\documentclass[times, 08pt,twocolumn]{article}
\usepackage{latex8}

\usepackage{titlesec}
\usepackage[margin=0.5in]{geometry}
\usepackage{graphicx}

\titleformat{\section}{\large\bfseries}{\thesection}{1em}{}

\begin{document}
\pagestyle{empty}

\title{A Baysian Approach to Collaborative Dish Selection}
\author{Team 10}
\date{February 23, 2012}

\maketitle

\section*{Introduction}
As anyone who has ever planned a catered event can attest, attempting
to satisfy the various palates, dietary requirements and tastes of a
group of diners can be a daunting task.  This is particularly true
given the exponential number of dishes which can be created from a
small number of ingredients, as well has hard constraints such as
allergies and religious beliefs.  Many professional catering services
handle this problem by allowing guests to select from a very limited
menu. We propose to develop a dish recommendation system
based on Bayesian Networks modeling user preferences and
which proposes meals that most likely match the varied tastes
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.

\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
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.

\section*{Proposed Approach}

The approached problem is to pick a single meal which best meets the requirements
and tastes of different people dining together.  

%\subsection*{Application Framework}
First, we will accumulate a diverse collection of sample recipes using the open source AnyMeal application
to convert freely available MealMaster format (flat file) recipes to XML format for input into the Java Bayesian network / optimization
application we propose.

%\subsection*{Data Collection}
Next, we will gather data representing several diners' preference for approximately 20 meals using a simple survey of the type 'rate on a scale of 1 to 10, 10 being favorite and 1 being least favorite'.  A value of 0 for a given dish will be taken to mean that one or more ingredients trigger and allergy or violate a religous constraint, and the diner cannot consume the dish.

%\subsection*{Model}
We will model each individual user's preferences and needs
as a Bayesian network, which means a set of independence and
conditional independence relationships between variables
\cite{russelnorvig}. Our model consists of 4 layers, 
each modeling a different aspect of taste and needs.
In the first layer we capture general meal preferences, like
being vegetarian or not liking your food steamed.
The second layer models a general preference towards 
different food categories like vegetables or beef.
As one can see, the food categories are dependent 
on the general meal preference. For example 
being vegetarian will exclude beef and will 
support vegetables. The third category models 
different ingredients. Each ingredient is conditioned 
by the food category it belongs to.
In the last layer we have hard constraints like allergies
(that will exclude a particular ingredient) or 
the overall calorie content of the meal given
someone suffers from diabetes.
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 as
$P(i_1 \wedge i_2 \wedge ... \wedge i_n) = \Pi_{i =
1}^{n} p(i_i \mid parents(i_i))$ \cite{russelnorvig}. 

\begin{figure}
\centering
\includegraphics[width=\linewidth]{bayes.jpeg}
\caption{Our Baysian net modeling user preferences}
\label{img:bayes_net}
\end{figure}

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.

%\subsection*{Meal Optimization}
When learning the rest of the variables (that are not observed and therefore
hidden / latent) we will use Expectation Maximization \cite{russelnorvig}.

\section*{Evaluation}
The application model will be trained using a sparse subset (25-50\%) of the survey data and the optimization problem soled for the inferred constraints.
Next, we will 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.

\bibliographystyle{plain}
\bibliography{p2refs}

\end{document}