Paper:
Learning Concave Conditional Likelihood Models for Improved Analysis of Tandem Mass Spectra
The most widely used technology to identify the proteins present in a complex biological sample is tandem mass spectrometry, which quickly produces a large collection of spectra representative of the peptides (i.e., protein subsequences) present in the original sample. In this work, we greatly expand the parameter learning capabilities of a dynamic Bayesian network (DBN) peptide-scoring algorithm, Didea [25], by deriving emission distributions for which its conditional log-likelihood scoring function remains concave. We show that this class of emission distributions, called Convex Virtual Emissions (CVEs), naturally generalizes the log-sum-exp function while rendering both maximum likelihood estimation and conditional maximum likelihood estimation concave for a wide range of Bayesian networks. Utilizing CVEs in Didea allows efficient learning of a large number of parameters while ensuring global convergence, in stark contrast to Didea's previous parameter learning framework (which could only learn a single parameter using a costly grid search) and other trainable models [12,13,14] (which only ensure convergence to local optima). The newly trained scoring function substantially outperforms the state-of-the-art in both scoring function accuracy and downstream Fisher kernel analysis. Furthermore, we significantly improve Didea's runtime performance through successive optimizations to its message passing schedule and derive explicit connections between Didea's new concave score and related MS/MS scoring functions.

Review:
The manuscript “Learning Concave Conditional Likelihood Models for Improved Analysis of Tandem Mass Spectra” extends a dynamic Bayesian network approach called DIDEA by introducing a new class of emission distributions. The conditional log-likelihood of those functions remains concave leading to an efficient global optimization method for parameter estimation. This is in stark contrast to the previous variant, for which the best parameter had to be found by grid search. In comparison to other state-of-the-art methods, the new approach outperforms the other methods, while being faster at the same time.  Quality Overall the quality of the manuscript is good. There were some errors in the formulas, but the authors promised to fix them at the author response period.  Clarity Overall the clarity is good, there are just some parts, where the reader has to guess certain details (e.g., regarding b and y). It is a little bit confusing that in the introduction it is mentioned that DRIP outperformed DIDEA (line 39), but then in the comparison on the data sets where the authors show the performance of the old DIDEA approach (Figure 4, Didea-0), the Didea-0 performance seems to be superior to the performance of DRIP (shown in Figure 3). It would have been better to show Didea-0 also in Figure 3. Showing this separately does not make a good impression especially in light of the above mentioned observation. Figure 4 also seems to imply that the performance gain is not as substantial as claimed in line 281.  Author response: ...Please see the introductory DRIP paper [1] being referred to on line 39, where the authors show that DRIP outperforms Didea... We note, though, that the authors of [1] only test algorithms by assuming a fixed observed precursor charge of 2, rather than the harder charge-varying case considered in this paper.  answer: But then you are saying now that in the charge-varying case DRIP is worse than the old DIDEA. One should at least discuss this and not just copy an old statement from a paper with a non-extensive evaluation.   It is good to see a statement about the runtime in the manuscript (with actual values) and not just in the supplement. This seems to be the main selling point in case the performance of Didea and Didea-0 is really that close.  Significance The introduced distributions, called convex virtual emissions (CVEs), seem interesting and might have applicability beyond DBNs, but the focus of the manuscript is only on this one application of DBNs with CVEs for Tandem Mass Spectra analysis. If the authors could make plausible that CVEs could be useful for other models, then this would be of even higher interest to the general NIPS community.