CP-nets: A Tool for Representing and Reasoning withConditional Ceteris Paribus Preference Statements (1107.0023v1)

Abstract: Information about user preferences plays a key role in automated decision making. In many domains it is desirable to assess such preferences in a qualitative rather than quantitative way. In this paper, we propose a qualitative graphical representation of preferences that reflects conditional dependence and independence of preference statements under a ceteris paribus (all else being equal) interpretation. Such a representation is often compact and arguably quite natural in many circumstances. We provide a formal semantics for this model, and describe how the structure of the network can be exploited in several inference tasks, such as determining whether one outcome dominates (is preferred to) another, ordering a set outcomes according to the preference relation, and constructing the best outcome subject to available evidence.

• The paper presents CP-nets as a novel graphical model that formalizes conditional ceteris paribus preferences using rigorous semantics.
• It introduces efficient linear-time algorithms for outcome optimization and preference ordering in acyclic networks.
• The study examines the computational complexity of dominance queries and provides practical heuristics for tractable preference reasoning.

An Overview of CP-nets: A Tool for Representing and Reasoning with Conditional Ceteris Paribus Preference Statements

The paper "CP-nets: A Tool for Representing and Reasoning with Conditional Ceteris Paribus Preference Statements" by Craig Boutilier, Ronen I. Brafman, Carmel Domshlak, Holger H. Hoos, and David Poole introduces CP-nets (Conditional Preference networks), a novel graphical model tailored for expressing and reasoning about qualitative user preferences. These preferences are articulated under a ceteris paribus (all else being equal) assumption, focusing on capturing conditional dependencies and independencies among preference statements.

Conditional Preferences and Graphical Modeling

CP-nets are designed to allow users to specify their preferences in a structured, intuitive manner, capturing both conditional dependencies and independencies among variables. Each variable in a CP-net has a set of parents whose values influence the user's preferences over the possible values of the variable in question. This information is encoded using graphical structures where nodes represent variables, and directed edges indicate preferential dependence. The preferences themselves are recorded in Conditional Preference Tables (CPTs) for each variable, specifying how the preference over this variable’s values depends on its parent variables.

Formal Semantics and Properties

The paper provides a rigorous formal semantics for CP-nets. A preference ranking satisfies a CP-net if it respects all local preference statements encoded in the CPTs under the ceteris paribus interpretation. The authors prove that every acyclic CP-net has at least one consistent preference ordering, making them satisfiable.

Outcome Optimization

Outcome optimization within CP-nets is a critical feature, allowing the determination of the most preferred outcome given partial constraints. The paper presents a linear-time forward sweep algorithm that constructs the optimal outcome by sequentially setting each variable to its most preferred value given its parents' assignments. This simple procedure benefits significantly from the structured nature of CP-nets, ensuring efficiency.

Dominance and Ordering Queries

CP-nets also support two main forms of preferential comparison between outcomes: dominance queries and ordering queries. Dominance queries ascertain whether one outcome is preferred to another under all satisfiable rankings, whereas ordering queries determine if there is at least one ranking consistent with the CP-net where one outcome is preferred over another. Although dominance queries are more stringent, the authors show that ordering queries can be answered efficiently in linear time for acyclic CP-nets, thanks to the graphical structure and ceteris paribus semantics.

Computational Complexity

The computational complexity of dominance queries is examined in depth. While dominance testing in general is NP-hard, specific cases are shown to be tractable. For instance, polynomial-time algorithms exist for tree-structured and polytree-structured binary-valued CP-nets. However, when more complex structures are considered, such as multiply connected networks or those involving multi-valued variables, the problem remains computationally challenging.

Search Strategies and Heuristics

The paper explores various search strategies to find improving or worsening sequences to handle dominance queries. These include suffix fixing, least-variable flipping, and forward pruning. These techniques enable efficient pruning of the search space, offering substantial improvements in practical scenarios without compromising the completeness of the search procedure.

Practical Implications and Applications

The practical implications of CP-nets are diverse, with applications spanning adaptive multimedia document presentation, distributed meeting scheduling, and preference-driven product configuration in e-commerce. The compact representation and intuitive modeling of preferences make CP-nets particularly suited for domains where preference elicitation from non-expert users is critical.

Conclusion and Future Work

The introduction of CP-nets represents a significant step in qualitative preference modeling. The paper lays a strong theoretical and computational foundation while also hinting at potential future directions. These include addressing cyclic networks, enhancing the expressive power of CP-nets, incorporating quantitative elements, and optimizing user interaction during preference elicitation.

In summary, CP-nets and their associated algorithms provide a robust framework for reasoning with qualitative, conditional preferences. The paper's contributions in establishing the formal semantics, computational properties, and practical applications make it a foundational work in the field of preference-based reasoning.