From 28aec2a148d72ebdc28d004cdc1b62e2605d82a4 Mon Sep 17 00:00:00 2001 From: dkohl Date: Tue, 13 Mar 2012 00:16:22 -0400 Subject: [PATCH] Writing up --- writeup/P2 Proposal.aux | 15 +- writeup/P2 Proposal.bbl | 73 +++++---- writeup/P2 Proposal.blg | 79 ++++++---- writeup/P2 Proposal.log | 337 +++++++++++++++++++++++++--------------- writeup/P2 Proposal.pdf | Bin 190917 -> 199213 bytes writeup/P2 Proposal.tex | 246 +++++++++++++++++++++-------- writeup/bayes.png | Bin 69122 -> 61355 bytes writeup/missfont.log | 2 - writeup/p2refs.bib | 10 +- writeup/p2refs.log | 11 -- writeup/texput.log | 20 --- 11 files changed, 501 insertions(+), 292 deletions(-) delete mode 100644 writeup/missfont.log delete mode 100644 writeup/p2refs.log delete mode 100644 writeup/texput.log diff --git a/writeup/P2 Proposal.aux b/writeup/P2 Proposal.aux index 35a856e..34e7e31 100644 --- a/writeup/P2 Proposal.aux +++ b/writeup/P2 Proposal.aux @@ -3,14 +3,19 @@ \citation{corney} \citation{janzenxiang} \citation{truyen} +\citation{truyen} \citation{murphy} +\citation{murphy} +\citation{russelnorvig} +\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces Our Baysian net modeling user preferences. The top layer describes the categories Meat and Vegetable. We have a control variable vegetarian for Meat, such that it will always evaluate to $0$ when there is meat involved in a dish and we have a vegetarian diner. The mid layer describes the preference for different ingredients. The last layer is a gaussian predicting the users preferences.}}{2}} +\newlabel{img:bayes_net}{{1}{2}} \bibstyle{plain} \bibdata{p2refs} \bibcite{corney}{1} \bibcite{janzenxiang}{2} \bibcite{murphy}{3} -\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces Our Baysian net modeling user preferences}}{2}} -\newlabel{img:bayes_net}{{1}{2}} -\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces Estimated vs. Actual Survey Dish Ratings}}{2}} -\bibcite{truyen}{4} -\bibcite{vanboekel}{5} +\bibcite{russelnorvig}{4} +\bibcite{truyen}{5} +\bibcite{vanboekel}{6} +\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces Estimated vs. surveyed dish ratings}}{3}} +\newlabel{result}{{2}{3}} diff --git a/writeup/P2 Proposal.bbl b/writeup/P2 Proposal.bbl index 2092b90..c999c61 100644 --- a/writeup/P2 Proposal.bbl +++ b/writeup/P2 Proposal.bbl @@ -1,34 +1,39 @@ -\begin{thebibliography}{1} - -\bibitem{corney} -David Corney. -\newblock {Designing Food} with {Bayesian Belief Networks}. -\newblock {\em ACDM}, 2000. - -\bibitem{janzenxiang} -M.~Janzen and Y.~Xiang. -\newblock {Probabilistic Reasoning} in {Meal Planning} in {Intelligent - Fridges}. -\newblock {\em 16th Conference of the Canadian Society for Computational - Studies of Intelligence}, 2003. - -\bibitem{murphy} -Kevin Murphy. -\newblock A {Brief Introduction} to {Graphical Models} and {Bayesian Networks}. -\newblock http://www.cs.ubc.ca/~murphyk/Bayes/bnintro.html, 1998. -\newblock [Online; accessed 22-Feb-2012]. - -\bibitem{truyen} -Tran~The Truyen, Dinh~Q. Phung, and Svetha Venkatesh. -\newblock Preference {Networks}: {Probabilistic} {Models} for {Recommendation} - {Systems}. -\newblock {\em Proceedings of the {Sixth Australasian Conference} on {Data - Mining}}, 2007. - -\bibitem{vanboekel} -Stein~A. van Boekel, M.A.J.S. and A.H.C. van Bruggen. -\newblock {Bayesian Statistics} and {Quality Modelling} in the {Agro-food - Production Chain}. -\newblock {\em Proceedings of the Frontis workshop}, 2004. - -\end{thebibliography} +\begin{thebibliography}{1} + +\bibitem{corney} +David Corney. +\newblock {Designing Food} with {Bayesian Belief Networks}. +\newblock {\em ACDM}, 2000. + +\bibitem{janzenxiang} +M.~Janzen and Y.~Xiang. +\newblock {Probabilistic Reasoning} in {Meal Planning} in {Intelligent + Fridges}. +\newblock {\em 16th Conference of the Canadian Society for Computational + Studies of Intelligence}, 2003. + +\bibitem{murphy} +Kevin Murphy. +\newblock A {Brief Introduction} to {Graphical Models} and {Bayesian Networks}. +\newblock http://www.cs.ubc.ca/~murphyk/Bayes/bnintro.html, 1998. +\newblock [Online; accessed 22-Feb-2012]. + +\bibitem{russelnorvig} +S.~Russel and P.~Norvig. +\newblock {\em Artificial Intelligence; A Modern Approach}. +\newblock Prentice Hall, third edition, 2010. + +\bibitem{truyen} +Tran~The Truyen, Dinh~Q. Phung, and Svetha Venkatesh. +\newblock Preference {Networks}: {Probabilistic} {Models} for {Recommendation} + {Systems}. +\newblock {\em Proceedings of the {Sixth Australasian Conference} on {Data + Mining}}, 2007. + +\bibitem{vanboekel} +Stein~A. van Boekel, M.A.J.S. and A.H.C. van Bruggen. +\newblock {Bayesian Statistics} and {Quality Modelling} in the {Agro-food + Production Chain}. +\newblock {\em Proceedings of the Frontis workshop}, 3, 2004. + +\end{thebibliography} diff --git a/writeup/P2 Proposal.blg b/writeup/P2 Proposal.blg index 81f4791..aa8e381 100644 --- a/writeup/P2 Proposal.blg +++ b/writeup/P2 Proposal.blg @@ -1,28 +1,51 @@ -This is BibTeX, Version 0.99dThe top-level auxiliary file: P2 Proposal.aux -The style file: plain.bst -Database file #1: p2refs.bib -I was expecting a `,' or a `}'---line 14 of file p2refs.bib - : - : CITY = {Wageningen} -(Error may have been on previous line) -I'm skipping whatever remains of this entry -I was expecting a `,' or a `}'---line 23 of 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+\usepackage[margin=0.88in]{geometry} \usepackage{graphicx} \usepackage{amsmath} @@ -11,7 +11,7 @@ \begin{document} \pagestyle{empty} -\title{A Bayesian Approach to Collaborative Dish Selection} +\title{A Baysian Approach to Collaborative Dish Selection} \author{Team 10} \date{February 23, 2012} @@ -31,19 +31,42 @@ We predict the meals from a data base of recepices that most likely match the va of the customers, using a limited set of ingredients. This type of expert system would be of great use to a catering service or restaurant which needs to rapdily decide on a small number of dishes which would be acceptable for a large dinner party, -given diverse requirements and preferences. +given diverse requirements and preferences. + +\paragraph*{Baysian Catering: A use case.} +Imagine, you run a catering service and have to +plan an event with a customer. You can +create a variaty of dishes and now you +want to discuss with your clients which one to +serve. In order to get a better idea of which preferences +and needs you clients will have, you let them fill +out a survey in advance, where they rate a small amount of +your dishes on a scale from $1 - 10$ and inform you about +hard constraints like allergies, religous constraints +or vegetarians. You then use those results in order to predict +the ratings for the rest of your dishes and present the clients +the top $k$ results. If such a system works this will save time and will lead +to a better cutomer satisfaction since you can present them dishes +they will most probably like but still suprise them (since you have +not presented them what the already rated). After the dinner +participants could rate the dishes served at the party which would +improve your work for that client in the future. \section*{Related Work} Boekel and Corney propose using Bayesian Networks to model consumer needs in food production chains \cite{vanboekel} \cite{corney}. Janzen and Xiang propose an intelligent refrigerator capable of generating meal plans based on inventory -and past food choices \cite{janzenxiang}. Baysian networks have also been +and past food choices \cite{janzenxiang}. +We suggest that these approaches are limited in that they +only consider the preferences of a single (or supposed 'typical') +user rather than a group. Baysian networks have also been applied to recommendation systems before in on-line social networks \cite{truyen} making predictions of the form ``if you bought those items what is the probability you would like to -buy that''. We suggest that these approaches are limited in that they -only consider the preferences of a single (or supposed 'typical') user rather than a group. +buy that''. This method also uses baysian networks +for prediction and our approach is similar or inspired by +some of Truyens \cite{truyen}. \section*{Approach} @@ -66,57 +89,103 @@ value for different recipes. \paragraph*{Data accuisition} We first accumulated a diverse collection of license-free sample recipes from web sites such as \emph{Darkstar's Meal-Master Recipes} (http://home.earthlink.net/~darkstar105/). Next, we converted these recipes from flat text files to well-formed XML using the Krecipes application for Debian Linux. Finally, we created a representative data set representing several diners' preference for 24 of these recipes, using a simple survey of the type 'rate on a -scale of 1 to 10, 10 being favorite and 1 being least favorite'. Furthermore, users were allowed to specify a vegetarian or nut-free meal preference. +scale of 1 to 10, 10 being favorite and 1 being least favorite'. +Furthermore, users were allowed to specify a vegetarian +or nut-free meal preference. -%daniel is here \paragraph*{Knowledge Engineering} We model the diners' various taste preferences using -a Bayes net. We model the taste - -\begin{description} -\item[Layer 1] The first layer models a general preference towards -different food categories like vegetables or meat. -As one can see, the food categories are dependent -on the general meal preference. For example -being vegetarian will exclude meat and will -support vegetables. - -\item[Layer 2] Specific flavors and ingredients. Each ingredient is conditioned -by the food category to which it belongs. -\end{description} - -If we need to model hard constraints, like - - +a Bayes net. The net consists of three node types. +We call them ``control nodes'', ``taste nodes'' +and ``rating nodes''. A ``preference node'' +models the probability of a diners' preference towards an +ingredient ($P(likes tomato)$, $P(likes potato)$) or a category +($P(likes meat)$). These variables are discrete. The ingredients +are conditional independent from each other but conditioned +by the food category they belong to (see Figure \ref{img:bayes_net} +the two top layers). A control node can definitely reject a dish, +by evaluating to $0$ in certain conditions. For +example if someone is vegetarian and the presented dish contains +meet, the control variable for vegetarian will evaluate to $0$ and +so the probability for the whole dish will become $0$. +So the vegetarian variable is conditioned by meat. +The third type in the net is a preference node, it is continuos +and models the dish rating given a set of ingredients. The overall net is shown in Figure \ref{img:bayes_net}. -Given a recipe with a list of ingredients $I = i_1,...,i_n$ -and a Bayesian network capturing user preferences -we can calculate the probability of users liking the dish given -the probabilities of liking each ingrediant. -\begin{figure} +\begin{figure}[ht] \centering -\includegraphics[width=\linewidth]{bayes} -\caption{Our Baysian net modeling user preferences} +\includegraphics[width=0.9\linewidth]{bayes} +\caption{Our Baysian net modeling user preferences. The top layer + describes the categories Meat and Vegetable. We have a control + variable vegetarian for Meat, such that it will always evaluate to + $0$ when there is meat involved in a dish and we have a vegetarian + diner. The mid layer describes the preference for different + ingredients. The last layer is a gaussian predicting the users preferences.} \label{img:bayes_net} \end{figure} %\subsection*{implementation} -\paragraph*{Learning and Predicting} +\paragraph*{Learning user preferences} In order to estimate the model parameters, the system will be trained with statistics about taste and preferences given a set of dishes with ratings -from multiple users. From that information we can directly calculate -the probabilities for the ingredients using Maximum Likelihood Learning \cite{murphy}. +from multiple users. The training set is generated from +the questionnaires we distributed. +An example for a survey output could look like this (Ingredients, Rating): ``Pork, +Potatoes, 8''. In order to perform normal Maximum Likelihood Learning +\cite{murphy} we have to have information about all variables +(``Pork, Potatoes, Tomatoes, Beef, Meat, Vegetables, Rating''). +We perform several steps in order to transform from the survey input +to a training instance. +First we discretize the values such that all given variables (in our +case Pork and Potatoes) are set to ``true'' if the value is above +a certain threshold (in our experiments $5$) and ``false'' otherwise. +In that way ``liking things rated $>$ 5'' appear more often in the +training set and will be assigned with a higher probability. +We add categories by including the category of each ingredient +from the survey. If the ingredient is liked, the category is too +and if it is not, the category is not liked too. The last step +is to add all values that are not in the recipe as ``false'' +to the training instance. +From a set of those preprocessed assignments, we can directly calculate +the probabilities for the ingredients using Maximum Likelihood +Learning \cite{murphy}. For example for an assignment of a +conditional variable $P(X = x \mid Y_1 = y_1, ... Y_2 = y2)$, +we count how often we observe the configuration $X = x, Y_1 = y_1, +... Y_2 = y2$ and how often we count $Y_1 = y_1, ... Y_2 = y2$ +in our data set. The maximum likelihood is then defined as +\begin{align} +P(X = x| Y_1 = y_1, ... Y_2 = y2) =\\ +N(X = x| Y_1 = y_1, ... Y_2 = y2) \over N(Y_1 = y_1, ... Y_2 = y2) +\end{align} +where $N(A)$ is the number of times event $A$occurs in the data set. +For a continuos variable like rating, we estimate a gaussian for +each combination of it's parents. For example if the rating variable +is dependent on beef and tomatos, we would estimate 4 gaussians, +one for each possible combination of beef and tomatos. So during +training we would estimate mean and variance for all cases where +$(tomato = true, potato = true)$, $(tomato = false, potato = true)$ +and so on. -%\subsection*{Meal Optimization} +\paragraph*{Inferring maximum likelihood rating} +Having estimated the probabilities of such a net, we can infer +the maximum likelihood rating of a unseen dish while observing only +a set of ingredients. Therefore we will iterate over all possible +ratings ($1 - 10$) and compute the probability of this rating. +The maximum probability is the maximum likelihood rating +for that dish. We use the enumerateAll algorithm \cite{russelnorvig}, +for the probability calculations. + +\paragraph*{Implementation} In order to model food preferences, we implemented -a custom Baysian net library in java with minimal use of third party libraries (e.g. for XML input). -We chose to implement our own Library, for maximum flexibility and to ensure that the learning algorithm functions precisely as follows: - -The library -uses the sum-product algorithm for +a custom Baysian net library in java with +minimal use of third party libraries (e.g. for XML input). +We chose to implement our own Library, +for maximum flexibility and to ensure that the learning algorithm +functions precisely as follows: +The library uses the sum-product algorithm for inference and maximum likelihood learning for parameter estimation. In our implementation we support discrete as well as continous @@ -124,39 +193,94 @@ probability distributions. Discrete distributions can be modeled as tables or as trees. In our implementation only continous distributions with discrete parents are supported. A continous distribution is then modeled as a mapping -of all possible combination of it' s parents to a gaussian. -Given a data set, the parameters of a discrete variable $X$ are -estimated as -\begin{align} -P(X = x| Y_1 = y_1, ... Y_2 = y2) =\\ -N(X = x| Y_1 = y_1, ... Y_2 = y2) \over N(Y_1 = y_1, ... Y_2 = y2) -\end{align} -where $N(A)$ is the number of times event $A$occurs in the data set. +of all possible combination of it' s parents to a gaussian set. \section*{Evaluation} -The application model will be trained using a sparse subset (50\%) of the survey data and the optimization problem solved for the inferred constraints. As shown below, the calculated preferences for recipes which were not used to train the Bayes net are quite close to the actual survey data, which essentially reflects the following preferences (Sample ratings are on a 1-10 scale): +In an experiment we collected $XXX$ ratings from $XXX$ persons. +We trained the Bayes net using a sparse subset (50\% of the rated +recipes) of the survey data. Then we evaluated the rest of the +recipes (which are all unseen) and calculated +the maximum likelihood rating. +As shown below, the calculated preferences for recipes +which were not used to train the Bayes net are quite close to the +actual survey data, which essentially reflects the following +preferences +(Sample ratings are on a 1-10 scale): -\begin{description} -\item[Diner 1] No allergies, prefers all dishes equally (5) +%\begin{description} +%\item[Diner 1] No allergies, prefers all dishes equally (5) -\item[Diner 2] Vegetarian, meat dishes are (1), remainder are (9) +%\item[Diner 2] Vegetarian, meat dishes are (1), remainder are (9) -\item[Diner 3] Nut Alleregy, prefers meat (6) to vegetarian (4) to desert (3) +%\item[Diner 3] Nut Alleregy, prefers meat (6) to vegetarian (4) to desert (3) -\item[Diner 4] No allergies, prefers Pork and Desserts (9), remainder are (3) +%\item[Diner 4] No allergies, prefers Pork and Desserts (9), remainder are (3) -\end{description} +%\end{description} -Next, we calculate the correlation between the application's ranking of all dishes and the actual ranking as determined by the user surveys. We suggest that a high degree of correlation indicates that the system has the potential to accurately appraise constrained group food preferences for dishes which are not part of the survey, given sufficiently detailed recipe information. As \ref{rms-table} shows, the estimated food preferences are quite close to the actual mean ratings over all diners for the dishes which were not used to train the Bayes net. The root mean-square-error for calculated vs. surveyed meal preferences is approximately 1.0. +Next, we calculate the error between the application's ranking of all +dishes and the actual ranking as determined by the user surveys. We +suggest that a low error indicates that the system has the potential +to accurately appraise constrained group food preferences for dishes +which are not part of the survey, given sufficiently detailed recipe +information. As the Table and Figure \ref{result} show, the estimated food preferences are quite close to the actual mean ratings over all diners for the dishes which were not used to train the Bayes net. The root mean-square-error for calculated vs. surveyed meal preferences is approximately 1.92. -\begin{figure}[h!] +\begin{table}[ht] +\begin{tabular}{ | l | l | l | } +\hline +Southwest Smoothie: & &\\ +DAIRY & 5 & 5.5 \\ \hline +Bayou Shrimp Creole: & &\\ +TOMATO & 9 & 3.75 \\ \hline +Crab Burgers: & &\\ +EGGS & 5 & 3.75 \\ \hline +Broiled Flounder: & &\\ +GENERIC NUTS, EGGS & 5 & 3.75 \\ \hline +Baked Steak And Lima Beans: & &\\ +TOMATO, SUGAR & 2 & 3.75 \\ \hline +Eggplant Lasagna: & &\\ +GLUTEN & 5 & 5.25 \\ \hline +Salisbury Steak with Mushroom Sauce: & &\\ +GLUTEN, DAIRY, BEEF & 6 & 3.75 \\ \hline +Meatless Loaf: & &\\ +SPICE & 5 & 5.25 \\ \hline +Lemon Pork Chops: & &\\ +PORK, SUGAR & 5 & 5.25 \\ \hline +Fava Bean Burgers: & &\\ +EGGS, POTATO & 3 & 5.25 \\ \hline +Angel Hair Pesto Primavera: & &\\ +GENERIC NUTS, SPICE & 5 & 5.25 \\ \hline +%\hline +\end{tabular} +\end{table} + +\begin{figure}[ht] \centering \includegraphics[width=0.5 \textwidth]{BayesChefChart.png} -\caption{Estimated vs. Actual Survey Dish Ratings} +\caption{Estimated vs. surveyed dish ratings} +\label{result} \end{figure} -Note the outlier at Dish \#2 (Bayou Shrimp Creole). The strong preference for this dish is a result of the ingredient list containing primarily shrimp and tomato. Unlike beef and pork, the seafood category was not implemented in the knowledge enginerring of the net. Consequently, this dish is incorrectly deemed to be vegetarian-compatible. The same issue had previously occurred at Dish \#5 (Baked Steak and Lima Beans) until 'steak' was added to the recipe parser as a synonym for beef, and therefore a type of meat. - +\section*{Conclusion} +We proposed, implemented and evaluated a food preference prediction system that +is capable of predicting how much a user would like a new, unseen recipes. +We discussed how to encode user preference towards ingredients and +categories in a Bayes Net and how to add control variables in order +to exclude dishes that users have to avoid like no meat for +vegetarians. Furthermore, we presented our learning +scheme for such a Bayes net using data from a small survey +and how to predict the user rating for unseen dishes. +In an evaluation we showed that the net can predict +preferences when learned from a sparse data set. +So in a real life setting, where people plan +a dinner with a catering service, +a few participants could rate a small amount of recipes +in an online service +and the system could actually predict the scores +on the rest of the caterers data base. +The top $k$ with the answers highest predicted +rating of the system could be used to assemble the final +dinner. \bibliographystyle{plain} \bibliography{p2refs} diff --git a/writeup/bayes.png b/writeup/bayes.png index 7d131608b6ac11cc020e6921a48ad892c88583ba..28de665149b49fef27f6f95e2454ae4a96e37514 100644 GIT binary patch delta 55731 zcmce8WmH_<(k2i*IKkcBEjYp5-QC^&;I6^l-95qGgS%^R2pT-odFQjaYu$e{^Q%{% z?$f(=ow8l^JROt`S+)IvBvMgc0ude;9t;c&QA$!&84T>hFc=v46D$Pi%A`>JNCQb5 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