Methodology (continued)

1. Generating partial COP-nets on demand • Henry Bediako-Asare1, Michael Fleming1, Scott Buffett2 • Faculty of Computer Science, University of New Brunswick 2. National Research Council of Canada Background Information The idea of agents representing users in negotiations has encouraged research in preference elicitation and user preference modeling. The Conditional Outcome Preference Network (COP-net) is used to predict preferences over an entire set of possible outcomes, given a (typically very small) number of elicited preferences. n7 n7 Methodology (continued) 1.) 2.) 3.) 4.) Second pair of paths generated from n3 to n4 1.) 2.) 3.) First pair of pathsSecond pair of paths Resulting partial COP-net The first and second pairs of paths are merged to obtain a partial COP-net involving 8 outcomes instead of all 64 possible outcomes Utilities – quantitative measures of how desirable an outcome is – are estimated for the outcomes in the partial COP-net, using an existing technique. In this case, since the estimated utility for n3 is greater than that for n4, it is predicted that the outcome represented by n3 is preferred over the outcome represented by n4. Estimated utilities for the nodes in the partial COP-net Final COP-net used to estimate utilities n7 n7 n7 n5 n5 n7 n19 n6 n6 n6 n6 n6 n3 n3 n6 n5 n3 n5 n3 n5 n4 n4 n4 n5 n3 n5 n3 n3 n1 n1 n3 n3 n3 n4 n4 n2 n2 n2 n2 n2 n4 n4 n1 n4 n1 n4 n1 n4 n1 n2 n0 n0 n0 n0 n0 n2 n0 n0 n0 n0 n0 Problem Definition The existing methodology uses all possible outcomes to construct a COP-net. Thus for very large numbers of outcomes, the construction of the COP-net becomes infeasible. The table below gives an idea of the exponential growth of possible outcomes. n0 Proposed Solution Using A* Search, a partial COP-net involving only some of the outcomes that are relevant in making a prediction, instead of one with all possible outcomes, is constructed. Methodology Four paths are built using A* Search. They are then merged to obtain the partial COP-net, as shown in the following example. Six attributes of a BMW 7 series, each having two values, resulting in 64 possible outcomes Colour = {white, silver} Engine = {V8, V10} Drive train = {FWD, RWD} Wheels = {18” star, 19” star} Interior = {brown leather, black leather} Package = {premium, sport} Elicited preferences from a user silver > white; V8 > V10; FWD > RWD; 18” star > 19” star; brown leather > black leather; premium > sport Suppose we want to find out if a BMW 7 series which is white in Colour, has a V8 Engine, is Rear Wheel Drive, has 19’’ star shaped alloy Wheels, has a black leather Interior and has a sports Package (wV8R19blsp or n3) is preferred over one that is silver in Colour, has a V10 Engine, is Front Wheel Drive, has 19’’ star shaped alloy Wheels, has a black leather Interior and has a sports Package (sV10F19blsp or n4). Nodes created for the 8 outcomes involved in the partial COP-net 1.) 2.) 3.) 4.) First pair of paths generated from n4 to n3 n20 n14 n38 n39 n23 n7 n16 n44 n30 n54 n53 n56 n17 n9 n51 n27 n15 n11 n21 Current Results The charts below show the current results of how the existing methodology compares with the proposed methodology in terms of the average accuracy in predicting preferences of outcomes, the time it takes to make one prediction, and the number of outcomes involved in both methodologies’ COP-nets. n13 n60 n17 n25 n22 2187 outcomes : 1 sec