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creativity, and provides a much-needed set of customisable evaluation  guidelines, the \emph{Standardised Procedure for Evaluating Creative  Systems} (SPECS) \cite{jordanous:12}. Originally designed to evaluate the concept of creativity, the three step SPECS process firstly requires the evaluator to define the concept(s) they are evaluating the system on. This definition is then converted into standards that can eventually be used to test and evaluate individual systems, or comparatively evaluate multiple systems.  %  We give follow  a slightly modified version of her earlier evaluation guidelines, in that rather than attempt a definition and evaluation of  {\em creativity}, we follow the three steps for \emph{serendipity}.  %\newpage  \subsubsection*{Step 1: A computational definition of serendipity}  \begin{quote} {\em Identify a definition of serendipity that your  system should satisfy to be considered serendipitous.}\end{quote}  \noindent We adopt theSection \ref{sec:our-model} model as our  definition of serendipity for Step 1.  %% This situation can be pictured schematically as follows: described above.         

\begin{quote} {\em Using Step 1, clearly state what standards you use to evaluate the serendipity of your  system. }\end{quote}  \noindent With our definition and other features of the model  in mind, we propose the following standards for evaluating serendipity in computational systems. They represent These criteria allow  the key parts of our definition in a form that allows evaluator  to assess the degree to which they are met: of seredipity that is present in a given system's operation.  %% Serendipity relies on a reassessment or reevaluation -- a \emph{focus shift} in which something that was previously uninteresting, of neutral, or even negative value, becomes interesting. 

\begin{quote} {\em Test your serendipitous system against the standards stated in Step 2 and report the  results.}\end{quote}  \noindent We will devote the entire next section In Section  \ref{sec:computational-serendipity} to testing we pilot  our framework in respect to by examining the degree of serendipity of  existing computational systems focussing on serendipity. systems, looking for ways that they could become more serendipitous enhanced. We will also use the framework to guide the high-level design of a novel system.         

The 13 criteria from Section \ref{sec:literature-review} specify the  conditions and preconditions that are conducive to serendipitous  discovery. These criteria have been further formalised  in Section \ref{specs-overview}.  % \ref{specs-overview} using SPECS.  %%  \citeA{pease2013discussion} used a slightly different version variant  of the these  SPECS criteria to discuss analyse  three examples of potentially  serendipitous behaviour:in  dynamic investigation problems, model generation, and poetry flowcharts. Two additional examplesusing the revised criteria  are described below. These example serve the purpose of illustrating discussed below using  our revised criteria, criteria.  As Campbell \citeyear{campbell2005serendipity} writes, ``serendipity  presupposes a smart mind,''  and also show forays of computational intelligence  into domains known these examples suggest potential  directions  for serendipity further work  in their everyday cultural context. computational intelligence.  We then turn to a more elaborated thought experiment that evaluates  these ideas in the course of developing describes  a new system design.   As designed with our criteria in mind.  Before describing these examples, as  a contrast, baseline,  we introduce the notion of \emph{minimally serendipitous systems}: systems}.  According to our standards, there are various ways to achieve a result with \emph{low} serendipity: if the observation was likely, if further developments happened with little skill, and if the the value of the result was low, then we would not say the outcome was serendipitous. We would be prepared to attribute ``minimal serendipity'' to cases where the observation was \emph{moderately} likely, \emph{some} skill or effort was involved, and the result was only \emph{fairly good}. For However,  for  computational systems, if most of the skill involved lies with the user, then there is little reason to call the system's operation  serendipitous -- even if it consistently does its job very well. For  example, machines can learn to recognise instances or approximate certain types  of a given pattern  quite consistently, patterns,  but it is an interesting surprise if more surprising when  a computational system independently finds an entirely new kind of pattern. Furthermore, the position of the evaluator is important: a spell-checking system might suggest a particularly fortuitous substitution, but we would not expect the spell-checker to know when it was being clever. In such a case, we may say serendipity has occurred, but not that we have a serendipitous system. %% If the system learns an $N$th fact or  %% If applied to a system which could be described as minimally 

%% more for infelicities than for exceptional wit.  \subsection{Case Studies: Prior art}  \label{sec:priorart}  \paragraph{Evolutionary music improvisation systems.}  \citeA{jordanous10} reported a computational jazz improvisation system using genetic algorithms. Genetic algorithms, and evolutionary computing more generally, could encourage computational serendipity. We examine Jordanous's system (later given the name {\em {\sf  GAmprovising} \cite{jordanous:12}) as a case study for evolutionary computing in the context of our model of computational serendipity: to what extent does GAmprovising {\sf GAmprovising}  model serendipity? GAmprovising {\sf GAmprovising}  uses genetic algorithms to evolve a population of \emph{Improvisors}. Each Improvisor is able to randomly generate music based on various parameters such as the  range of notes to be used, preferred notes to be used, rhythmic implications around note lengths and other musical parameters \cite{jordanous10}. These parameters are what defines the Improvisor at any point in evolution. After a cycle of evolution, each Improvisor is evaluated via a fitness function based on Ritchie's \citeyear{ritchie07} criteria of how creative the Improvisor is. Ritchie's criteria use for creativity. This model relies on  user-supplied ratings of how novel the novelty  and how appropriate appropriateness of  the music produced by the Improvisoris,  to calculate 18 criteria that collectively evaluate indicate  how creative a system is. The most successful Improvisors (as deemed by the (according to this  fitness function) are used to seed a new generation of Improvisors, through crossover and mutation operations. The GAmprovising {\sf GAmprovising}  system can be said to have a \textbf{prepared mind} through its background knowledge of what musical knowledge concepts  to embed in the Improvisors and the evolutionary abilities to evolve Improvisors. A \textbf{serendipity trigger} comes from the combination of the mutation and crossover operations previously  employed in the genetic algorithm, and the user input feeding into the fitness function to evaluate produced music. A \textbf{bridge}, from the genetic algorithm operations and user input, to the result \textbf{bridge}  is built by the through  creation of new Improvisors. The \textbf{results} are the various musical improvisations produced by the fittest Improvisors (as well as, perhaps, the parameters that have been considered fittest).%  The likelihood of serendipitous evolution is greatly enhanced by the use of mutation and crossover operations within the genetic algorithm, to increase the diversity of search space covered by the system during evolution. However the \textbf{chance} of any particular Improvisor being discovered is low, given the massive dimensions of the search space. Interesting developments in evolution would be guided by \textbf{curiosity} through the particular human user identifying Improvisors as interesting at that time. \textbf{Sagacity} is determined by how likely the user is to appreciate the same Improvisor's music (or similar music) over time, as tastes of the user may change. The \textbf{value} of the results are maximised through employing a fitness function.  Evolutionary systems such as GAmprovising necessarily operate in a \textbf{dynamic world} which The likelihood of serendipitous evolution  is evolving continuously and may also be affected greatly enhanced  bychanges in user tastes as they evaluate musical output from Improvisors. The \textbf{multiple contexts} arise from  the possibility use  of having multiple users evaluate random mutation and crossover operations within  the musical output (though this is as yet not implemented formally) or through genetic algorithm, which increase  the user changing their preferences over time. \textbf{Multiple tasks} are carried out diversity of search space covered  by the system including evolution of Improvisors, generation during evolution. The \textbf{chance}  of music by individual Improvisors, capturing any particular pair  of Improvisor and  user ratings of a sample evaluation is low, given the massive dimensions  of the Improvisors' output, and fitness calculations. \textbf{Multiple influences} are captured through search space. The evolution of  the various combinations population  of parameters that Improvisors  could be set and described as \textbf{curiosity} about how to satisfy  the potential range musical tastes  ofvalues for each parameter. Table \ref{caseStudies} summarizes how serendipity in such  a system can be described in terms particular human user who identifies certain Improvisors as interesting. The system's \textbf{sagacity} corresponds to the likelihood that the user will appreciate a given Improvisor's music (or similar music) over time. One challenge here is that the tastes  of our model. the user may change. The \textbf{value} of the results are maximised through employing a fitness function.  Evolutionary systems such as {\sf GAmprovising} necessarily operate in a \textbf{dynamic world} which is evolving continuously and that must, in particular, take into account the evolution of the user's tastes. The \textbf{multiple contexts} arise from the possibility of having multiple users evaluate the musical output or through the user changing their preferences over time. A variant of the system that would cater to multiple users is not yet implemented formally -- a revised system with these features would be curious about the more complex problem of satisfying multiple different users' preferences simultaneously. \textbf{Multiple tasks} are carried out by the system including evolution of Improvisors, generation of music by individual Improvisors, capturing of user ratings of a sample of the Improvisors' output, and fitness calculations. \textbf{Multiple influences} are captured through the various combinations of parameters that could be set and the potential range of values for each parameter.   %% Table \ref{caseStudies} summarizes how serendipity in such a system can be described in terms of our model.  \paragraph{Recommender systems.}   % Stress distinction between serendipity on the system- vs. serendipity on the user's side.  As discussed in Section \ref{sec:related}, recommender systems are one  of the primary contexts in computing where serendipity is addressed. considered.  Most discussions of serendipity in recommender systems focus on suggesting items to a user that will be likely to introduce new ideas that are unexpected, but close to what the user is already interested in. If the latter connection exists, such a system must A recommendation of this type will  be called pseudoserendipitous. (possibly pseudo-)serendipitous.  As we noted, these systems mostly focus on supporting  discovery, but some architectures also seem to take account of invention, such as the Bayesian methods surveyed in Chapter 3 of \citeNP{shengbo-guo-thesis}. Recommender systems \emph{stimulate} serendipitous discovery, by \emph{simulating} when this is likely to occur. In respect to related work, we therefore have to distinguish serendipity on theside of  the user side  from serendipity in the system. Current As we have indicated, most current  research mainly addresses in this area  the first aspect and tries to find and assess \textbf{serendipity triggers} by exploiting patterns in the search space. For example, \cite{Herlocker2004} \citeA{Herlocker2004}  as well as \cite{Lu2012} \citeA{Lu2012}  associate less popular items with a higher high  unexpectedness. Clustering was is  also frequently used to discover latent structures in the search space. For example, \cite{Kamahara2005} \citeA{Kamahara2005}  partition users into clusters of common interest, while \cite{Onuma2009} \citeA{Onuma2009}  as well as \cite{Zhang2011} \citeA{Zhang2011}  perform clustering on both users and items. In the work by \cite{Oku2011}, \citeA{Oku2011},  the user is allowed to select two items in order to mix their features in some a  sort of conceptual blending. blend.  Note that in the course of evolution of these and other systems  it is typically generally  the system's developers who adapt the system; plan and perform adaptations;  even in the Bayesian case, the system has limited autonomy. Nevertheless, the impetus to develop increasingly autonomous recommender  systems is present, especially in complex domains where hand-tuning is either very cost-intensive or infeasible. In the context of With  this paper, challenge in mind,  wetherefore want to  investigate how serendipity could be achieved on the system side, and potentially be reflected back to the user. In terms of our model, current systems have at least the makings of a \textbf{prepared mind}, comprising both a user- and a domain model, both of which can be updated dynamically. User behaviour (e.g.~following up on these recommendations) may serve as a \textbf{serendipity trigger} for the system, and change the way it makes recommendations in the future. A \textbf{bridge} to a new kind of recommendation may be found by pattern matching, and especially by looking for exceptional cases: when  new elements are introduced into the domain which do not cluster well, or different clusters appear in the user model that do not have obvious connections between them. The intended outcome of recommendations depends on the organisational mission, and can in most cases be situated between making money and empowering the user. The serendipitous \textbf{result} on the system side would resemble be learning  a novel learnt new  approach that helps to address these goals. %%%  \begin{table}[Ht!] 

\multicolumn{1}{c}{} & \multicolumn{1}{c}{\textbf{Evolutionary music systems}} & \multicolumn{1}{c}{\textbf{Recommender systems}} \\[-.1in]  \multicolumn{1}{l}{\em Components} & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} \\  \cline{2-3}  \textbf{Serendipity trigger} & Evolutionary Previous evolutionary  operations and together with  user input & Input from user behaviour \\ % \cline{2-3}  \textbf{Prepared mind} & Musical knowledge, evolution mechanisms & Through user/domain model \\  % \cline{2-3} 

\cline{2-3}  \textbf{Chance} & If discovered in huge search space & Through imperfect knowledge/if learning from user behaviour \\  % \cline{2-3}  \textbf{Curiosity} & If Aiming to have  a particular user notes take note of  an Improvisor & Making unusual recommendations \\ % \cline{2-3}  \textbf{Sagacity} & User appreciation of Improvisor over time & Updating models recommendation model  after user behaviour \\ % \cline{2-3}  \textbf{Value} & Via fitness function (proxy (as a proxy measure  of creativity) & As per business metrics/objectives \\ \cline{2-3}  \multicolumn{1}{l}{\em Factors} & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} \\  \cline{2-3}  \textbf{Dynamic world} & Continuous computational evolution and changes in user tastes& As precondition for testing system's influences on user behaviour\\  %\cline{2-3}  \textbf{Multiple contexts} & Multiple users opinions? opinions -- would change the curiousity profile  & User model and domain model\\ % \cline{2-3}  \textbf{Multiple tasks} & Evolving Improvisors, generating music, collecting user input, fitness calculations & Making recommendations, learning from users, updating models \\  % \cline{2-3} 

\end{tabular}  \par}  \bigskip  \caption{Summary: applying our  computational serendipity model to positive two  case studies\label{caseStudies}} \end{table}%  \normalsize  %%%  The imperfect knowledge about the user's preferences and interests represents a main component source  of \emph{chance}. Furthermore, chance can play an important role if a system had the capacity to learn from user behaviour. \textbf{chance}.  Combined with the ability to learn, \textbf{curiosity} could be described as the urge to make recommendations specifically for the purposes of finding out more about users, possibly to the detriment of other metrics over the short term. Measures of \textbf{sagacity} would relate to the system's ability to draw inferences from user behaviour. For example, the system might do decide to initiate an  A/B testing test  to decide how a  novel recommendation strategies influence strategy influences  conversion. The \textbf{value} of recommendation strategies can be measured in terms of traditional business metrics or other organisational objectives. Recommender systems have to cope with a \textbf{dynamic world} of changing user preferences and a changing collection of items to recommend. A dynamic environment which nevertheless exhibits some degree of regularity represents a precondition for useful A/B testing. As mentioned above the primary \textbf{(multiple) contexts} are the user model and the domain model. A system matching the description here would have \textbf{multiple tasks}: making useful recommendations, generating new experiments to learn about users, and building new models. Such a system could avail itself of \textbf{multiple influences} related to  experimental design, psychology, and domain understanding.  Recommender systems have to cope with a \textbf{dynamic world} of changing user preference ratings and new items in the system. At the same time, such a dynamic environment which nevertheless exhibits some regularity represents a precondition for useful A/B testing. As mentioned above the primary \textbf{(multiple) contexts} are the user model and the domain model. A system matching the description here would have \textbf{multiple tasks}: making useful recommendations, generating new experiments to learn about users, and building new models. Such a system could avail itself of \textbf{multiple influences} related to  experimental design, psychology, and domain understanding. Table \ref{caseStudies} summarizes summarises  how the components, dimensions and factors of our model could of serendipity can  be mapped torecommender systems, in comparison to  evolutionary music systems from computational creativity. and the ``next-generation'' recommender systems discussed above.  % As a general comment, we would say that this is largely how  % \emph{research and development} of recommender systems works, but         

The features of our model matches match  and expands expand  upon Merton's \citeyear{merton1948bearing} description of the ``serendipity pattern.'' $T$ is an unexpected observation; $T^\star$ highlights its interesting or anomalous features and recasts them as ``strategic data''; and, finally, the result $R$ may include updates to $p$ or $p^{\prime}$ that inform further phases of research.%% Although they do not directly figure in our definition, the supportive  %% dimensions and factors can be interpreted using this schematic to  %% flesh out the description of serendipity in working systems.  From the point of view of the system under consideration, $T$ is  indeterminate. Furthermore, one must assume that relatively few of 

asks how these features \emph{might} be useful. These routines   suggest the relevance of a computational model of \textbf{curiosity}.  %  Rather than a simple look-up rule, $p^{\prime}$ involves creating new knowledge. A simple example is found in clustering systems, which generate new categories on the fly. A more complicated example, necessary in the case of updating $p$ or $p^{\prime}$, is automatic programming. There is ample room a need  for \textbf{sagacity} in this sort of  affair. %  Judgment of the \textbf{value} of the result $R$ may be carried out  ``locally'' (as an embedded part of the process of invention of $R$)         

\section{Our computational model of serendipity} \label{sec:our-model}  Figure \ref{model-diagram} recapitulates the ideas from the previous  section. Dashed paths show some of  thevarious  things that could go wrong. The serendipity trigger might not arise, or might not attract  interest. If interest is aroused, a path to a useful result may not  be sought, or if it is sought, may not be found. If a result is  developed, it may turn out not be of value. Prior experience with  related problems may help with the exploration, but may also restrict  innovative thinking. Multiple tasks, influences, and contexts canplay a varied role: they can provide vital material and  help to foster an inventive frame of mind, andcan help  send the investigator in a new and fruitful direction -- but they can also be distractions.  Failures of curiousity or sagacity will undermine the process -- and  although serendipity does not reduce to luck, there is some  luck involved as well.  \begin{figure}[h!] 

\caption{A heuristic map of the features of serendipity introduced in  Section \ref{sec:by-example}. The central black line traces first  the process of \emph{discovery} in which an initial trigger combines  with mounting curiousity to effect a focus shift; \emph{focus shift},  followed by a process of \emph{invention} in which a prepared mind draws on  various resources and makes use of its powers of  sagacity to find a bridge to a valuable result. In a typical chaotic fashion,even  paths with that are initially  nearbyinitial conditions  can have very different outcomes: some end in failure of one form or another, while others yield results of  differing value.}  \label{model-diagram} 

of the environmental factors listed above.  \begin{quote}  \begin{enumerate}[itemsep=2pt,labelwidth=9em,leftmargin=6em,rightmargin=2em] \begin{enumerate}[itemsep=2pt,labelwidth=9em,leftmargin=9em,rightmargin=2em]  \item[\emph{(\textbf{1 - Discovery})}] \emph{Within a system with a prepared mind, a previously uninteresting serendipity trigger arises due to circumstances that the system does not control, and is classified as interesting by the system; and,}  \item[\emph{(\textbf{2 - Invention})}] \emph{The system, by subsequently processing this trigger and background information together with relevant reasoning, networking, or experimental techniques, obtains a novel result that is evaluated favourably by the system or by external sources.}  \end{enumerate}         

\end{itemize}  \begin{itemize}  \item \textbf{Sociality}:As Campbell \citeyear{campbell2005serendipity} writes:  ``serendipity presupposes a smart mind.''  We may be aided in our pursuit of the ``smart mind'' required for serendipity  by recalling Turing's proposal that computers should ``be able to converse with each other to sharpen their wits''  \cite{turing-intelligent}. Other fields, including computer Chess,  Go, and argumentation have achieved this, and to good effect.         

An active research community investigating computational models of serendipity exists in the field of information retrieval, and specifically, in recommender systems \cite{Toms2000}. In this domain, \citeA{Herlocker2004} and \citeA{McNee2006} view serendipity as an important factor for user satisfaction, alongside accuracy and diversity. Serendipity in recommendations is  understood to imply that the system suggests \emph{unexpected} items, which the user considers to be \emph{useful}, \emph{interesting}, \emph{attractive} or \emph{relevant}.   % \cite{Herlocker2004} \cite{Lu2012},\cite{Ge2010}.   Definitions differ as to the requirement of \emph{novelty}; \citeA{Adamopoulos2011}, for example, describe systems that suggest items that may already be known, but are still unexpected in the current context. While standardized standardised  measures such as the $F_1$-score or the (R)MSE are used to determine the \emph{accuracy} of a recommendation (i.e.~the recommended item is very close to what the user is already known to prefer), there is no common agreement on a measure for serendipity yet, although there are several proposals \cite{Murakami2008, Adamopoulos2011, McCay-Peet2011,iaquinta2010can}. In terms of our model, these systems focus mainly on producing a \emph{serendipity trigger} and predicting the potential for serendipitous discovery on the side of the user. Intelligent user modeling could bring other components of serendipity into play, as we will discuss in Section \ref{sec:computational-serendipity}.  Recent work has examined related topics of \emph{curiosity}         

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