comparison draft.tex @ 24:79ede31feb20

Stuffed a load more figures in.

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 \usetikzlibrary{patterns}
 \usetikzlibrary{arrows}
 
 \let\citep=\cite
-\newcommand{\colfig}[2][1]{\includegraphics[width=#1\linewidth]{figs/#2}}%
+\newcommand{\colfig}[2][1]{\includegraphics[width=#1\linewidth]{ifigs/#2}}%
 \newcommand\preals{\reals_+}
 \newcommand\X{\mathcal{X}}
 \newcommand\Y{\mathcal{Y}}
 \newcommand\domS{\mathcal{S}}
 \newcommand\A{\mathcal{A}}

 	degrees of belief about the various proposition which may or may not
 	hold, and, as has been argued elsewhere \cite{Cox1946,Jaynes27}, best
 	quantified in terms of Bayesian probability theory.
    Thus, we suppose that
 	when we listen to music, expectations are created on the basis of our
-	familiarity with various stylistic norms %, that is, using models that
-	encode the statistics of music in general, the particular styles of
-	music that seem best to fit the piece we happen to be listening to, and
+	familiarity with various stylistic norms that apply to music in general,
+	the particular style (or styles) of music that seem best to fit the piece 
+	we are listening to, and
 	the emerging structures peculiar to the current piece.  There is
 	experimental evidence that human listeners are able to internalise
 	statistical knowledge about musical structure, \eg
 	\citep{SaffranJohnsonAslin1999,EerolaToiviainenKrumhansl2002}, and also
 	that statistical models can form an effective basis for computational
 	analysis of music, \eg
 	\cite{ConklinWitten95,PonsfordWigginsMellish1999,Pearce2005}.
 
 	\subsection{Music and information theory}
-	Given a probabilistic framework for music modelling and prediction,
-	it is a small step to apply quantitative information theory \cite{Shannon48} to
-	the models at hand.
+	With a probabilistic framework for music modelling and prediction in hand,
+	we are in a position to apply quantitative information theory \cite{Shannon48}.
 	The relationship between information theory and music and art in general has been the 
 	subject of some interest since the 1950s 
 	\cite{Youngblood58,CoonsKraehenbuehl1958,HillerBean66,Moles66,Meyer67,Cohen1962}. 
 	The general thesis is that perceptible qualities and subjective
 	states like uncertainty, surprise, complexity, tension, and interestingness

 	with `low entropy'. These values were determined from some known `objective'
 	probability model of the stimuli,%
 	\footnote{%
 		The notion of objective probabalities and whether or not they can
 		usefully be said to exist is the subject of some debate, with advocates of 
-		subjective probabilities including de Finetti \cite{deFinetti}.
-		Accordingly, we will treat the concept of a `true' or `objective' probability 
-		models with a grain of salt and not rely on them in our 
-		theoretical development.}%
+		subjective probabilities including de Finetti \cite{deFinetti}.} 
 	or from simple statistical analyses such as
 	computing emprical distributions. Our approach is explicitly to consider the role
 	of the observer in perception, and more specifically, to consider estimates of
 	entropy \etc with respect to \emph{subjective} probabilities.
 \subsection{Information dynamic approach}
 
-	Bringing the various strands together, our working hypothesis is that
-	as a listener (to which will refer gender neutrally as `it')
-	listens to a piece of music, it maintains a dynamically evolving statistical
-	model that enables it to make predictions about how the piece will
-	continue, relying on both its previous experience of music and the immediate
-	context of the piece.
-	As events unfold, it revises its model and hence its probabilistic belief state,
-	which includes predictive distributions over future observations.
-	These distributions and changes in distributions can be characterised in terms of a handful of information 
-	theoretic-measures such as entropy and relative entropy.
-%	to measure uncertainty and information. %, that is, changes in predictive distributions maintained by the model.
-	By tracing the evolution of a these measures, we obtain a representation
-	which captures much of the significant structure of the
-	music. 
-	This approach has a number of features which we list below.
-
-		\emph{Abstraction}:
-	Because it is sensitive mainly to \emph{patterns} of occurence, 
-	rather the details of which specific things occur, 
-	it operates at a level of abstraction removed from the details of the sensory 
-	experience and the medium through which it was received, suggesting that the 
+	Bringing the various strands together, our working hypothesis is that as a
+	listener (to which will refer as `it') listens to a piece of music, it maintains
+	a dynamically evolving statistical model that enables it to make predictions
+	about how the piece will continue, relying on both its previous experience
+	of music and the immediate context of the piece.  As events unfold, it revises
+	its model and hence its probabilistic belief state, which includes predictive
+	distributions over future observations.  These distributions and changes in
+	distributions can be characterised in terms of a handful of information
+	theoretic-measures such as entropy and relative entropy.  By tracing the
+	evolution of a these measures, we obtain a representation which captures much
+	of the significant structure of the music, but does so at a high level of
+	\emph{abstraction}, since it is sensitive mainly to \emph{patterns} of occurence, 
+	rather the details of which specific things occur or even the sensory modality
+	through which they are detected.  This suggests that the 
 	same approach could, in principle, be used to analyse and compare information 
 	flow in different temporal media regardless of whether they are auditory, 
 	visual or otherwise. 
 
-		\emph{Generality} applicable to any probabilistic model.
-
-		\emph{Subjectivity}:
-	Since the analysis is dependent on the probability model the observer brings to the
-	problem, which may depend on prior experience or other factors, and which may change
-	over time, inter-subject variablity and variation in subjects' responses over time are 
-	fundamental to the theory. It is essentially a theory of subjective response
+	In addition, the information dynamic approach gives us a principled way
+	to address the notion of \emph{subjectivity}, since the analysis is dependent on the 
+	probability model the observer starts off with, which may depend on prior experience 
+	or other factors, and which may change over time. Thus, inter-subject variablity and 
+	variation in subjects' responses over time are 
+	fundamental to the theory. 
 			
 	%modelling the creative process, which often alternates between generative
 	%and selective or evaluative phases \cite{Boden1990}, and would have
 	%applications in tools for computer aided composition.
 
 
 \section{Theoretical review}
 
+	\subsection{Entropy and information in sequences}
 	In this section, we summarise the definitions of some of the relevant quantities
 	in information dynamics and show how they can be computed in some simple probabilistic
 	models (namely, first and higher-order Markov chains, and Gaussian processes [Peter?]).
 
 	\begin{fig}{venn-example}

 					I_{12|3} + I_{123} &= I(X_1;X_2) 
 				\end{align*}
 			}
 		\end{tabular}
 		\caption{
-		Venn diagram visualisation of entropies and mutual informations
+		Information diagram visualisation of entropies and mutual informations
 		for three random variables $X_1$, $X_2$ and $X_3$. The areas of 
 		the three circles represent $H(X_1)$, $H(X_2)$ and $H(X_3)$ respectively.
 		The total shaded area is the joint entropy $H(X_1,X_2,X_3)$.
 		The central area $I_{123}$ is the co-information \cite{McGill1954}.
 		Some other information measures are indicated in the legend.

 	the entropy rate and the erasure entropy rate: $b_\mu = h_\mu - r_\mu$.
 	These relationships are illustrated in \Figrf{predinfo-bg}, along with
 	several of the information measures we have discussed so far.
 
 
+  \begin{fig}{wundt}
+    \raisebox{-4em}{\colfig[0.43]{wundt}}
+ %  {\ \shortstack{{\Large$\longrightarrow$}\\ {\scriptsize\emph{exposure}}}\ }
+    {\ {\large$\longrightarrow$}\ }
+    \raisebox{-4em}{\colfig[0.43]{wundt2}}
+    \caption{
+      The Wundt curve relating randomness/complexity with
+      perceived value. Repeated exposure sometimes results
+      in a move to the left along the curve \cite{Berlyne71}.
+    }
+  \end{fig}
+
+
 	\subsection{First order Markov chains}
 	These are the simplest non-trivial models to which information dynamics methods
 	can be applied. In \cite{AbdallahPlumbley2009} we, showed that the predictive information
 	rate can be expressed simply in terms of the entropy rate of the Markov chain.
 	If we let $a$ denote the transition matrix of the Markov chain, and $h_a$ it's

 \section{Information Dynamics in Analysis}
 
  	\subsection{Musicological Analysis}
 	refer to the work with the analysis of minimalist pieces
 	
+    \begin{fig}{twopages}
+%      \colfig[0.96]{matbase/fig9471}  % update from mbc paper
+      \colfig[0.97]{matbase/fig72663}\\  % later update from mbc paper (Keith's new picks)
+			\vspace*{1em}
+      \colfig[0.97]{matbase/fig13377}  % rule based analysis
+      \caption{Analysis of \emph{Two Pages}.
+      The thick vertical lines are the part boundaries as indicated in
+      the score by the composer.
+      The thin grey lines
+      indicate changes in the melodic `figures' of which the piece is
+      constructed. In the `model information rate' panel, the black asterisks
+      mark the
+      six most surprising moments selected by Keith Potter.
+      The bottom panel shows a rule-based boundary strength analysis computed
+      using Cambouropoulos' LBDM.
+      All information measures are in nats and time is in notes.
+      }
+    \end{fig}
+
+    \begin{fig}{metre}
+      \scalebox{1}[0.8]{%
+        \begin{tabular}{cc}
+       \colfig[0.45]{matbase/fig36859} & \colfig[0.45]{matbase/fig88658} \\
+       \colfig[0.45]{matbase/fig48061} & \colfig[0.45]{matbase/fig46367} \\
+       \colfig[0.45]{matbase/fig99042} & \colfig[0.45]{matbase/fig87490} 
+%				\colfig[0.46]{matbase/fig56807} & \colfig[0.48]{matbase/fig27144} \\
+%				\colfig[0.46]{matbase/fig87574} & \colfig[0.48]{matbase/fig13651} \\
+%				\colfig[0.44]{matbase/fig19913} & \colfig[0.46]{matbase/fig66144} \\
+%        \colfig[0.48]{matbase/fig73098} & \colfig[0.48]{matbase/fig57141} \\
+%       \colfig[0.48]{matbase/fig25703} & \colfig[0.48]{matbase/fig72080} \\
+%        \colfig[0.48]{matbase/fig9142}  & \colfig[0.48]{matbase/fig27751}
+ 
+        \end{tabular}%
+      }
+      \caption{Metrical analysis by computing average surprisingness and
+      informative of notes at different periodicities (\ie hypothetical
+      bar lengths) and phases (\ie positions within a bar).
+      }
+    \end{fig}
+
 	\subsection{Content analysis/Sound Categorisation}.  
 	Using Information Dynamics it is possible to segment music.  From there we
 	can then use this to search large data sets. Determine musical structure for
 	the purpose of playlist navigation and search.
 	\emph{Peter}
 
 \subsection{Beat Tracking}
  \emph{Andrew}  
 
 
-\section{Information Dynamics as Design Tool}
+\section{Information dynamics as compositional aid}
 
 In addition to applying information dynamics to analysis, it is also possible
 use this approach in design, such as the composition of musical materials.  By
 providing a framework for linking information theoretic measures to the control
 of generative processes, it becomes possible to steer the output of these processes

 triangle, the corresponding transition matrix is returned.  Figure \ref{TheTriangle}
 shows how the triangle maps to different measures of redundancy, entropy rate
 and predictive information rate.\emph{self-plagiarised}
  \begin{figure}
 \centering
-\includegraphics[width=\linewidth]{figs/TheTriangle.pdf}
+\includegraphics[width=0.85\linewidth]{figs/TheTriangle.pdf}
 \caption{The Melody Triangle\label{TheTriangle}}
 \end{figure}	
 Each corner corresponds to three different extremes of predictability and
 unpredictability, which could be loosely characterised as `periodicity', `noise'
 and `repetition'.  Melodies from the `noise' corner have no discernible pattern;