Merge pull request #176 from markovmodel/details

[manuscript] [WIP] simplify HMM section, restructure citations

Author: marscher

manuscript/literature.bib

@@ -756,3 +756,22 @@ @article{Ribeiro2018-rave
     URL = {https://doi.org/10.1063/1.5025487},
     DOI = {10.1063/1.5025487}
 }
+
+@article{wu2015projected,
+  title={Projected metastable Markov processes and their estimation with observable operator models},
+  author={Wu, Hao and Prinz, Jan-Hendrik and No{\'e}, Frank},
+  journal={J. Chem. Phys.},
+  volume={143},
+  number={14},
+  pages={10B610\_1},
+  year={2015},
+  publisher={AIP Publishing}
+}
+
+@Misc{mdtutorial,
+  author =    {Efrem Braun and Justin Gilmer and Heather B. Mayes and David L. Mobley and Jacob I. Monroe and Samarjeet Prasad and Daniel M. Zuckerman},
+  title =     {Best Practices for Foundations in Molecular Simulations [Article v1.0]},
+  year =      {2018},
+  url = "https://github.com/MobleyLab/basic_simulation_training",
+  note = "Accessed November 15, 2018."
+}

manuscript/manuscript.tex

@@ -86,18 +86,18 @@ \section{Introduction}
 
 \subsection{Scope}
 
-In this tutorial, we assume that the reader is familiar with MD simulation and standard analysis of MD simulations of peptides and proteins, such as computation of torsion angles and distances (see~\cite{dror2012biomolecular} for a review).
+In this tutorial, we assume that the reader is familiar with MD simulation and standard analysis of MD simulations of peptides and proteins, such as computation of torsion angles and distances (see Ref.~\cite{dror2012biomolecular} for a review on the MD simulation of biomolecules, and Ref.~\cite{mdtutorial} for a tutorial on MD simulations).
 
 We further assume that the reader is familiar with the basic ideas and theory underlying Markov modeling and will only give a brief reminder of the basic concepts in Section 2.
 
-For those seeking further resources, ``\emph{Markov State Models: From an Art to a Science}''~\cite{msm-brooke} provides a recent overview,
-while ``\emph{Markov models of molecular kinetics: Generation and validation}''~\cite{msm-jhp} describes the basic MSM theory and methodology in detail.
+For those seeking further resources, the recent perspective ``\emph{Markov State Models: From an Art to a Science}''~\cite{msm-brooke} provides a timeline of methods advances with relevant citations,
+while ``\emph{Markov models of molecular kinetics: Generation and validation}''~\cite{msm-jhp} describes the basic MSM theory and methodology and provides the underlying mathematics in detail.
 Additionally, two textbooks have been published that focus on computational methods and applications~\cite{msm-book} and mathematical theory~\cite{schuette-sarich-book}.
 
 In addition to publications on the theory and application of Markov state modeling~\cite{schuette-msm,buchete-msm-2008,noe-tmat-sampling,bowman-msm-2009,noe-folding-pathways,sarich-msm-quality,noe-fingerprints,noe-dy-neut-scatt,Chodera2014,ben-rev-msm,simon-mech-mod-nmr,oom-feliks,simon-amm},
-we also recommend the literature on TICA~\cite{tica,tica3,tica2,kinetic-maps},
+we also recommend the literature on TICA~\cite{tica,tica3,kinetic-maps,tica2},
 transition path theory (TPT)~\cite{weinan-tpt,metzner-msm-tpt},
-hidden Markov state models (HMMs)~\cite{noe-proj-hid-msm,hmm-baum-welch-alg,hmm-tutorial,jhp-spectral-rate-theory,bhmm-preprint},
+hidden Markov state models (HMMs)~\cite{noe-proj-hid-msm,jhp-spectral-rate-theory,bhmm-preprint},
 and variational techniques~\cite{noe-vac,vamp-preprint,gmrq},
 as these topics play important roles within the standard MSM workflow.
 
@@ -183,7 +183,7 @@ \subsection{Variational approach and TICA}
 \begin{itemize}
 	\item Featurization -- The Cartesian coordinates characterizing each frame of the MD trajectory are transformed into an intuitive basis such as the protein's dihedral angles or contact distance pairs.
 	\item Dimensionality reduction -- Optionally, a basis set transformation can be performed that produces a linear (or nonlinear) combination of the features in the previous step.
-	Frequently, time-lagged independent component analysis (TICA)~\cite{tica,tica3,tica2,kinetic-maps} is used to transform the features into a set of slow coordinates.
+	Frequently, time-lagged independent component analysis (TICA)~\cite{tica,tica3,kinetic-maps} is used to transform the features into a set of slow coordinates.
 	\item Clustering -- This is the step at which the state decomposition occurs.
 	The features or TICs are grouped into a set of states using a clustering algorithm such as $k$-means.
 	\item Transition matrix approximation -- At this stage, transitions are counted at a pre-specified lag time, and the estimation and validation described in the previous section are performed.
@@ -259,7 +259,7 @@ \subsection{Hidden Markov state models}
 We illustrate this point in notebook~07.
 
 An alternative, which is much less sensitive to poor discretization,
-is to estimate a hidden Markov model (HMM)~\cite{hmm-baum-welch-alg,hmm-tutorial,jhp-spectral-rate-theory,noe-proj-hid-msm,bhmm-preprint}.
+is to estimate a hidden Markov model (HMM)~\cite{hmm-baum-welch-alg,jhp-spectral-rate-theory,noe-proj-hid-msm,bhmm-preprint}.
 HMMs are less sensitive to the discretization error as they sidestep the assumption of Markovian dynamics in the discretized space (illustrated in Fig.~\ref{fig:hmm-scheme}).
 Instead, HMMs assume that there is an underlying (hidden) dynamic process which is Markovian
 and gives rise to our observed data, e.g., the ($n$~states) discretized trajectories $s(t)$.
@@ -272,17 +272,15 @@ \subsection{Hidden Markov state models}
 and a row-stochastic matrix ($\bm{\chi}$) of probabilities $\chi\left( s \middle| \tilde{s} \right)$
 to emit the discrete state $s$ conditional on being in the hidden state $\tilde{s}$.
 
-We can further compute a reversal of the emission matrix $\bm{\chi}\in\mathbb{R}^{m \times n}$:
-the membership matrix $\mathbf{M}\in\mathbb{R}^{n \times m}$ which encodes
-a fuzzy assignment of each of the $n$ observable microstates $s$ to the $m$ hidden states $\tilde{s}$ and,
-thus, defines the \emph{coarse graining} of microstate.
-
 An HMM estimation always yields a model with a small number of (hidden) states
 where each state is considered to be metastable and,
 thus, the number of hidden states is a new hyper-parameter which needs to be chosen carefully (see notebook~07).
 As the HMMs---like MSMs---approximate the full phase-space dynamics,
 we can similarly compute the metastable kinetics, apply TPT, visualize the network, and obtain physical observables.
 
+For an extensive discussion of details about HMM properties and the estimation algorithm in general, we suggest Ref.~\cite{hmm-tutorial}.
+For its specific application to the discretization of MSMs using HMMs, we suggest Ref.~\cite{noe-proj-hid-msm}. A generalized extension for estimating this type of low-dimensional projection from the data is given in Ref.~\cite{wu2015projected}.
+
 \subsection{Software and installation}
 
 We utilize Jupyter~\cite{jupyter} notebooks to show code examples along with figures and interactive widgets to display molecules.
@@ -389,7 +387,7 @@ \subsection{Feature selection}
 
 \subsection{Dimensionality reduction}
 
-Subsequently, we perform TICA~\cite{tica,kinetic-maps} in order to reduce the dimension from the feature space,
+Subsequently, we perform TICA~\cite{tica,tica3,kinetic-maps} in order to reduce the dimension from the feature space,
 which typically contains many degrees of freedom,
 to a lower dimensional space that can be discretized with higher resolution and better statistical efficiency.
 TICA is a special case of the variational principle~\cite{noe-vac,nueske-vamk} and is designed to find a projection preserving the long-timescale dynamics in the dataset.
@@ -595,7 +593,6 @@ \subsection{Modeling large systems}
 
 Additional technical challenges for large systems include high demands on memory and computation time;
 we explain how to deal with those in the tutorials (notebook~01).
-
 More details on how to model complex systems with the techniques presented here are described, e.g., by~\cite{plattner_protein_2015,plattner_complete_2017}.
 We further examine some symptoms that may indicate problematic or difficult datasets, and demonstrate how to deal with them in notebook~08.
 
@@ -612,6 +609,7 @@ \subsection{Advanced Methods}
 MEMMs consequently enable users to combine enhanced sampling methods such as umbrella sampling or replica exchange
 with conventional molecular dynamics simulations to more efficiently study rare event kinetics~\cite{trammbar}. 
 MEMMs are implemented in PyEMMA.
+Since the many publications associated with the development of these methods are beyond the scope of this tutorial, we refer the reader to Sec.~8.3 of Ref.~\cite{msm-brooke} and the references therein.
 
 Another issue often faced during Markov state modeling is a lack of quantitative agreement with complementary experimental data. 
 This issue is not intrinsic to the Markov state modeling approach as such,