# SUNNY: A New Algorithm for Trust Inference in Social Networks Using Probabilistic Confidence Models

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SUNNY: A New Algorithm for Trust Inference in Social Networks Using Probabilistic Confidence Models Ugur Kuter Jennifer Golbeck Department of Computer Science and College of Information Studies, Institute of Advanced Computer Studies, University of Maryland, College Park, University of Maryland, College Park, College Park, MD 20742, USA College Park, MD 20742, USA jgolbeck@umd.edu ukuter@cs.umd.edu available, as well as a measure of confidence in the com- puted trust value. Given a social network, existing inference algorithms either compute only trust, or conflate trust and confidence, yielding erroneous and ambiguous inferences. As an example, consider the network in Figure 1 which de- picts a network with trust values on a 0 to 1 scale. When making a recommendation to A, one may be inclined to de- crease the recommended trust value for H because it is de- Figure 1: A sample social network with trust values (on a rived from nodes who are not trusted much and the path from 0-1 scale) as edge labels. A to H is long. However, this is an incorrect approach since there is no way to tell if we are very certain that H should be trusted at that recommended level, or if we believe H is Abstract more trustworthy but simply do not have confidence in the In many computing systems, information is produced and sources of that information. The result of an algorithm that processed by many people. Knowing how much a user trusts merges trust and confidence is not a trust value, but rather a a source can be very useful for aggregating, filtering, and or- new variable that is an amalgamation of the two concepts. dering of information. Furthermore, if trust is used to support decision making, it is important to have an accurate estimate In this paper, we describe a new approach that gives an of trust when it is not directly available, as well as a measure explicit probabilistic interpretation to confidence in social of confidence in that estimate. This paper describes a new trust networks. Our contributions are as follows: approach that gives an explicit probabilistic interpretation for confidence in social networks. We describe SUNNY, a new trust inference algorithm that uses a probabilistic sampling • A formal representation mapping that takes a trust net- technique to estimate our confidence in the trust information work and produces a Bayesian Network suited for approx- from some designated sources. SUNNY computes an esti- mate of trust based on only those information sources with imate probabilistic reasoning. This mapping also gener- high confidence estimates. In our experiments, SUNNY pro- ates a probabilistic model for the result Bayesian Net- duced more accurate trust estimates than the well known trust work, using similarity measures computed over the pre- inference algorithm T IDALT RUST (Golbeck 2005), demon- vious decisions of the entities in the input trust network. strating its effectiveness. • A new algorithm, called SUNNY, for trust inference based on probabilistic confidence models. To the best of Introduction our knowledge, SUNNY is the first trust inference algo- Trust is used in different ways in a variety of systems. Social rithm that includes a confidence measure in its compu- trust is emerging as interesting and important, but it is as yet tation. SUNNY performs a probabilistic logic sampling not well understood from a computational perspective. As procedure as in (Kuter et al. 2004) over the Bayesian Net- with all social relationships, it is difficult to quantify trust work generated by our representation mapping. In doing and its properties are fuzzy. Still, developing methods for so, it computes estimates of the lower and upper bounds accurately estimating trust between people is important for on the confidence values, which are then used as heuris- the future of many systems; it holds promise for improving tics to generate the most accurate estimates of trust values Web policy systems, as a component of provenance in scien- of the nodes of the Bayesian Network. tific workflows and intelligence databases, and as a value for • An experimental evaluation of SUNNY in comparison filtering, ordering, and aggregating data in many domains. to the well-known existing work on TidalTrust (Gol- If trust is being used to support decisions, it is important beck 2005). Our experiments show that SUNNY signif- to have an accurate estimate of trust when it is not directly icantly outperforms T IDALT RUST in the commonly-used FilmTrust social network.

Background in A then x is in PARENTS(x0 ). x is a terminal variable in We use the usual definitions for social trust networks as in B, if PARENTS(x) is the empty set. (Golbeck 2005). We define a social domain S as a tuple Each variable x in B is associated with a conditional of the form (N, E, R, D). N is a finite set of information- probability table (CPT), which describes the conditional processing nodes (or IP nodes, for short). For example, in probability of x being T RUE (or FALSE) given its parents. social environments, an IP node corresponds to a person; Note that if PARENTS(x) = {x1 , x2 , . . . xk } then the con- on the Semantic Web, an IP node may also correspond to ditional probability table associated with x has 2k entries a Web service, a database, or any entity on the Web that for each possible combination of the truth values for each of takes information as input from other entities, processes that its parents. If x is a terminal variable in B, then the con- information, and relays it to other entities. ditional probability table associated with x specifies the a In S, E is a finite set of information elements and R is priori probabilities of x being T RUE or FALSE. an interval of the form [0, r], for some predefined positive We make the usual conditional independence assumption number r. A decision by an IP node n is an assignment of a in Bayesian Networks: given PARENTS(x), x is condition- number from R to an information element e ∈ E. Thus, D, ally independent from rest of the variables in B. That is, the decision function of S, is a function defined as whether the computation of the probability that x will be T RUE or FALSE depends only on the truth values of x’s par- D : N × E → R. ents and on no other state variable in B. If D(n, e) = 0 then n does not have a decision over e. Modeling Confidence in Social Networks As an example, consider a social domain in which peo- ple make decisions over the ratings of a predefined set of We now describe a probabilistic interpretation of confidence movies. In this setting, N is the set of all people who partic- in a given trust network T and a way to compute a proba- ipate in such decisions and E is the set of all of the possible bilistic confidence model C for T . The next section describes movies that can be considered by the participants. If a per- a simple method that takes the trust network T and its con- son n makes a decision about a movie e, then D(n, e) 6= 0, fidence model C, and generates a Bayesian Network B such and it is the rating that n has assigned to e. that B structurally corresponds to T and is used for approx- A trust network is a directed graph T = (S, V, α), where imate probabilistic reasoning to assist trust computation. S = (N, E, R, D) is the social domain in which T is de- Let S = (N, E, R, D) be a social domain, and n and fined, V is the value function, and α > 0 is the maximum n0 be two IP nodes in N . We define the confidence that possible absolute value of trust that appears in T . Intuitively, n has in n0 as n’s belief on the correctness of information the value function V describes the weights of the trust rela- provided by n0 . We model the confidence of n for n0 as the tions between the IP nodes in the network. Formally, V is a conditional probability P (n|n0 ) defined as follows: given function defined as that n0 conveys some information to n, the probability that n believes in the correctness of that information is P (n|n0 ). V : N × N → [0, α]. A confidence model C for the trust network T = (S, V, α) is the set of conditional probabilities as above such that C If V (n, n0 ) = 0 for two IP nodes n, n0 ∈ P , then there is no specifies P (n|n0 ) for every pair of (n, n0 ) in T such that direct trust relation (i.e., no edge) between n and n0 ; i.e., we V (n, n0 ) 6= 0; i.e., if there is an arc from n to n0 in T . have no knowledge about whether n trusts n0 or not. A confidence model for T can usually be generated in two We say that an IP node n is an T-ancestor of n0 , if there ways. First is to take the confidence model as input from a exists a directed path in the trust network T that starts at n “domain expert.” This is the assumption made by most prob- and ends in n0 . Similarly, n0 is a T-descendant of n in T . abilistic reasoning and planning systems in the literature (see A trust inference problem is a triple (T, n0 , n∞ ), where (Russell & Norvig 2003; Boutilier, Dean, & Hanks 1999) for T = (S, V, α) is a trust network, and n0 and n∞ are the two excellent surveys on these topics). source and the sink nodes in T , respectively. A solution to The second way to obtain a confidence model for T is a trust-inference problem is a trust value 0 < t ≤ α that to use approximation techniques such as statistical sam- describes the amount of trust that the source has for the sink pling and/or profile similarity measures. (Golbeck 2006) in T . If there is no solution, then the amount of trust that the described how a combination of profile similarity measures source has for the sink remains unknown. reflect social opinions more accurately than overall similar- We use the usual definitions for Bayesian Networks as ity alone. Assume that all D(n, e) are in the 0 to 1 range, in (Pearl 1988). A Bayesian Network is a directed acyclic where n is an IP node and e is an information element. The graph B = (X, A), where X is the set of state variables and three profile features identified in (Golbeck 2006) were: A is the set of arcs between those nodes. Each variable in X describes a set of possible logical relations in the world. We 1. Overall Difference (Θn,n0 ): Given the decisions that n assume in this paper that each state variable in X is Boolean, and n0 have made in common in the past (i.e., the set of with the two possible truth values T RUE and FALSE. If there values D(n, e) and D(n0 , e) for all information items e is an arc x → x0 in A, such that x, x0 ∈ X, then this means such that D(n, e) 6= 0 and D(n0 , e) 6= 0), Θn,n0 is mea- that the truth value of x0 depends on the truth value of x. sured as the average absolute difference in their D values. The parents of a variable x in B is the set of variables, 2. Difference on extremes (χn,n0 ): A decision D(n, e) is denoted as PARENTS(x), such that if there is an arc x → x0 considered extreme if it is in the top 20% or the bottom

20% of the overall decisions made by n. χn,n0 is com- Procedure G ENERATE BN(T, n0 , n∞ ) puted as the average absolute difference on this set. K ← the immediate neighbors of n∞ in T K0 ← ∅ 3. Maximum difference (∇n,n0 ): The single largest dif- while K 6= K 0 and n0 6∈ K do ference on the same decision made by two IPs (i.e., K 0 ← K; K 00 ← ∅ max{(D(n, e) − D(n0 , e))}, ∀e such that D(n, e) 6= 0 while K 00 6= K do and D(n0 , e) 6= 0). K 00 ← K To indicate belief or disbelief, we define a coefficient K ← K ∪ W EAK P RE I MG(K, T ) σn,n0 in the range -1 to +1 such that if σ(n, n0 ) > 0, then the K ← P RUNE -S TATES(K) if n0 ∈ K then return K conditional probability P (n|n0 ) denotes the amount of be- return FAILURE lief of n in the information provided by n0 (i.e., the amount of the causal supportive influence that the information from Figure 2: The algorithm for generating a Bayesian Network, n0 has on n’s decisions). Otherwise, P (n|n0 ) denotes the given a trust network T and two nodes, n0 and n∞ , that are amount of disbelief of n in the information provided by n0 the source and the sink in T , respectively. (i.e., the amount of inhibitory influence that the information from n0 has on n’s decisions). We compute σn,n0 as follows. If Θn,n0 is more than one a variant of backward breadth-first search over the nodes of standard deviation above the mean Θ, then the IPs should T towards the source. The basis of this backward search is be considered to generally disbelieve in one another, so a weak preimage computation, which was originally devel- σn,n0 = −1. If Θn,n0 is more than one standard deviation oped and used in a number of automated AI planning algo- below the mean, then the IPs should be considered to gen- rithms (Cimatti et al. 2003). Formally, the weak preimage erally believe in one another, so σn,n0 = 1. When Θn,n0 is of a given set of nodes, say K, in a trust network T in the within one standard deviation of the mean, it is not as clear context of our representation mapping is defined as follows: whether there is belief or disbelief. In these cases, we used as a multiplier the Pearson correlation coefficient (ρ) over all W EAK P RE I MG(K, T ) = {n | n is a node in T , n 6∈ K, common decisions made by n and n0 : σn,n0 = ρ. The result is Equation 1. Note that weights wi may n0 ∈ K and V (n, n0 ) 6= 0}. vary from network to network. The weight assignment Intuitively, a W EAK P RE I MG of a set K of nodes in a trust (w1 , w2 , w3 , w4 ) = (0.7, 0.2, 0.1, 0.8) followed from our network contains each node n that is not in K and that has a experiments and also provided the best results (Golbeck direct trust relation with some node n0 in K. 2006). The backward breadth-first search does successive σij |1 − 2(w1 Θn,n0 + w2 ∇n,n0 + w3 χn,n0 )|, W EAK P RE I MG computations starting from the leaf nodes 0 1 B B if χn,n0 exists C C in L. The search stops when there no new nodes left to be 0 P (n|n ) = B B C C visited. This generates a subnetwork of the original trust B @ σij |1 − 2(w4 Θ 0 + (1 − w4 )∇ 0 )|, C network T in which every possible path is guaranteed to end in T ’s sink node. However, the generated subnetwork A n,n n,n otherwise may contain redundant nodes that are not reachable from the (1) source as well as cyclic paths. Since such redundant nodes In the next section, we will use the above formula for and cyclic paths will not provide any new social information computing confidence values (i.e., a conditional probabili- to the source node in determining its trust value of the sink, ties of belief and disbelief) between two information pro- we perform a forward search in the result network in order to cessors are already connected in the network. eliminate the redundancies and cycles. The P RUNE -S TATES subroutine in Figure 2 implements this forward search. A Bayesian Network Formulation of Trust After the redundancies are eliminated, there may be some Inference Problems nodes in the network that loose their connection to the Given a trust inference problem (T, n0 , n∞ ), we construct sink node, and therefore, become redundant. To identify BT = (X, A), a Bayesian Network that is suited for ap- and eliminate those nodes, G ENERATE BN successively per- proximate probabilistic confidence reasoning as follows. forms the W EAK P RE I MG and the P RUNE -S TATES compu- Let L be the set of nodes in T such that for each node n ∈ tations, until there are no redundant and cyclic nodes left in L, V (n, n∞ ) 6= 0 and n is a T -descendant of n0 , where n0 the network. At this point, if the source node is in set K of and n∞ are the source and the sink nodes in T . Intuitively, visited nodes, then G ENERATE BN returns the set K. Oth- the set L contains each n node in T that (1) has some direct erwise, it returns FAILURE since there is no trust connection trust information about the sink in T and (2) can relay that between the source and the sink in the trust network T . information to the source. The nodes in K returned by G ENERATE BN and the edges We compute the set N of nodes in BT as follows (see between those nodes constitute the Bayesian Network BT the G ENERATE BN pseudocode in Figure 2 for this proce- as follows. For each node n in K, we define a Boolean dure). The nodes in L described above correspond to the variable x that denotes the logical proposition that whether leaf variables in BT ; i.e., each n in L does not have any n believes in the sink node n∞ . In BT , X is the set of such parents in BT . Starting from the nodes in L, we perform logical propositions. A is the set of all of the edges between

Procedure SUNNY(T, n0 , n∞ ) trust computation or not. During its computation, SUNNY BT ← G ENERATE BN(T ) considers three types of decisions for a leaf node: include, for every leaf node n in BT do exclude, and unknown. Including a leaf node means that decision[n] ← U NKNOWN the trust information coming from that leaf node about the hP⊥ (n0 ), P> (n0 )i ← S AMPLE -B OUNDS(BT ) sink will be considered in the trust inference; otherwise, it for every leaf node n in BT do will not be considered since SUNNY will have a low con- set the lower and upper probability bounds such that P⊥ (n) = P> (n) = 1.0 fidence in that trust information. An unknown decision on a hP⊥0 (n0 ), P>0 (n0 )i ← S AMPLE -B OUNDS(BT ) leaf node means that SUNNY has not decided yet whether if |P>0 (n0 ) − P> (n0 )| < and |P⊥0 (n0 ) − P⊥ (n0 )| < to include or to exclude that node in its operation. then decision[n] ← T RUE SUNNY uses a probabilistic logic sampling technique in else decision[n] ← FALSE order to compute the confidence value of the source n0 in return ( C OMPUTE -T RUST(BT , decision) ) the sink n∞ in BT . A probabilistic logic sampling algo- rithm runs successive simulations over a Bayesian Network Figure 3: SUNNY, the procedure for computing trust and and samples whether each variable is assigned to T RUE or confidence in a trust network. FALSE (Henrion 1988). In SUNNY, we used a variant of probabilistic logic sampling described in (Kuter et al. 2004), with the following difference. In their sampling procedure, the nodes in K, with the directions of those edges reversed.1 Kuter et al. use a complex probabilistic approximation rule Then, we use Equation 1 of the previous section in order to for reasoning about the dependencies between the parents compute the conditional probabilities for every edge in BT . of a node that are not explicitly modeled in the network as Note that G ENERATE BN aggressively eliminates nodes well as for reasoning about unmodeled (i.e., hidden) nodes and edges from the original network, which may result in in the underlying Bayesian Network. In a social trust con- the elimination of certain acyclic paths as well. This aggres- text, we usually do not have complex unseen implicit depen- sive strategy guarantees the elimination of all possible cy- dencies nor hidden nodes since the trust information flows cles in trust networks with complicated structures, in order through the existing links between the existing nodes in the to create a Bayesian Network (i.e., a directed acyclic graph). network. Thus, our sampling algorithm does not include However, as our experimental evaluation in the subsequent these aspects; instead as an approximation rule, it simply sections demonstrate, this does not have any significant ef- uses a standard Noisy-OR computation (Pearl 1988). fect on the accuracy of the trust computation: our algorithm In Figure 3, the S AMPLE -B OUNDS subroutine performs was able to outperform the well-known T IDALT RUST algo- our probabilistic sampling procedure, which provides a way rithm, despite its aggressive edge elimination. to estimate the lower and upper bounds, P⊥ (n) and P> (n), Note also that the Bayesian Network generated as above on the confidence value of a node n. The lower and upper do not necessarily model a complete joint probability distri- bounds P⊥ (n) and P> (n) for a leaf node n is simply 0.0 bution, as one would expect from a standard Bayesian Net- and 1.0, respectively, if SUNNY decides to mark the node work. This is due to two reasons: (1) the network generated n as unknown. For include and exclude decisions, SUNNY above does not include all of the parents of a node since we sets the bounds to both 1.0’s and both 0.0’s, respectively. are aggressively eliminating nodes during its construction, The bounds P⊥ (n) and P> (n) for an intermediate node and (2) Equation 1 that we use for computing a confidence n is computed based on the current estimates of the lower model does not compute a full CPT, but only the conditional and upper bounds computed for the parents of n during probabilities between pairs of nodes. the probabilistic sampling process. In each simulation, S AMPLE -B OUNDS samples all of the parents of n before it SUNNY processes n. This way, the procedure always knows the truth values on the parents of a node n at the point it attempts to Figure 3 shows the pseudocode of the SUNNY procedure sample n, and therefore, for each parent ni of n, the con- for computing the confidence and trust values in a trust net- ditional probability P (n|ni ) can easily be determined from work. The input for the procedure is a trust-inference prob- the input confidence model. lem (T, n0 , n∞ ). With this input, SUNNY first generates For each intermediate node n, S AMPLE -B OUNDS proba- the Bayesian Network BT that corresponds to T using the bilistically samples two cases: (1) the case where n is T RUE G ENERATE BN procedure described above. SUNNY then with minimum probability and (2) the case where n is T RUE generates estimates of the lower and upper bounds on the with the maximum probability. The minimum and the max- confidence values of each node in BT in the sink node. imum probabilities that n is T RUE are computed using the SUNNY uses these estimates to make a decision on each conditional probabilities between n and its parents, and the leaf node in BT whether to include that node in the final truth values of each of the parent’s minimum and maximum 1 case. Note that, this is a recursive definition: at a leaf node, Note that it is correct to have the reverse edges in BT ; when there is a trust relation in T between two nodes n and n0 is rep- the minimum and maximum cases are sampled by using the resented as n → n0 , denoting “n knows n0 with some amount of confidence bounds that depends on S AMPLE -B OUNDS’s de- trust”, then the information flows from n0 to n, when we are com- cision on that node, as described above. puting trust values. Thus in BT , the reverse edge n ← n0 captures S AMPLE -B OUNDS keeps a counter for both minimum the correct direction of this information flow. and maximum case at each intermediate node, which are ini-

tialized to 0 at the very beginning of the sampling process. Table 1: The comparisons between the accuracies of If, in this simulation, the algorithm samples that n is T RUE SUNNY and T IDALT RUST on the FilmTrust network. in the minimum and/or in the maximum case, then the cor- responding counters are incremented. At the end of the suc- Algorithm Average Error Std. Dev cessive simulations, the counter values associated with each T IDALT RUST 1.986 1.60 node are divided by the total number of simulations in or- SUNNY 1.856 1.44 der to compute the estimates for the lower and upper bounds P⊥ (n) and P> (n). SUNNY uses the lower and upper bounds computed these ratings to compute confidence values as described in by the S AMPLE -B OUNDS subroutine as follows. First, the previous sections. Because it is publicly accessible on SUNNY invokes S AMPLE -B OUNDS with no decisions the Semantic Web, the FilmTrust network is a commonly made (i.e., every leaf node in BT is marked U NKNOWN). used data set for this type of analysis. This invocation produces a lower and an upper bound on the There are 575 people actively participating in the confidence of the source, which are essentially the minimum FilmTrust social network, with an average degree of 3.3. and the maximum possible confidence values, respectively. Each pair of users connected in the network shared an av- Then, SUNNY uses these bounds in a hill-climbing search erage of 7.6 movies in common. When pairs of users had no in order to actually finalize a decision on whether to include movies or only one movie in common, there was not suffi- or exclude a leaf node in the trust computation. More pre- cient information to compute confidence from similarity. In cisely, SUNNY invokes S AMPLE -B OUNDS for each leaf these cases, we scaled the trust value to a −1 to 1 scale and node n with the a priori probabilities on both of the bounds used the sign of that value as our belief/disbelief coefficient over n set to 1.0. If this invocation of S AMPLE -B OUNDS and the unsigned value as the confidence value. produces minimum and maximum possible confidence val- To gauge the accuracy of the trust inference algorithms, ues within an error margin of the ones computed before, we selected each pair of connected users, ignored the rela- then n should be included in the final trust computation, tionship between them, and computed the trust value. We since the source has these confidence bounds when it con- then compared the computed value to the known trust value siders the information coming from n. Otherwise, n should and measured error as the absolute difference. We per- be excluded from the final trust computation. formed this process for every connected pair of users in the Once the decisions on all of the leaf nodes of BT has been network where there were other paths connecting them. If made, SUNNY computes the trust value for the source by there is no path between users beside the direct connection, performing a backward search from the leaf nodes of BT it is impossible to make a trust computation from the net- towards the source. In Figure 3, C OMPUTE -T RUST subrou- work, and these pairs are ignored. In total, 715 relationships tine performs the backward search. At each iteration during were used in this evaluation. this search, the trust value of a node is computed based on As shown in Table 1, the average error for SUNNY is the trust values between that node and its immediate par- 6.5% lower than the average error for T IDALT RUST. A stan- ents and the trust values of the parents in the sink node that dard two-tailed t-test shows that SUNNY is significantly are already computed in the search. Although there are sev- more accurate than T IDALT RUST for p < 0.05. While accu- eral ways to combine these two pieces of trust information, racy will vary from network to network due to variations SUNNY uses the same weighted-averaging formula used in structure, users’ ratings, and confidences, these results in the T IDALT RUST algorithm, as we used that algorithm in demonstrate that SUNNY is an effective algorithm for com- our experiments with SUNNY described in the next section. puting trust in social networks. Experimental Evaluation Related Work Because SUNNY is the first trust inference algorithm that includes a confidence measure in its computation, there is (Pearl 1988) provides a comprehensive treatment of network no existing work against which the confidence component models of probabilistic reasoning. A probabilistic network can be judged. However, for both values to be useful the model defines a joint probability distribution over a given computed trust value must be accurate. We computed the set of random variables, where these variables appear as the accuracy of the trust values and compared them against the nodes of the network and the edges between these nodes de- performance of T IDALT RUST. T IDALT RUST is one of sev- note the dependencies among them. One widely-known net- eral well-known localized trust computation algorithms, and work model that we exploited in this work is Bayesian Net- previous work has shown it to perform as well as or better works (Pearl 1988). Bayesian networks are directed acyclic than its peer algorithms. graphs in which the arcs denote the causal and conditional We used the FilmTrust network as the data source for dependencies among the random variables of the probabilis- our experiments. FilmTrust2 is a social networking web- tic model. The inference mechanisms in Bayesian Networks site where users have assigned trust values to their relation- are due to Bayesian Inference, which provides an incremen- ships. Users also rate movies in the system, and we used tal recursive procedure to update beliefs when new evidence about the input probabilistic model is acquired. 2 Probabilistic Logic Sampling (Henrion 1988) is a tech- Detailed information on FilmTrust is available at http://trust. mindswap.org nique for performing stochastic simulations that can make

probabilistic inferences over a Bayesian Network with an trust as a prioritization tool for default logics. We plan to arbitrary degree of precision controlled by the sample size. integrate our approach into this syndication system to study It runs successive simulations to estimate the probabilities of the use of the confidence values as well as the effectiveness the nodes of a given Bayesian Network. As we run more and of trust for this sort of prioritization. more simulations, the estimates of the probability of each variable get progressively more accurate, and it is shown in Acknowledgments (Henrion 1988) that these estimates converge to the exact This work, conducted at the Maryland Information and Net- probability values in the limit. However, in practice, usually work Dynamics Laboratory Semantic Web Agents Project, a termination criterion is used to determine the number of was funded by Fujitsu Laboratories of America – Col- simulations (e.g., until the residual of every node becomes lege Park, Lockheed Martin Advanced Technology Labora- less than or equal to an epsilon value > 0 or until an upper tory, NTT Corp., Kevric Corp., SAIC, the National Science bound k on the number of simulations is reached). Foundation, the National Geospatial-Intelligence Agency, While there are no algorithms in the literature on social DARPA, US Army Research Laboratory, NIST, and other networks that compute both trust and confidence values (i.e., DoD sources. probabilistic belief models), there are several algorithms for computing trust. A thorough treatment can be found in (Gol- References beck 2005). The T IDALT RUST algorithm that we used in our experimental evaluation of SUNNY is one of several algo- Boutilier, C.; Dean, T. L.; and Hanks, S. 1999. Decision- rithms for computing trust in social networks and we chose theoretic planning: Structural assumptions and computa- it for our comparison because, like SUNNY, it outputs trust tional leverage. Journal of Artificial Intelligence Research ratings in the same scale that users assign them, and the val- 11:1–94. ues are personalized based on the user’s social context. Cimatti, A.; Pistore, M.; Roveri, M.; and Traverso, P. Trust has also been studied in the area of peer-to-peer sys- 2003. Weak, strong, and strong cyclic planning via sym- tems. Among others, (Wang & Vasilleva 2003) describes a bolic model checking. Artificial Intelligence 147(1-2):35– Bayesian Network based model of trust in peer-to-peer sys- 84. tems, where a naive Bayesian Network model is used to de- Golbeck, J. 2005. Computing and Applying Trust in Web- scribe the trust relations between two agents (i.e., informa- based Social Networks. Ph.D. Dissertation, University of tion processors in our context) and use a “small-world as- Maryland, College Park, MD, USA. sumption” that enables an agent to keep its decisions based Golbeck, J. 2006. Trust and nuanced profile similarity in on the trust values for only its local neighborhood of other online social networks. In MINDSWAP Technical Report agents. In this paper, on the other hand, we focused on the TR-MS1284. propagation of confidence (i.e., belief) and trust values over the entire network of information processors and used con- Henrion, M. 1988. Propagating uncertainty in bayesian fidence models to guide such a propagation to make it more networks by probabilistic logic sampling. In Uncertainty efficient and accurate. In future, we are intending to investi- and Artificial Intelligence II. Elsevier North Holland. gate to generalize our trust computation techniques by incor- Katz, Y., and Golbeck, J. 2006. Social network-based trust porating Bayesian Network-based models for trust values. in prioritized default logic. Proceedings of the Twenty-First National Conference onArtificial Intelligence (AAAI-06). Conclusions and Future Work Kuter, U.; Nau, D.; Gossink, D.; and Lemmer, J. F. 2004. When using social trust in many applications, it is important Interactive Course-of-Action Planning using Causal Mod- to have an accurate estimate of trust when it is not directly els. In Third International Conference on Knowledge Sys- available, as well as a measure of confidence in the com- tems for Coalition Operations (KSCO-2004). puted value. In this work, we have introduced a probabilistic Pearl, J. 1988. Probabilistic Reasoning in Intelligent Sys- interpretation of confidence in trust network, a formal rep- tems: Networks of Plausible Inference. San Fransisco, CA: resentation mapping from Trust Networks to Bayesian Net- Morgan Kaufmann. Chapters 2-3. works, and a new algorithm, called SUNNY, for computing Russell, S., and Norvig, P. 2003. Artificial Intelligence, A trust and confidence in social networks. In direct compar- Modern Approach (Second Edition). Upper Saddle River, isons, SUNNY was shown to significantly outperform the NJ: Prentice-Hall. well-known T IDALT RUST trust inference algorithm in terms of the accuracy of the computed trust values. Wang, Y., and Vasilleva, J. 2003. Bayesian Network-Based As future work we plan to integrate SUNNY into a work- Trust Model. In IEEE/WIC International Conference on ing application to evaluate its effectiveness. We are involved Web Intelligence, 372. IEEE Computer Society. in a project with the goal of developing a semantically rich web-based syndication framework. When matching queries over streaming news feeds, often times conflicting informa- tion will enter the knowledge base. If the source of each fact is known, trust can be used to prioritize information and select the most trusted of the inconsistent facts to include. Earlier work (Katz & Golbeck 2006) illustrated the use of

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