Neural models for text generation require a softmax layer with proper word em-beddings during the decoding phase.

In Section D we present the proofs for Section 5.1 In Section H we show the proofs of the lower bounds in Section 6. We outline briefly some other direct applications of our results. CORRAL will achieve regret O ( p | L | dT) . B.1 Original Corral The original Corral algorithm [2] is reproduced below. We reproduce the EXP3.P algorithm (Figure 3.1 in [ 's expected replay regret satisfies: Therefore total regret is bounded by 6 U ( T,) log( T) D.2 Applications of Proposition 5.1 We now show that several algorithms are ( U,, T) bounded: Lemma D.2.

We would like to thank the reviewers for their time. This is also the first result in literature that can combine multiple types of model selection. "The selection of the range": The regret is multiplied by at most a factor of the number of bases Thank you for your comments. B) We would present the full description of the algorithm before Section 4. C) "The assumption that Base algorithms only have access to rewards of rounds when they are selected...": This is not A) "I think it's not trivial to reproduce the results...": We would like more explanations as to why it would We believe we have provided all the details for our experiments. B) "...the instantaneous regret of Step 2 is 1/s times...": Let the cumulative regret of step 1 at round More details are in the proof in Lemma F1, page 24.

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This paper presents an approach to multilabel classification (MLC) with a large number of labels. Our approach is a reduction to binary classification in which label sets are represented by low dimensional binary vectors. This representation follows the principle of Bloom filters, a space-efficient data structure originally designed for approximate membership testing. We show that a naive application of Bloom filters in MLC is not robust to individual binary classifiers' errors. We then present an approach that exploits a specific feature of real-world datasets when the number of labels is large: many labels (almost) never appear together. Our approach is provably robust, has sublinear training and inference complexity with respect to the number of labels, and compares favorably to state-of-the-art algorithms on two large scale multilabel datasets.

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