Statistical Learning
0ff39bbbf981ac0151d340c9aa40e63e-Reviews.html
First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. The paper proposes a matrix completion approach to the cross domain classification task, which is capable of exploiting labeled data in an auxiliary domain and also unlabeled parellel data. The approach involves two steps. First, it constructs a single incomplete matrix that includes all documents and domains, and then completes this matrix while enforcing low-rank and sparsity conditions using the projected gradient descent algorithm. Second, it reduces the feature dimension of this completed matrix using LSI, and then trains a standard classifier on this new representation.
A Proofs of Theoretical Results Proposition 3.1. Both ˆ L and ˆ L
Notably, the log likelihood is not concave w.r.t. the joint pair The heavy lifting for this result has largely been achieved by Propositions 3.1 and 3.2, which The proof of this result can be found in Lemma 3.8 of Osband et al. The following Lemma will be useful in order to prove Proposition 3.5. We express the minimization problem as follows. It is then straightforward to extend this result to the noisy setting. Results are averaged over 5 runs. We consider 3 model selection settings in which to evaluate the practical performance of our estimators.