It is a truth universally acknowledged that e-commerce platform users in search of an item that best suits their preferences may be oered a lot of choices. An item may be characterised by many aributes, which can complicate the process. Here the classic approach in decision support systems - to put weights on the importance of each aribute - is not always helpful as users may nd it hard to formulate their priorities explicitly. Pairwise comparisons provide an easy way to elicit the user's preferences in the form of the simplest possible qualitative preferences, which can then be combined to rank the available alternatives. We focus on this type of preference elicitation and learn the individual preference by applying one statistical approach based on Support Vector Machines (SVM), and two logic-based approaches: Inductive Logic Programming (ILP) and Decision Trees. All approaches are compared on two datasets of car preferences and sushi preferences collected from human participants. While in general, the statistical approach has proven its practical advantages, our experiment shows that the logic-based approaches oer a number of benets over the one based on statistics.
•Information systems →Recommender systems;
Preference learning (PL) is a subtopic in machine learning that works with an ordinal dataset, either in partial or full order. Nowadays, PL plays an important role in machine learning research and practice because the ordinal data itself is used frequently in many areas, such as behavioural, medical, educational, psychological and IntRS 2017, Como, Italy 2017. Copyright for the individual papers remains with the authors. Copying permied for private and academic purposes. is volume is published and copyrighted by its editors.
DOI:
social science [
Pairwise Preferences
ere exist two main ways of modelling preferences: quantitative
and qualitative preferences. e rst modelling is associated with a
number (or a quantity) representing the values of preferences (e.g.,
“my preference for car type is a sedan”), while the second type of
modelling relates each item via pairwise comparisons (e.g., “I prefer
car 1 over car 2”). e rst model is not quite easy for everyone
since humans are not always comfortable to express their
preferences directly in terms of a value. It is normally much easier and
arguably more natural to provide information about preferences in
separate pieces, preferably in a qualitative way [
body type 1 engine size 1 body type 2 engine size 2 car 1 is-beer-than car 2 fuel consumption 1
fuel consumption 2 transmission 1
transmission 2
Figure 1 shows how we derive conclusions about preferences regarding combinations of individual aributes of the form “car 1 is-beer-than car 2”. e bold arrow represents the annotation from the user and the doed arrows show possible implications about individual aributes that the learning algorithm will consider. 1.2
Supervised learning is a type of machine learning algorithm in
which the learner receives a set of labelled examples as training
data and makes predictions for all unseen data points [
In this task, we learn about how the items relate to the other items through the “beer-than” relationship. (2) Learning the top preference class (the best of all).
While in this task, we learn the characteristics of the group of items that cannot be shown to be inferior to any other item.
We provide the evaluation of a number of existing supervised machine learning algorithms, explained in Section 3, to predict the users’ individual preferences. e experiments in this paper are focused only on the rst learning task, i.e. learning the relative order of preferences. 2
AI research has tended to fall into two largely separate approaches:
logical and statistical, in which the former tends to emphasize
handling complexity, while the laer focuses on the uncertainty [
Propositional Logic is concerned with propositions and their
interrelationships (logical connectives). e notion of a proposition
here will not be dened precisely – it suces to say that a
proposition is a possible condition of the world that is either true or
false, e.g., the possibility that it is raining, the possibility that it
is cloudy, and so forth [
First-Order Logics are more expressive than propositional logic,
as they make use of variables and quantiers (both universal and
existential) to describe a concept. Inductive Logic Programming
(ILP) is one of the learning algorithms which uses this logic to
represent both examples and concepts (models) learnt [
We compare the results of logic-based learning with a statistical
machine learning approach, namely, Support Vector Machines (SVM).
In a binary classication problem, the SVM searches for the optimal
linear separator of all data points in an n-dimensional space then
use it to make predictions for new data. e method has previously
been used by Qian et. al. [
We use two publicly available datasets [
3.1.1 Car preferences dataset. In the car preferences dataset [
We treat all of these aributes as categorical in order to make the experiment comparable, so the last column (engine size) was discretized as follows:
Small: for engine size under 3.5L Medium: for engine size from 3.5L and less than 4.5L
Large: for engine size of 5.5L and over. e other aributes are coded as:
Body type: sedan (1), suv (2)
Transmission: manual (1), automatic (2)
Fuel consumption: hybrid (1), non-hybrid (2)
3.1.2 Sushi preferences dataset. e sushi preferences dataset [
We run the SVM and Decision Tree CART algorithm on Matlab R2016a running on Mac OS X version 10.11.2. For the ILP algorithm, we run Aleph 5.0 on a Prolog compiler, yap 6.3.2. We use 10-fold cross validation method for all experiments. In this section, we explain all the examples and results using car dataset description. e experiment for sushi dataset follows the same seings as for the car dataset.
We feed the learner 2 sets, containing positive, resp. negative examples. e positive examples are a set of correctly ordered pairs for each user. en we build a set of negative examples from the opposite order of the user’s preferences. For each user, we have a complete set of 90 observations, consisting of 45 positive examples and 45 negative examples.
e numeric input for SVM and Decision Tree is shown as below: Transmission of the first car: automatic
Transmission of the second car: manual
Engine size of the first car: medium
Engine size of the second car: medium 1, 1, 1, 2, 1, 2, 2, 2, 2, 1
Fuel consumption of the second car: non-hybrid User ID: 1 Fuel consumption of the
first car: non-hybrid
Body type of the second car: sedan Body type of the first car: sedan pColassitsivleabel: Each row represents a user’s preference on a pair of cars. e rst column represents the user ID followed by the next 8 numeric aributes, and the last column is the class label (1=positive; -1=negative). bt(car8,car2). bt(car2,car9). bt(car3,car10).
bt(car2,car3). (a) File in ‘.f’ extension containing positive examples bt(car2,car8). bt(car9,car2). bt(car10,car3).
bt(car3,car2). (b) File in ‘.n’ extension containing negative examples e input for Aleph is shown in Figure 3. Aleph uses separate les to dierentiate between positive and negative examples. One line in the positive examples le (Figure 3a) states: bt(car8,car2), this means that we specify “car 8 is beer than car 2” as a positive example. As we learn about order of preferences, in the negative examples le we put the arguments (car8 and car2) in the opposite ways: bt(car2,car8)), which says that “car 2 is beer than car 8” is a negative example. We run the experiment for each user and using the same seings every time. :- modeh(1,bt(+car,+car)). :- modeb(1,carfuel(+car,#fuelconsumption,
+car,#fuelconsumption)). carfuel(A,X,B,Y):- hasfuelcons(A,X), car(A), car(B), hasfuelcons(B,Y), X\=Y . fuelconsumption(hybrid). fuelconsumption(nonhybrid). car(car1). car(car2). hasfuelcons(car1,nonhybrid). hasfuelcons(car2,hybrid).
Aleph has a dierent way to represent the data and hypothesis. It uses Horn clause as shown in Figure 4 which means that we want to allow Aleph to consider the hypotheses produced by the template ‘in a pair, the rst car is beer than the second car, if the rst car has fuel consumption of (hybrid or non-hybrid) and the second car has fuel consumption of (hybrid or non-hybrid), in which the two cars do not have the same type of fuel consumption’.
From the head mode (modeh), we can see that we want to allow Aleph to build hypothesis by looking for any examples that match this paern bt(+car,+car) (see Figure 3); bt() means a predicate ‘beer than’, while +car means it is an input of type ‘car’. We set the body modes (modeb) as a function carfuel(+car, #fuelconsumption, +car, #fuelconsumption) which has two types of input: ‘car’ and ‘fuel consumption’. How this function works is specied in the following line: carfuel(A,X,B,Y) :- hasfuelcons(A,X), car(A), car(B), hasfuelcons(B,Y), Xn=Y, which means that we want to create hypothesis for the pair of car that has dierent fuel consumption. 3.3
e accuracy of the three algorithms is shown in Table 3. Our experiment shows that in terms of accuracy, SVM signicantly outperformed Aleph and Decision Tree in car dataset, but Decision Tree shows the highest accuracy amongst the other algorithms on sushi dataset. According to ANOVA test, there is a signicant dierence amongst the accuracy of the algorithms as shown in Table 4. ANOVA is conceptually similar to multiple two-sample t-tests but is more conservative (results in less type I error). We also perform several experiments with the algorithms by varying the proportion of training examples and test it on 10% of examples. For a more robust result, we validate each cycle with 10-fold cross validation. We take the average accuracy of both datasets and the result of this experiment is shown in Figure 5.
Some of the rules produced by Decision Tree are shown in Figure 6. We interpret x1 as body type (see Figure 2) of the rst car, x2 as body type of the second car, x3 as transmission of the rst car, x4 as transmission of the second car, x5 as fuel consumption of the rst car, x6 as fuel consumption of the second car, x7 as engine size of the rst car and x8 as engine size of the second car. e Decision Tree uses the rules to predict the new unseen data. Some of the rules in Figure 6 can be read as below:
If the body type of the rst car is sedan and the body type of second car is sedan and the fuel consumption of second car is non-hybrid, then it is a positive class.
If the body type of the rst car is suv and body type of the second car is sedan, then it is a positive class.
bt(A,B) :
carbodytype(B,sedan,A,suv). bt(A,B) :
cartransmission(B,manual,A,automatic). bt(A,B) :
carfuel(B,nonhybrid,A,hybrid).
DISCUSSION AND ANALYSIS e results of the three dierent approaches are quite interesting. e statistical approach, SVM, works very well when we codify all the data into numerical and it can be very practical. On the other hand, Aleph and Decision Tree also show the good results with some advantages of a more readable model (a set of rules) and they can work well for both numerical or categorical data. In contrast to Decision Tree, Aleph, as the rst order logic learner algorithm, has a special feature to be more exible in dening 0.1 0.2 0.3 0.4 0.5 0.6 # training examples 0.7 0.8
SVM Decision Tree Aleph 0.9 1 the rules. For example, while the Decision Tree only expands the tree for each individual feature, we can let Aleph build the hypothesis based on the comparison of the same aributes in pair (e.g. bt(A,B):-carbodytype(B,sedan,A,suv)) means that the rule says ‘car A is beer than car B if car A is suv and car B is sedan’). e set of rules that has been produced by Aleph can be used for further analysis, i.e. to recommend the best characteristics of items to the users. 5
In this paper, we reported an experiment with the logic-based and statistical learning algorithms to predict user’s individual preferences. Although the statistical approach shows a very good result, the logical approaches can be more promising in such ways: e logical approach can be used to learn from a smaller number of examples, as we cannot guarantee that we will have enough responses from the users.
We can use the exibility of adding a background knowledge to the logical learner to limit the rules and built more meaningful result (e.g. using Aleph implementation). e results of logical approach are more readable and easier to be understood for the further use (i.e. provide a recommendation).
e main benet of the paper is methodological, establishing a comparison between statistical and logic-based methods, and that the full benets of logic-based methods are to be expected for richer representations, where a range of background concepts (either provided by the soware designers or gradually inferred from the data) can be used to model users with complex preferences.
All of this experiment can only be performed in batch mode. e dataset we used in this experiment only have a limited number of choices, which limits the number of possible combinations of features between the pairs. We plan to implement an algorithm which employs active learning to help with incremental learning. It will be tested in another forthcoming experiment, which will also oer the learner the choice of explicitly asking the users to conrm or reject parts of the model and its implications regarding the best choice of car.
is work is supported by Indonesia Endowment Fund for Education (LPDP) , Ministry of Finances, e Republic of Indonesia [grant no. 20130622010016].