Information Technology Reference
In-Depth Information
“Nothing is more practical than theory” [
77
]. After introducing the algorithms
and their applications, we will turn to the theoretical part of learning to rank. In
particular, we will discuss the theoretical guarantee of achieving good ranking per-
formance on unseen test data by minimizing the loss function on the training data.
This is related to the generalization ability and statistical consistency of ranking
methods. We will make discussions on these topics in Chaps. 15, 16, 17 and 18.
In Chaps. 19 and 20, we will summarize the topic and present some future re-
search topics.
As for the writing of the topic, we do not aim to be fully rigorous. Instead we try
to provide insights into the basic ideas. However, it is still unavoidable that we will
use mathematics for better illustration of the problem, especially when we jump into
the theoretical discussions on learning to rank. We will have to assume familiarity
with basic concepts of probability theory and statistical learning in the correspond-
ing discussions. We have listed some basics of machine learning, probability theory,
algebra, and optimization in Chaps. 21 and 22. We also provide some related mate-
rials and encourage readers to refer to them in order to obtain a more comprehensive
overview of the background knowledge for this topic.
Throughout the topic, we will use the notation rules as listed in Table
1.3
.Here
we would like to add one more note. Since in practice the hypothesis
h
is usually
defined with scoring function
f
, we sometimes use
L(h)
and
L(f )
interchangeably
to represent the loss function. When we need to emphasize the parameter in the
scoring function
f
, we will use
f(w,x)
instead of
f(x)
in the discussion, although
they actually mean the same thing. We sometimes also refer to
w
as the ranking
model directly if there is no confusion.
1.5 Exercises
1.1 How can one estimate the size of the Web?
1.2 Investigate the relationship between the formula of BM25 and the log odds of
relevance.
1.3 List different smooth functions used in LMIR, and compare them.
1.4 Use the view of the Markov process to explain the PageRank algorithm.
1.5 Enumerate all the applications of ranking that you know, in addition to docu-
ment retrieval.
1.6 List the differences between generative learning and discriminative learning.
1.7 Discuss the connections between different evaluation measures for informa-
tion retrieval.
1.8 Given text classification as the task, and given linear regression as the algo-
rithms, illustrate the four components of machine learning in this case.
1.9 Discuss the major differences between ranking and classification (regression).
1.10 List the major differences between the three approaches to learning to rank.
