Venue: ICLR 2020 Conference

Reviews:

final_score: rating: 6: Weak Accept
review_content: This paper developes a quantum algorithm for kernel-based support vector machine working in a semi-supervised learning setting. The motivation is to utilise the significant advantage of quantum computation to train machine learning models on large-scale datasets efficiently. This paper reviews the existing work on using quantum computing for least-squares svm (via solving quantum linear systems of equations) and then extends it to deal with kernel svm in a semi-supervised setting. 

Strengths: This is an interesting emerging research topic that has its significance. Also, this paper prodives a nice tutorial on the key ideas of quantum machine learning and provides detailed derivations and analysis on the proposed algorithm.

Weaknesses: The novelty of this work seems to be incremental. It largely extends the existing algorithms such as HHL and LMR. 

Minor issues:

1. Can any experimental study or applications be demonstrated, or only theoretical comptuational complexity can be compared? 
2. In Section 1.1, L is defined as L = G_I G^T_I. In this definition, whether and how the edge weights are considered? Please clarify.   
review_title: Official Blind Review #4

final_score: rating: 6: Weak Accept
review_content: The paper proposes a quantum computer-based algorithm for semi-supervised least squared kernel SVM. This work builds upon LS-SVM of Rebentrost et al (2014b) which developed a quantum algorithm for the supervised version of the problem. While the main selling point of quantum LS-SVM is that it scales logarithmically with data size, supervised algorithms shall not fully enjoy logarithmic scaling unless the cost for collecting labeled data is also logarithmic, which is unlikely. Therefore, semi-supervised setting is certainly appealing. Technically, there are two main contributions. The first is the method of providing Laplacian as an input to the quantum computer. The second contribution, which is about the computation of matrix inverse (K + KLK)^{-1}, is a bit more technical, and could be considered as the main contribution of the paper.

My main concern about the paper is on its organization. The paper provides a very gentle introduction to both semi-supervised LS SVM and quantum LS-SVM. While this helps readers to be equipped with relevant background, it is at the cost of having less space for the main contribution in Section 3.2. I would suggest to remove the content in page 2; most results about kernel methods are not really relevant to this paper. For a machine learning conference paper, one shall safely start with half-page intro in page 3. Some background in quantum computing offered in page 3, 4, 5 are quite nice, but for a conference paper, I think this is an overkill. I recommend providing the very minimal content needed to discuss Section 3.2, and then use more space to discuss the idea in 3.2 better. Specifically, Generalized LMR technique and Hermitian polynomials in Kimmel et al. (2017) could be discussed in more detail. 
review_title: Official Blind Review #1

final_score: rating: 6: Weak Accept
review_content: This paper proposes to extend a quantum-computing based solution of least-squares support-vector-machine to include use of unlabeled samples.  The formulation is analogous to the classical-computing case, in which semi-supervised learning introduces an additional term in the system of equations, which the authors show how to compute in the quantum setting without degrading big-O complexity.

I would lean toward rejecting this paper,  primarily on account of how the contribution relates to the publication venue.  The primary contribution lies in the procedure for preparing and propagating the quantum mechanical states needed to compute on the additional term.  Although the application is machine learning, the technique itself is still rather afar from this topic and would not appear to be of general benefit to conference-goers outside of quantum computing.  The overwhelming majority of quantum machine learning references in this paper appear in physics journals (all but one, which was ICML 2019).  Most of this paper is background material, which yet remains inadequate to convey insights into design decisions in the details of their main contribution, the derivations in section 3.2.  (I have a background in physics but not quantum computing.)   

Perhaps a paper organization more amenable to this venue would be to shift some of the lengthier equations into an appendix and use the space of the paper to discuss a more conceptual and contextual understanding of why this technique is desirable, at each step, relative to other possible quantum techniques.  For example, Figure 1 is not explained, and is not decipherable to someone outside the field, so doesn't itself add to the story.

Could be really good work, but the presentation doesn't quite come across.


EDIT:  See comments to do with paper revision, which significantly improved the presentation.
review_title: Official Blind Review #3

Meta-review: Three reviewers have assessed this paper and they have scored it 6/6/6 after rebuttal with one reviewer hesitating about the appropriateness of this submission to ML venues. The reviewers have raised a number of criticisms such as an incremental nature of the paper (HHL and LMR algorithms) and the main contributions lying more within the field of quantum computing than ML. The paper was discussed with reviewers, buddy AC and chairs. On balance, it was concluded that this paper is minimally below the acceptance threshold. We encourage authors to consider all criticism, improve the paper and resubmit to another venue as there is some merit to the proposed idea.

Decision: Reject