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Proposal revised down to data accuisition

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dkohl
2012-03-12 12:51:02 -04:00
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writeup/P2 Proposal.tex
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@@ -2,8 +2,9 @@
\usepackage{latex8}
\usepackage{titlesec}
\usepackage[margin=0.5in]{geometry}
% \usepackage[margin=0.5in]{geometry}
\usepackage{graphicx}
\usepackage{amsmath}
\titleformat{\section}{\large\bfseries}{\thesection}{1em}{}
@@ -24,9 +25,9 @@ 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
menu. We introduce a dish recommendation system
based on Bayesian Networks modeling user preferences.
We predict the meals from a data base of recepices 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,
@@ -41,26 +42,44 @@ 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.
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}
\section*{Approach}
The approached problem is to pick a single meal which best meets the requirements
and tastes of different people dining together.
and tastes of different people dining together. We learn a predictive
baysian net from a survey distributed to participants of the meal as
training data in order to capture their preferences. The dishes
in the questionaire are selected such that all ingrediants
are covered. The participants rate each dish on a scale from
one to ten and give additional information like vegetarians.
For new dishes we then predict the maximum likelihood
rating given our model.
In the following we will describe our approach in detail.
First we will discuss the data selection, then the
modeling of the user preference and in the
end how to train the modeled net from
gathered data and howe to predict the
value for a new recepice.
%\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.
\paragraph*{Data accuisition}
We accumulated a diverse collection of sample recipes using the open source AnyMeal application.
We converted to the freely available MealMaster format (flat file)
recipes to XML format for input into our application.
We will gathered 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'.
Furthermore we collected data for vegetarians and vegans.
%\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}
%daniel is here
\paragraph*{Knowledge Engineering}
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,
\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.
@@ -79,26 +98,48 @@ 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}.
we can calculate the probability of users liking the dish given
the probabilities of liking each ingrediant.
\begin{figure}
\centering
\includegraphics[width=\linewidth]{bayes.jpeg}
\includegraphics[width=\linewidth]{bayes}
\caption{Our Baysian net modeling user preferences}
\label{img:bayes_net}
\end{figure}
%\subsection*{implementation}
\paragraph*{Learning and Predicting}
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.
the probabilities for the ingredients using Maximum Likelihood Learning \cite{murphy}.
%\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}.
In order to model food preferences, we implemented
a baysian net library in java. 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
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.
We decided to implement our own Library,
so we understand what is going on and
we can debug and fix the models
and algorithms easily.
\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.