Cross-Domain Matching for Bag-of-Words Data via Kernel Embeddings of Latent Distributions
We propose a kernel-based method for finding matching between instances across different domains, such as multilingual documents and images with annotations. Each instance is assumed to be represented as a multiset of features, e.g., a bag-ofwords representation for documents. The major difficulty in finding cross-domain relationships is that the similarity between instances in different domains cannot be directly measured. To overcome this difficulty, the proposed method embeds all the features of different domains in a shared latent space, and regards each instance as a distribution of its own features in the shared latent space. To represent the distributions efficiently and nonparametrically, we employ the framework of the kernel embeddings of distributions. The embedding is estimated so as to minimize the difference between distributions of paired instances while keeping unpaired instances apart. In our experiments, we show that the proposed method can achieve high performance on finding correspondence between multi-lingual Wikipedia articles, between documents and tags, and between images and tags.
The authors propose a kernel-based algorithm for cross domain matching task where the goal is to retrieve a matching instance in the target set given an instance in the source set. Each instance of the two different domains is treated as a bag of features (e.g., for words) and is embedded to the common space (RKHS) with kernel embedding for matching purpose. The features of the two domains are learned jointly by maximizing a likelihood which is (intuitively) inversely proportional to the distance (i.e., MMD) of the embedded instances in RKHS. With real data, the proposed method outperforms standard approaches like CCA and kernel CCA on document-document, document-tag, and tag-image matching tasks.The writing is clear and easy to follow. The experimental results are impressive as the method consistently outperforms all other methods in all the three experiments. In machine learning (excluding information retrieval), I understand that cross domain matching is mainly tackled by CCA or kernel CCA. So the paper provides a starting point for further exploration in this direction. Regarding the originality, the idea of embedding a bag of hidden features with kernel and learn the features is, however, not new as this was considered in [18] (Latent Support Measure Machines for Bag-of-Words Data Classification, NIPS 2014). The part which is original seems to be the use of such approach for cross-domain matching with a proposed probabilistic model similar to the one in kernel logistic regression. Although the experimental results provide an evidence that the method performs better than KCCA on certain tasks, the paper does not give enough motivation, justification and description of the advantages of the method for better understanding. My comments/questions in descending order of importance.1. From lines 70-78, the problem of kernel CCA is not clearly stated. This is an important motivating paragraph in the paper.2. Presumably the learned latent vectors x_f, y_g play more role in the algorithm than the kernel k. How does the Gaussian kernel k compare to a linear kernel with a large latent dimension q ? I have a feeling that with large q, the learned latent vectors will have enough degree of freedom to perform the task even with linear kernel. This is to say that, if my intuition is correct, a kernel is not needed. 3. What is the motivation for the likelihood in Eq. 8 ? To me, this appears to be an ad-hoc choice. What is wrong with using just ||m(X)-m(Y)||^2 as the loss in Eq. 11 ? Since the log term in Eq. 11 will disappear, this should make optimization simpler and cheaper.4. How does the method compare qualitatively (not numerically) with kernel CCA ? I suggest that the authors shorten Sec. 4.1 and Sec. 4.3 and explain it. 5. It would be interesting to see the effect of varying q (latent dimension) on the precision and run time. The experiments only focus on one aspect which is the precision.6. What is the computational cost of the method as compared to kernel CCA ? It seems kernel CCA can be more efficient. The gradient in Eq. 12 must be expensive and the objective is highly non-convex. This should be addressed in the paper.7. Line 284-286: Are the hyper-parameters chosen by cross validation ? By "development data", is it the same as a validation set ?8. In the experiments, does KCCA use the same learned featured x_f, y_g from the proposed method ? If not, what is the kernel of KCCA i.e., Gaussian kernel on what ? What is the result if you do so ?9. In abstract, lines 27-28, "..while keeping unpaired instances apart." How is this criterion implemented in the method ?10. Lines 100-102, "..can learn a more complex representation..." How ? If possible, can you show this experimentally ?Minor:1. Eq. 3: ||m(X)-m(Y)||^2 is not a distance; ||m(X)-m(Y)|| (or MMD) is.2. Should mention that x_f is a latent vector for word (feature) f in the experiments.3. In the references, the format is not consistent. Some entries are written with abbreviated author names.===== after rebuttal ======= I have considered the authors' rebuttal which answered only some of my questions.