one seeks to minimize (referred to as the 	extit{test distribution}) but is still defined on the same measurable space as and dominates it. In the unrealistic case where the likelihood ratio is known, one may straightforwardly extends the Empirical Risk Minimization (ERM) approach to this specific 	extit{transfer learning} setup using the same idea as that behind Importance Sampling, by minimizing a weighted version of the empirical risk functional computed from the *biased* training data with weights . Although the 	extit{importance function} is generally unknown in practice, we show that, in various situations frequently encountered in practice, it takes a simple form and can be directly estimated from the *s and some auxiliary information on the statistical population . By means of linearization techniques, we then prove that the generalization capacity of the approach aforementioned is preserved when plugging the resulting estimates of the *s into the weighted empirical risk. Beyond these theoretical guarantees, numerical results provide strong empirical evidence of the relevance of the approach promoted in this article.
user
<think>Okay, to do a decent peer review, I should start with summarizing what the work is about. This includes novelty, contributions, clarity, and impact. I might include suggestions to issues that I find critical to the usefulness of the work. Starting with novelty, there are different types of novelty. The first aspect of novelty is scope and scale. Is the work covering a broader perspective than previous works? The second aspect is methodology. Is the proposed methodology novel compared to previous methods? Do they provide any significant advantage over previous methodologies? The third aspect is results. Are the results different compared previous work? Does this lead to any novel theories or an extension of current theories? Next is clarity, I will be reading the work in depth and analyze if any sentences can be potentially ambiguous or misleading. If any sentences are ambiguous, I will state them and give a suggestion on how to rephrase such sentence or how to make more clear to the audience. Lastly, impact is important. I will attempt to predict how such work will impact the scientific community. This might include the applications of such work and how the work might transform the way we study a certain topic. Finally, I will might only mention issues that are critical. This is to keep the review as concise and helpful as possible.</think>



The authors consider the problem of a mismatch between the distribution of the training observations and the test distribution (a transfer learning setup). The paper seems technically sound but it is not easy to read. Even Section 2 it is difficult to read. - Main drawback: Please define the weights w_i of Eq. (5) in Section 2. - I have a question: is it possible to extend your work considering Multiple Importance Sampling and Generalized Multiple Importance Sampling schemes? please discuss.
assistant
The authors consider the problem of a mismatch between the distribution of the training observations and the test distribution (a transfer learning setup). The paper seems technically sound but it is not easy to read. Even Section 2 it is difficult to read. - Main drawback: Please define the weights w_i of Eq. (5) in Section 2. - I have a question: is it possible to extend your work considering Multiple Importance Sampling and Generalized Multiple Importance Sampling schemes? please discuss.