Gradients of Generative Models for Improved Discriminative Analysis of Tandem Mass Spectra
Tandem mass spectrometry (MS/MS) is a high-throughput technology used to identify the proteins in a complex biological sample, such as a drop of blood. A collection of spectra is generated at the output of the process, each spectrum of which is representative of a peptide (protein subsequence) present in the original complex sample. In this work, we leverage the log-likelihood gradients of generative models to improve the identification of such spectra. In particular, we show that the gradient of a recently proposed dynamic Bayesian network (DBN) [7] may be naturally employed by a kernel-based discriminative classifier. The resulting Fisher kernel substantially improves upon recent attempts to combine generative and discriminative models for post-processing analysis, outperforming all other methods on the evaluated datasets. We extend the improved accuracy offered by the Fisher kernel framework to other search algorithms by introducing Theseus, a DBN representing a large number of widely used MS/MS scoring functions. Furthermore, with gradient ascent and max-product inference at hand, we use Theseus to learn model parameters without any supervision.
This paper introduces Theseus, an algorithm for matching MS/MS spectra to peptide in a D.B. 
This is a challenging and important task. It is important because MS/MS  is currently practically the only common high-throughput method to identify which proteins are present in a sample. It is challenging because the data is analog (intensity vs. m/z  graphs) and extremely noisy. Specifically, insertions, deletions, and variations due to natural losses (e.g. carbon monoxide) can occur compared to a theoretical peptide spectra. 
This work builds upon an impressive body of work that has been dedicated to this problem. Specifically, the recently developed DRIP (Halloran et al 2014, 2016)  is a DBN, i.e. a generative model that tries to match the observed spectra to a given one in the D.B. modeling insertions/deletions etc. and computes for it a likelihood and the most likely assignment using a viterbi algorithm.
A big issue in the field is calibration of scores (in this case - likelihoods for possible peptide matches from the D.B to an observed spectra) as these vary greatly between spectra (e.g. different number of peaks to match) so estimating which score is “good enough” (e.g. in terms of overall false positive rate) is challenging.  Another previous algorithm, Percolator, has been developed to address this by training an SVM to discriminate between “good” matching peptides scores and “negative” scores from decoy peptides. A recent work  (Halloran et al 2016) tried to then map the DRIP viterbi path to a fixed sized vector so Percolator could be applied atop of DRIP.
Here, the authors propose an alternative to the above heuristic mapping. Instead, they employ Fisher Kernels where two samples (in our case - these would be the viterbi best path assigned to two candidates matches) are compared by their derivative in the feature space of the model. This elegant solution to apply discriminative models (here Percolator) to generative models (here DRIP) was suggested for other problems in the comp bio domain by Jaakkola and Haussler 1998. They derive the likelihood and its derivatives and the needed update algorithms for this, and show employing this to several datasets improve upon state of the art results.
Pros:
This work tackles an important problem. It results in what seems to be a significant improvement upon state of the art. It offers a new model (Theseus) and an elegant application Jaakkola and Haussler’s Fisher Kernel idea to the problem at hand. Overall, this appears to be high-quality computational work advancing an important topic.
Cons:
Major points of criticism:
1. Writing: While the paper starts well (intro) it quickly becomes impenetrable. It is very hard to follow the terms, the variables and how they all come together. For example, Fig1 is referred to in line 66 and includes many terms not explained at that point. Sec. 2.1 refers to c_b which is not defined (is it like c(x) ?) How are the natural losses modeled in this framework, Lines 137-145 are cryptic, evaluation procedure is too condensed (lines 221-227). In general, the authors spend too much space deriving all the equations in the main text instead of actually explaining the model and what is new compared to previous work. This makes evaluating both the experiments and the novelty hard. To make things worse, the caption of the main figure (Fig3) refers to labels/algorithms (“Percolator”, “DRIP Percolator Heuristic”) which do not appear in the figure. 
Given the complexity of the domain and the short format of NIPS papers, we recommend the authors revise the text to make the overall model (Theseus) and novel elements more clear, and defer some of the technical details to a longer more detailed supplementary (which in this case seems mandatory).