Learning Graphical Models
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The reviewer seems to have clearly understood the approach and our intended contribution. We feel that the reviewer's objections mostly involve technical issues that we did not explain or justify clearly enough, but which do not undermine the novelty or soundness of the basic results. We apologize for not explaining / justifying these issues more carefully, and feel they will be straightforward to address in the revision. We thank the reviewer for raising them.
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First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. This paper develops a new method of performing blind source separation, by formulating the problem as an additive factorial HMM (AFHMM), and then applying signal aggregate constraints (SACs). The motivation behind this is that additional domain knowledge can be incorporated to improve the separation of the time series into components. The example used throughout the paper is energy disaggregation, where the components of domestic energy use (relating to individual appliances) can be better separated, when information relating to total (expected) usage of each appliance in a time period is incorporated. The objective function that is maximized to perform the separation (which is the log of the posterior distribution of the hidden chains given the observed data) is then transformed into a convex optimization problem.
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First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. Summary: The authors consider the problem of learning a mixture of Hidden Markov Models. The authors first suggest using a spectral learning algorithm to learn a set of parameters for a hidden Markov model, and then provide a method for resolving the permutation ambiguity in the transition matrix to recover it's underlying block-diagonal structure. I found this paper to be very well written for the most part. The experimental results section could be fleshed out a bit. In particular the 2. The authors rely on the fact that a mixture of Hidden Markov Models can be expressed as a single HMM.