Mercurial > hg > cip2012

--- a/draft.tex	Mon Mar 05 21:43:04 2012 +0000
+++ b/draft.tex	Tue Mar 06 12:13:58 2012 +0000
@@ -6,6 +6,10 @@
 \usepackage{epstopdf}
 \usepackage{url}
 \usepackage{listings}
+\usepackage{tools}
+
+\let\citep=\cite
+\def\squash{}

 %\usepackage[parfill]{parskip}

@@ -24,11 +28,188 @@
 }


-\section{Intro}
-\subsection{Information Theory and prediction}
-Bayesian probability and modelling the building of predictions
-\subsection{Link to music}
-Music as a temporal pattern.  Meyer, Narmour. Music unfolding in time.  How listeners see different kinds of predictability in musical patters..
+\section{Expectation and surprise in music}
+\label{s:Intro}
+
+	One of the more salient effects of listening to music is to create
+	\emph{expectations} of what is to come next, which may be fulfilled
+	immediately, after some delay, or not at all as the case may be.
+	This is the thesis put forward by, amongst others, music theorists
+	L. B. Meyer \cite{Meyer67} and Narmour \citep{Narmour77}.
+	In fact, %the gist of
+	this insight predates Meyer quite considerably; for example,
+	it was elegantly put by Hanslick \cite{Hanslick1854} in the
+	nineteenth century:
+	\begin{quote}
+			`The most important factor in the mental process which accompanies the
+			act of listening to music, and which converts it to a source of pleasure,
+			is %\ldots
+			frequently overlooked. We here refer to the intellectual satisfaction
+			which the listener derives from continually following and anticipating
+			the composer's intentions---now, to see his expectations fulfilled, and
+			now, to find himself agreeably mistaken. It is a matter of course that
+			this intellectual flux and reflux, this perpetual giving and receiving
+			takes place unconsciously, and with the rapidity of lightning-flashes.'
+	\end{quote}
+
+	An essential aspect of this is that music is experienced as a phenomenon
+	that `unfolds' in time, rather than being apprehended as a static object
+	presented in its entirety. Meyer argued that musical experience depends
+	on how we change and revise our conceptions \emph{as events happen}, on
+	how expectation and prediction interact with occurrence, and that, to a
+	large degree, the way to understand the effect of music is to focus on
+	this `kinetics' of expectation and surprise.
+
+	The business of making predictions and assessing surprise is essentially
+	one of reasoning under conditions of uncertainty and manipulating
+	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 assume that musical schemata are encoded as probabilistic %
+%\citep{Meyer56} models, and
+   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
+	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{Pearce2005}.
+	analysis of music, \eg
+	\cite{ConklinWitten95,PonsfordWigginsMellish1999,Pearce2005}.
+%               \cite{Ferrand2002}. Dubnov and Assayag PSTs?
+
+	\squash
+	\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.
+	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
+	are closely related to
+	information-theoretic quantities like entropy, relative entropy,
+	and mutual information.
+%	and are major determinants of the overall experience.
+	Berlyne \cite{Berlyne71} called such quantities `collative variables', since
+	they are to do with patterns of occurrence rather than medium-specific details,
+	and developed the ideas of `information aesthetics' in an experimental setting.
+%	Berlyne's `new experimental aesthetics', the `information-aestheticians'.
+
+%	Listeners then experience greater or lesser levels of surprise
+%	in response to departures from these norms.
+%	By careful manipulation
+%	of the material, the composer can thus define, and induce within the
+%	listener, a temporal programme of varying
+%	levels of uncertainty, ambiguity and surprise.
+
+
+	Previous work in this area \cite{Berlyne74} treated the various
+	information theoretic quantities
+	such as entropy as if they were intrinsic properties of the stimulus---subjects
+	were presented with a sequence of tones with `high entropy', or a visual pattern
+	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.}%
+%		since probabilities are almost always a function of the state of knowledge of the observer
+	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.
+	% !!REV - DONE - explain use of quoted `objective'
+
+	% !!REV - previous work on information theory in music
+	More recent work on using information theoretic concepts to analyse music in
+	includes Simon's \cite{Simon2005} assessments of the entropy of
+	Jazz improvisations and Dubnov's
+	\cite{Dubnov2006,DubnovMcAdamsReynolds2006,Dubnov2008}
+	investigations of the `information rate' of musical processes, which is related
+	to the notion of redundancy in a communications channel.
+	Dubnov's work in particular is informed by similar concerns to our own
+	and we will discuss the relationship between it and our work at
+	several points later in this paper
+	(see \secrf{Redundancy}, \secrf{methods} and \secrf{RelatedWork}).
+
+
+	% !!REV - DONE - rephrase, check grammar (now there are too many 'one's!)
+\squash
+\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.
+
+		(1) \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
+	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.
+
+		(2) \emph{Generality}:
+	This approach does not proscribe which probabilistic models should be used---the
+	choice can be guided by standard model selection criteria such as Bayes
+	factors \cite{KassRaftery1995}, \etc
+
+		(3) \emph{Richness}:
+	It may be effective to use a model with time-dependent latent
+	variables, such as a hidden Markov model. In these cases, we can track changes
+	in beliefs about the hidden variables as well as the observed ones, adding
+	another layer of richness to the description while maintaining the same
+	level of abstraction.
+	For example, harmony (\ie, the `current chord') in music is not stated explicitly, but rather
+	must be inferred from the musical surface; nonetheless, a sense of harmonic
+	progression is an important aspect of many styles of music.
+
+		(4) \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
+
+	% !!REV - clarify aims of paper.
+	Having outlined the basic ideas, our aims in pursuing this line of thought
+	are threefold: firstly, to propose dynamic information-based measures which
+	are coherent from a theoretical point of view and consistent with the general
+	principles of probabilistic inference, with possible applications in
+	regulating machine learning systems;
+	% when heuristics are required to manage intractible models or limited computational resources.
+	secondly, to construct computational models of what human brains are doing
+	in response to music, on the basis that our brains implement, or at least
+	approximate, optimal probabilistic inference under the relevant constraints;
+	and thirdly, to construct a computational model of a certain restricted
+	field of aesthetic judgements (namely judgements related to formal structure)
+	that may shed light on what makes a stimulus interesting or aesthetically
+	pleasing. This would be of particular relevance to understanding and
+	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{Information Dynamics Approach}

 \subsection{Re-iterate core hypothesis}
@@ -74,4 +255,6 @@
    Any results from this study
 \section{Conclusion}

+\bibliographystyle{unsrt}
+{\bibliography{all,c4dm}}
 \end{document}