Title: A Survey of Preference for Ranking
1A Survey of Preference for Ranking
2Preferences
- Preference in top-k query
- score-based preference
- partial-ordering base preference
- Preference in other scenarios
- Decision making
- Utility theory (Skip in this talk)
- Conjoint Analysis
- Voting (Skip in this talk)
3Strategy of Decision Making
- Deterministic strategy
- Select the only one among many
- Given u1 u2 u3 select u2 w.r.t. the utility
function - Randomized strategy
- Select a distribution
- Given u1 u2 u3 select u2 is equal to select
0 1 0
4Deterministic strategy
- Let U be a set of possible choices
u1u2...un. - Let L UR be a utility function.
- We want to select a ui in U that maximizes L(ui).
5Randomized strategy
- Let U be a set of possible choices
u1u2...un. - Let L UR be a utility function.
- Let p UR be the probability of selecting a
particular choice ui denoted by p(ui) pi. - We want to select a u in U that maximizes EL
SL(ui)pi.
6Where is top-k
- Currently top-k is deterministic strategy
- no idea whether top-k fits the randomized
scenario
7A Game Against Nature
- Incomplete knowledge about the utility function
L. - There may be uncertainty involved
- How to describe this uncertainty
- Introduce a special decision-maker called Nature
- T the set of choices for nature
- in T a particular choice by nature
8An Example of Nature
L U x T R
U
T
9Strategy with Nature
- The best strategy to adopt depends on what model
we have of what nature will do - Nondeterministic
- choose the column with the least maximum value
- or choose the column with the least average loss.
- Probabilistic
- use Bayesian analysis to calculate a probability
distribution P() of the actions of nature and
use that to make decisions
10Where is top-k
- What is the Nature
- It seems that T can be the parameters (cr cs) in
the cost model - C crnr csns
- Sampling can be used as get P()
- So we can use the probabilistic strategy
11Taxonomy of Decision Making
- Normative Interaction
- Things ought to be
- Descriptive Interaction
- Things are
- Prescriptive Interaction
- Things might to be
12Normative Interaction
- What is a good preference
- Satisfying axioms built by experts
- If A B and B C A C (Transitivity)
- Axioms are rational and intelligent
13Descriptive Interaction
- The axioms may not be correct
- The transitivity may not hold
- In reality it is possible A B B C and C A
- Then what is a good preference
- Satisfying empirical behavior
- Hard to modelize
14Prescriptive Interaction
- What is a good preference
- Hard to say depends on how to sell
- Given A and C
- if the expert finds a B so that A B B C
then we prefer A - Maybe there is also a B so that C B B A
then - The preference can be affected by
- The way to present A and C
- The way to find such a B (or B)
15What the top-k should be
- Now normative
- In reality can be prescriptive
- Consider the scenario to find a house
- The distance presented in miles and kilometers
may affect users choice - The way to present the payment ratio may also
affect - But how to model it in mathematical way
16Conjoint Analysis
- Analyze the value of each factor (attribute
component predicate). - Play an important role in marketing.
- In the design of new products it is valuable to
know which components carry what kind of utility
for the customer.
17A simple example
- A car producer plans to introduce a new car with
two features - of doors 2 4 5
- of air bags 1 2
- By asking a user we get the ranking as
18A simple example (cont.)
- What do we want to know
- Elementary utilities
- Utility of 2-door
- Utility of 4-door
- Utility of 5-door
- Utility of 1-airbag
- Utility of 2-airbag
- Conjoint analysis aims at explaining the rank
order given by the test person as a function of
these elementary utilities.
19Estimation of Preference Orderings
- Conjoint analysis uses an additive model
- Xj denote the features xjl are the levels of
each Xj - ßjl are the elementary utilities
- the constant µ denotes an overall level
- Yk is the observed preference for each situation
20An example of modeling
- Given the table
- We have
- 1 ß11ß21µ
- 3 ß11ß22µ
- 2 ß12ß21µ
- 6 ß12ß22µ
- 4 ß13ß21µ
- 5 ß13ß22µ
21How to estimate
- There are two types of solutions to estimate the
elementary utilities - metric solution
- non-metric solution
22Relation to top-k
- Conjoint analysis looks like query by example
- Given a set of simple examples and let the user
choose - We will know what she wants and then query for her