Time sensitive sequential myopic information gathering

Time Sensitive Sequential Myopic Information GatheringChiu-Che Tseng Department of Computer ScienceEngineering University of Texas at Arlington Arlington, Texas 76011tseng@Piotr J. Gmytrasiewicz Department of Computer ScienceEngineering University of Texas at Arlington Arlington, Texas 76011piotr@AbstractDIGS (Decision Support Information Gathering System) uses the value of information to guide the information gathering process and uses the gathered information to provide the decision recommendations to the human users. DIGS uses an influence diagram as a modeling tool. In this paper, we create a model to represent the investment scenario of a novice stock investor. By using the sequential myopic information gathering technique, DIGS generates a sequence of information gathering actions. The actions are dependent on each other in that the action DIGS executes at time t1will be based on the results of the pervious action at time t0. DIGS also employs a stopping mechanism for the information gathering actions based on the information value and time constraints. Thus, DIGS can be used as an anytime system. Compared to a pre-generated sequence of actions, our technique has the flexibility to react to the gathered information, and to use it to guide the subsequent gathering actions. Therefore, our system can adapt to the newly acquired information and avoid the computational complexity of planning the series of actions in advance.1. IntroductionAn influence diagram is a compact representation emphasizing the qualitative features of decision problem [13]. We describe a Decision Support Information Gathering System (DIGS) that uses influence diagrams as models of the decision-making situations of the user, and suggests to the user how best to retrieve information related to his or her decision situations. Thus, we assume that a user is engaged in making a decision, and that there are many alternative information sources that can be used to aid this process. Since the information may not be available for free, and it may take substantial time to deliver the information to the user, our system evaluates beforehand whether consulting an information source, such as a WWW page, is worthwhile. Furthermore, in order to take advantage of multiple information sources, we develop an information gathering strategy to execute a sequence of information gathering actions to better aid the user’s decision making process.Recent approaches for the similar problem include Matheson (1990), Jensen and Dittmer (1997), Jensen and Liang (1992); their approaches concentrate on the obtaining the most valuable test to perform. Horvitz, et al. (1993), present an approach that deals with the time critical information display. Zilberstein and Lesser (1996) use nonmyopic approach for gathering small amounts of information. In this paper, we describe a method that combines the temporal cost, which is an important factor in time critical domain such as stock market, with the information value theory to guide the information gathering process. Our paper proposes a sequential myopic strategy that incorporates the temporal cost of the information accessing delay using influence diagram. We use this strategy to overcome the infeasible nonmyopic approach and the inaccuracy of decision making based on the query result from one single information source. We apply the sequential myopic strategy to the information gathering process and demonstrate the idea using a simple stock investor application.To accomplish its task, DIGS has to consider the following factors.Information costs. Some information providers may charge for the information provided either per line or pertuple. The system has to calculate the cost of the information gathering and keep it within the user’s budget. Moreover, the system needs the cost of information in order to determine if it is worthwhile to continue the information gathering process.Time constraint. In realistic situations, say financial or defense-related, the quality of decisions deteriorates with time delay. Once an opportunity is missed, one may not be able to take advantage of the situation again. The system has to be able to perform its duty under these time constraints, which means that the system has to gather the information and present it to the human user before it is too late.Quality of the information. The information providers seldom can provide perfect information regarding the situation at hand. The information often contains some degree of uncertainty and inaccuracy. The system has to be able to assess and reason with the reliability of the information it can expect from a given source.DIGS uses the notion of value of information, as defined in decision theory, to guide the information gathering process, and is able to provide the user with the decision suggestion. The system’s five major modules are shown in Figure 1.Knowledge base- contains the information aboutthe information sources.User model - stores a library of influence diagramsthat represent the human decision models.Strategy module – produces the sequentialinformation gathering strategy.Executor- performs actual information gatheringactions.Interface - provides communication with the human user.Figure 1. Decision Support Information GatheringSystemIn the remainder of this paper, Section 2 provides some background on the influence diagram; Section 3 addresses the basic value of information theory and the time sensitive myopic strategy. Section 4 gives the description of each module in the system. Section 5 illustrates the implementation of the time sensitive sequential information gathering using a novice stock investor example. Section 6 contains conclusions and some future enhancements.2. Influence DiagramsThe Decision Support Information Gathering System (DIGS) uses influence diagrams as models of the decision-making situation of the user. An influence diagram can be viewed as a Bayesian network with decision and utility nodes, where the value of each decision variable is not determined probabilistically, but rather is computed to meet some optimization objectives.Influence diagrams are extensions of Bayesian networks, introduced by Howard and Matheson [13], with three types of nodes – chance nodes, decision nodes and utility nodes. Chance nodes, usually shown as ovals, represent random variables in the environment. The decision nodes, usually shown as squares, represent the choices available to the decision-maker. Utility nodes, shown as diamond or flattened hexagon shapes, represent the usefulness of the consequences of the decisions measured on a numerical scale called utility. The arcs in the graph have different meanings based on their destinations. The arcs that point to the utility or chance nodes are dependency arcs that represent probabilistic or functional dependence. The arcs that point to the decision nodes are informational arcs; they imply that the parent nodes will be known to the decision-maker before the decision is made.There are several methods for determining the optimal decision policy from an influence diagram. One, by Howard and Matheson [13], consists of converting the influence diagram to a decision tree and solving for the optimal policy within the tree, using the exp-max labeling process. Another, by Shachter [14], consists of eliminating nodes from the diagram through a series of value preserving transformations. Each transformation leaves the expected utility intact, and at every step the modified graph is still an influence diagram. Shachter proved that the transformation does not affect the optimal decision policy and the expected value of the optimal policy. Pearl [10] has suggested a hybrid method using branch and bound technique to prune the search space of the converted decision tree from the influence diagram.3. Sequential Myopic Strategy Approach3.1 Value of Imperfect InformationBefore performing an information gathering task,DIGS uses the values of imperfect information to decide which information are worth retrieving. The system uses an influence diagram, described further in Section 4, to calculate the net value of retrieving imperfect information for each information source in the diagram.Suppose that the current information available is C,which can be represented as belief regarding the values of the different random variables (chance nodes) in the influence diagram. Let Result i (A) be the i-th possible outcome of the user’s action A. The current best action,a , is one with the highest expected utility computed with information C:EU(a |C)=Amaxi∑U(Result i (A))P(Result i (A)|C,Do(A))(1)Now consider the situation in which the user can get additional information that will provide some evidence,X n . The value of the best action a Xn after obtaining the evidence X n is:EU(a Xn |C,X n )=Amaxi∑U(Result i (A)) ×P(Result i (A)|C, X n ,Do(A)))(2)But X n is a random variable whose value is currently unknown, so we must average over all possible value X n kthat we might discover for X n , using system’s current belief about its value. The Value of Information (VI) on node Xn is:VI(X n ) = (∑kP(X n =X n k |C)EU(a Xn k |C, X n =X n k )) -EU(a |C)(3)The VI is the value of the perfect information but,interestingly, it can be made to express the value originated from unreliable information sources (see section 5).Another effect that we must consider is the cost. The cost function of the investor domain can be viewed as a combination of two sub costs. One is the monetary cost, the actual price we have to pay for the information, and the other one is the opportunity cost, or the temporal cost. The temporal cost is the cost of delaying action in a possibly urgent situation the decision-maker is in. For example, to consult the Charles Schwab’s SchwabNOW Online Investments one is charged $6 per report, but getting the report andreasoning about its results takes time during which the investor might be losing money. In section 3.3, we describe how to calculate the temporal cost in more detail.We define the net value of retrieving imperfect information, NVI, to be:NVI(Xn) = VI(Xn) – C Xn(4)C Xn = CM Xn + CT Xn(5)Where C Xn is the total cost, CM Xn is the monetary cost of source Xn and CT Xn is the temporal cost of source Xn.3.2 Sequential Myopic StrategyIn order to produce a sequence of information gathering actions, the system should consider all possible ordered sequences of such actions. This, however, is intractable. Therefore, myopic strategy that gathers information one at a time can avoid the burden of the nonmyopic approach. There has been some investigation of the accuracy of the myopic strategy; Kalagnanm and Henrion [7] showed that a myopic policy is optimal when the decision maker’s utility function is linear, and the relationship between hypotheses and evidence is deterministic. Gorry [6] demonstrated that the use of a myopic approach does not significantly diminish the diagnostic accuracy of an expert system for congenital heart disease.For the information gathering task, we use the sequential myopic approach as a way to avoid the computational burden of the non-myopic approach and to overcome the disadvantage of not gathering enough information before making the decision. We cannot guarantee optimality since the conditions described in Kalagnanm and Henrion do not hold in our domain,however, we believe that our strategy will be a good approximation to optimality as in Gorry’s congenital heart disease example. Additional advantage is that our design functions as an anytime system that can produce a result to the human user at any point in time.The information sources are ranked according to the information value of each imperfect source. The top ranking source is used to direct the information retrieval agents that reside in the executor module of our system to perform the information retrieval task from that source. After the first information gathering action, the system can decide either to continue gathering the information from other sources or stop and give the human user decision suggestion, given the newly acquired information. In order to define a criterion for the system to stop performing information gatheringaction, we defined the value of gathering (VG). The value of gathering is defined as the maximum value of information that can be obtained from yet unexplored information sources, and is based on all of the information obtained previously. After an information gathering action is completed, the system incorporates the newly acquired information and re-calculates the net value of imperfect information for the remaining information sources.VG =EXn∉max VI(Xn|E) - C Xn , (6) where E is the previously acquired information.The system will continue to calculate and perform the information gathering action and incorporate the new information into the system to provide the human user with a more refined and accurate decision suggestion.The stopping criterion for the system is defined as VG < 0, or anytime the decision maker requests the current best decision suggestion. Thus, our system can be used as an anytime system, producing a result anytime during its operation.3.3 Temporal CostThe actual monetary cost of accessing a source of information is easily included in our system. However, in order to represent the temporal cost a number of external factors are required. Horvitz and Barry [2] and Gmytrasiewicz and Durfee [15] explored the idea of using the cost of time, or urgency, in their systems. Their approaches took the cost of time as a discount factor in their calculation, but this is not always true in the financial domain. For our stock investor example, we defined a runtime algorithm that calculates the temporal cost. The algorithm needs to constantly monitor the stock price in order to provide the information for the algorithm to perform the calculation. Our algorithm only looks back one time period due to the myopic strategy we used for the system. For a highly uncertain domain like the stock price, our algorithm provides an approximate estimation of the temporal cost, but we intend to further investigate this estimate to provide more realistic values. Temporal Cost AlgorithmFor all the information sources Xn{Trend = | stock-price(t 0)– stock-price(t -1) | /(t 0 – t –1)CT Xn = ∑iTrend × p(Process-time Xn i ) ×Process-time Xni}Here, the Trend parameter represents the positive amount of the stock price movement within some time period. The stock-price(t) is the actual stock price at time t (t0 represents the current time and t–1represents the previous time step) and the Process-time Xn i is the possible value of the sum of the information turnaround time and the time needed to include the information from source Xn into the decision-making model. Since the Process-time Xn i is not a constant due to variable network conditions, the process time is described as a probability distribution over its discretized possible values. For each information source, Xn the probability distribution of the Process-time Xn can be obtained from prior access delay time of each information source that is stored in the knowledge base module. Thus, CT Xn is the expected temporal cost for the information source Xn.4. System ModulesThe user model of DIGS uses the influence diagram as the representation for the human user’s decision model. We built the influence diagrams for the decision-making of a stock investor by consulting the human expert of the field. The model can be stored in a library contained in the knowledge base, and can be reused whenever the similar situation occurs. The model reflects the decision criteria and the attitude toward risk of the stock investor as in Figure 2. The user model requests the needed information from the knowledge base (CPTs, etc.) and outputs the additional information source query suggestions to the strategy module to form an information gathering plan. By using the information value criteria, the system will return the information from the source(s) to the user to assist the investor in making the investment decisions.The user model coordinates with the strategy module in order to provide the sequential information gathering plan for the executor to execute. The model includes the chance nodes that represent the results obtained from the investment advisor sources such as the First Call, Zacks Investment Inc., etc. that could be accessed by the system. The model also contains the external variables of the domain, the Future stock trend node that represents the future price movement of the stock. The other part of the model to be elicited was the utility model, which is used to compare possible outcomes as a function of the decisions. The utility was expressed as the monetary gain or loss to the stock investor, and it is determined by the price difference, the buy/sell decision, and the information selection decision. To represent our model in Howard canonical form [12] we used a group of deterministic nodes such as Zacks Result, etc. to represent the information query results from the chancenodes that represent the information query results, and the information selection decision node. The conditional probability tables, each associated with an information query result node, represent the accuracy of each information source. They can be obtained from the historic accuracy data for each source, and are stored in the knowledge base module. The conditional probability tables of the Price Diff node (representing the possible values of the price change for that particular stock within one week) can also be obtained from historical data, and is stored in the knowledge base module. For the probability table of the Future stock trend node, we assume uniform probability distribution for the values in that node.DIGS uses this model to choose among the information sources (e.g., Zacks Investment Inc., etc.). It also returns the retrieved information (the recommendation from the financial experts on the web) to the user in order to assist the user in making the investment decision for a certain stock.Figure 2. Novice stock investor user modelThe strategy module handles the sequential information gathering process and calculates the total cost of the gathering process (temporal cost plus monetary cost). It uses the user model described above and incorporates the newly information into it. The module is also responsible for checking the stopping criteria of the system and directs the executor module for the sequential information gathering.The knowledge base contains the information about the alternative information sources that are not directly included in the influence diagram. This includes data on the sources turnaround time, the historic prediction accuracy data of each source and their availability. It also lists the type of information the sources provide and the information needed to interact with the sources.The executor module contains the retrieval agents that are used by DIGS system to get the information from the sources. These agents are responsible for generating the visual reports from their information gathering results. The executor module then sends the report generated from the retrieval agents to the interface module.The interface module handles the interaction between the human user and the system. Further, the module displays the information that the executor module gathers and the decision suggestion from the system.5. ImplementationWe constructed the experimental prototype of the DIGS system for the financial domains using the belief network library NeticaAPI provided by the Norsys Inc., and the internet agent building platform LiveAgent Pro from AgentSoft. DIGS returns the buy/sell suggestion to the user based on the query result from the additional information source. The decision on which additional information source to query is provided by the user model. DIGS also continues to gather more information based on the method described in the previous sections, or stops the gathering process. Based on the additional information, the system suggests that the user take an appropriate action. In order to account for imperfections of information sources, we represent them as separate nodes in the network, causally connected to the node about which they provide information. The strength of this connection is the representation of the faithfulness of the information source and correlates the actual value of the node to the values reported by the information source. We have included this effect in our implementations, as depicted below, in the domain of stock investor decision-making.We tested the DIGS system using the user models described in the Section 4. Below is a run from the financial domain prototype.Novice Stock Investor ScenarioAn investor is to decide whether to invest in a certain stock. He or she wants to gather valuable (cost sensitive) and useful information before making such decision.DIGS’s model for the stock investor will be responsible for giving the best information source(s) to retrieve the information based on the current information, and the decision suggestion on whether or not to invest in the company’s stock is based on theadditionalinformation.In this run, the investor is looking at the stock of IBM. Given this information, DIGS calculated the information values for each of the additional sources (see Table 1), and suggested obtaining the information from CDAInvest. (CDA Investnet Inc.) Thus, CDA Investnet will provide the most valuable query result under this situation.Table 1. The Net Imperfect Information Value foreach sourceInformation Sources Net Value Of Imperfect InformationCDA Invest138.25SP76.529FC-10Innovest54.609Zacks120.04. In this case, the query returned the value “neutral”for the CDAInvest’s expert opinion of the IBM’s stock trend. After obtaining the information from CDAInvest, DIGS incorporates that information into user model (see Figure 3) and calculates the value of information of the remaining information sources (see Table 2). In this case, the DIGS performs the information gathering action on the next information source, which is Zacks (Zacks investment Inc.). DIGS will continue gathering the information from the information sources until the stopping criteria is met. At this point, DIGS will return a decision suggestion to the user.Table 2. The Net Imperfect Information Value forthe remaining sourcesInformation Sources Net Value Of Imperfect InformationSP 2.5847FC-10Innovest0Zacks22.7716. Conclusion and Future WorkWe presented our work on the use of myopic sequential information gathering which uses the net value of imperfect information to guide the information gathering process, and used the previously gathered information to provide the decision recommendations to the human users. Our technique provides a time sensitive myopic way to perform a sequence of information gathering actions, and provides an alternative to the traditional myopic analyses for determining the next best action to take. In our future work, we will improve on the current model of the temporal cost to represent the situation more accurately. Furthermore, we intend to expand our system to handle multiple stocks and portfolio allocation problems. 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