Preference learning is a subfield of machine learning that focuses on modeling and predicting preferences based on observed preference information. Preference learning typically involves supervised learning using datasets of pairwise preference comparisons, rankings, or other preference information.
The main task in preference learning concerns problems in "learning to rank". According to different types of preference information observed, the tasks are categorized as three main problems in the book Preference Learning:[1]
In label ranking, the model has an instance space
X=\{xi\}
Y=\{yi|i=1,2, … ,k\}
yi\succxyj
x
yi
yj
It was observed that some conventional classification problems can be generalized in the framework of label ranking problem:[2] if a training instance
x
yi
\forallj ≠ i,yi\succxyj
x
L\subseteqY
\{yi\succxyj|yi\inL,yj\inY\backslashL\}
Instance ranking also has the instance space
X
Y
y1\succy2\succ … \succyk
xl
yl
Object ranking is similar to instance ranking except that no labels are associated with instances. Given a set of pairwise preference information in the form
xi\succxj
There are two practical representations of the preference information
A\succB
A
B
a
b
a>b
V(A,B)\in\{0,1\}
(A,B)
A\succB
B\succA
If we can find a mapping from data to real numbers, ranking the data can be solved by ranking the real numbers. This mapping is called utility function. For label ranking the mapping is a function
f:X x Y → R
yi\succxyj ⇒ f(x,yi)>f(x,yj)
f:X → R
Finding the utility function is a regression learning problem which is well developed in machine learning.
The binary representation of preference information is called preference relation. For each pair of alternatives (instances or labels), a binary predicate can be learned by conventional supervised learning approach. Fürnkranz and Hüllermeier proposed this approach in label ranking problem.[3] For object ranking, there is an early approach by Cohen et al.[4]
Using preference relations to predict the ranking will not be so intuitive. Since observed preference relations may not always be transitive due to inconsistencies in the data, finding a ranking that satisfies all the preference relations may not be possible or may result in multiple possible solutions. A more common approach is to find a ranking solution which is maximally consistent with the preference relations. This approach is a natural extension of pairwise classification.
Preference learning can be used in ranking search results according to feedback of user preference. Given a query and a set of documents, a learning model is used to find the ranking of documents corresponding to the relevance with this query. More discussions on research in this field can be found in Tie-Yan Liu's survey paper.[5]
Another application of preference learning is recommender systems. Online store may analyze customer's purchase record to learn a preference model and then recommend similar products to customers. Internet content providers can make use of user's ratings to provide more user preferred contents.