Information processing is the change (processing) of information in any manner detectable by an observer. As such, it is a process which describes everything which happens (changes) in the universe, from the falling of a rock (a change in position) to the printing of a text file from a digital computer system. In the latter case, an information processor is changing the form of presentation of that text file. Information processing may more specifically be defined in terms used by Claude E. Shannon as the conversion of latent information into manifest information[citation needed]. Latent and manifest information is defined through the terms of equivocation (remaining uncertainty, what value the sender has actually chosen), dissipation (uncertainty of the sender what the receiver has actually received) and transformation (saved effort of questioning - equivocation minus dissipation)[citation needed].
Within the field of cognitive psychology, information processing is an approach to the goal of understanding human thinking. It arose in the 1940s and 1950s. The essence of the approach is to see cognition as being essentially computational in nature, with mind being the software and the brain being the hardware. The information processing approach in psychology is closely allied to cognitivism in psychology and functionalism in philosophy although the terms are not quite synonymous. Information processing may be sequential or parallel, either of which may be centralized or decentralized (distributed). The parallel distributed processing approach of the mid-1980s became popular under the name connectionism. In the early 1950s Friedrich Hayek was ahead of his time when he posited the idea of spontaneous order in the brain arising out of decentralized networks of simple units (neurons). However, Hayek is rarely cited in the literature of connectionism.
In the 1970s, Abraham Moles and Frieder Nake were among the first to establish and analyze links between information processing and aesthetics.
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Monday, August 30, 2010
Monday, August 23, 2010
Value of Information
Value of information
From Wikipedia, the free encyclopedia
Jump to: navigation, search
Value of information (VOI or VoI) is the amount a decision maker would be willing to pay for information prior to making a decision.
Contents [hide]
1 Similar terms
2 Definitions
2.1 Simple
2.2 Formal
2.2.1 Standard
2.2.2 Generalized
3 Characteristics
4 Computation
5 Notes
6 Bibliography
7 See also
[edit] Similar terms
VoI is sometimes distinguished into value of perfect information, also called value of clairvoyance (VoC), and value of imperfect information. They are closely related to the widely known expected value of perfect information and expected value of sample information. Note that VoI is not necessarily equal to "value of decision situation with perfect information" - "value of current decision situation" as commonly understood.
[edit] Definitions
[edit] Simple
A simple example best illustrates the concept. Consider a decision situation with one decision, for example deciding on a 'Vacation Activity'; and one uncertainty, for example what will the 'Weather Condition' be? But we will only know the 'Weather Condition' after we have decided and begun the 'Vacation Activity'.
The Value of perfect information on Weather Condition captures the value of being able to know Weather Condition even before making the Vacation Activity decision. It is quantified as the highest price the decision-maker is willing to pay for being able to know Weather Condition before making the Vacation Activity decision.
The Value of imperfect information on Weather Condition, however, captures the value of being able to know the outcome of another related uncertainty, e.g., Weather Forecast, instead of Weather Condition itself before making Vacation Activity decision. It is quantified as the highest price the decision-maker is willing to pay for being able to know Weather Forecast before making Vacation Activity decision. Note that it is essentially the value of perfect information on Weather Forecast.
[edit] Formal
The above definition illustrates that the value of imperfect information of any uncertainty can always be framed as the value of perfect information, i.e., VoC, of another uncertainty, hence only the term VoC will be used onwards.
[edit] Standard
Consider a general decision situation having n decisions (d1, d2, d3, ..., dn) and m uncertainties (u1, u2, u3, ..., um). Rationality assumption in standard individual decision-making philosophy states that what is made or known are not forgotten, i.e., decision-maker has perfect recall. This assumption translates into the existence of a linear ordering of these decisions and uncertainties such that;
di is made prior to making dj if and only if di comes before dj in the ordering
di is made prior to knowing uj if and only if di comes before uj in the ordering
di is made after knowing uj if and only if di comes after uj in the ordering
Consider the case where the decision-maker is enabled to know the outcome of some additional uncertainties earlier in his/her decision situation, i.e., some ui are moved to appear earlier in the ordering. In such case, VoC is quantified as the highest price which the decision-maker is willing to pay for all those moves.
[edit] Generalized
The standard definition is further generalized in team decision analysis framework where there is typically incomplete sharing of information among team members under the same decision situation. In such case, what is made or known might not be known in later decisions belonging to different team members, i.e., there might not exist linear ordering of decisions and uncertainties satisfying perfect recall assumption. VoC thus captures the value of being able to know "not only additional uncertainties but also additional decisions already made by other team members" before making some other decisions in the team decision situation.
[edit] Characteristics
There are two extremely important characteristics of VoI that always hold for any decision situation;
Value of information can never be less than zero since the decision-maker can always ignore the additional information and makes decision as if such information is not available.
No other information gathering/sharing activities can be more valuable than that quantified by value of clairvoyance.
[edit] Computation
VoC is derived strictly following its definition as the monetary amount that is big enough to just offset additional benefit of getting more information. In other words; VoC is calculated iteratively until;
"value of decision situation with perfect information while paying VoC" = "value of current decision situation".
A special case is when the decision-maker is risk neutral where VoC can be simply computed as;
VoC = "value of decision situation with perfect information" - "value of current decision situation"
This special case is how expected value of perfect information and expected value of sample information are calculated where risk neutrality is implicitly assumed. For cases where decision-maker is risk averse or risk seeking, this simple calculation does not necessary yield correct result, and iterative calculation is the only way to ensure correctness.
Decision tree and influence diagram are most commonly used in representing and solving decision situation as well as associated VoC calculation. Influence diagram, in particular, is structured to accommodate team decision situation where incomplete sharing of information among team members can be represented and solved very efficiently. While decision tree is not designed to accommodate team decision situation, it can do so by augmenting it with information set widely used in game tree.
[edit] Notes
Special care is needed when the choice being made for a decision can influence how an uncertainty resolves in the future. Having a perfect or imperfect information on such uncertainty implies that the choice to be made can be inferred prior to making such choice. This circular logic is against free will principle and thus extra works are needed to represent and solve for VoI properly.
[edit] Bibliography
Detwarasiti, A. (2005). Team decision analysis and influence diagrams. Ph.D. Dissertation, Department of Management Science and Engineering, Stanford University.
Howard, R.A. (1966). Information value theory. IEEE Transactions on Systems Science and Cybernetics (SSC-2), 22-26.
Howard, R.A. and J.E. Matheson, "Influence diagram" (1981), in Readings on the Principles and Applications of Decision Analysis, eds. R.A. Howard and J.E. Matheson, Vol. II (1984), Menlo Park CA: Strategic Decisions Group.
Kuhn, H.W. (1953). Extensive games and the problem of information. Contributions to the Theory of Games II, eds. H.W. Kuhn and A.W. Tucker, 193-216.
Stratonovich, R. L. (1965). On value of information. Izvestiya of USSR Academy of Sciences, Technical Cybernetics 5, 3–12. In Russian.
Source
From Wikipedia, the free encyclopedia
Jump to: navigation, search
Value of information (VOI or VoI) is the amount a decision maker would be willing to pay for information prior to making a decision.
Contents [hide]
1 Similar terms
2 Definitions
2.1 Simple
2.2 Formal
2.2.1 Standard
2.2.2 Generalized
3 Characteristics
4 Computation
5 Notes
6 Bibliography
7 See also
[edit] Similar terms
VoI is sometimes distinguished into value of perfect information, also called value of clairvoyance (VoC), and value of imperfect information. They are closely related to the widely known expected value of perfect information and expected value of sample information. Note that VoI is not necessarily equal to "value of decision situation with perfect information" - "value of current decision situation" as commonly understood.
[edit] Definitions
[edit] Simple
A simple example best illustrates the concept. Consider a decision situation with one decision, for example deciding on a 'Vacation Activity'; and one uncertainty, for example what will the 'Weather Condition' be? But we will only know the 'Weather Condition' after we have decided and begun the 'Vacation Activity'.
The Value of perfect information on Weather Condition captures the value of being able to know Weather Condition even before making the Vacation Activity decision. It is quantified as the highest price the decision-maker is willing to pay for being able to know Weather Condition before making the Vacation Activity decision.
The Value of imperfect information on Weather Condition, however, captures the value of being able to know the outcome of another related uncertainty, e.g., Weather Forecast, instead of Weather Condition itself before making Vacation Activity decision. It is quantified as the highest price the decision-maker is willing to pay for being able to know Weather Forecast before making Vacation Activity decision. Note that it is essentially the value of perfect information on Weather Forecast.
[edit] Formal
The above definition illustrates that the value of imperfect information of any uncertainty can always be framed as the value of perfect information, i.e., VoC, of another uncertainty, hence only the term VoC will be used onwards.
[edit] Standard
Consider a general decision situation having n decisions (d1, d2, d3, ..., dn) and m uncertainties (u1, u2, u3, ..., um). Rationality assumption in standard individual decision-making philosophy states that what is made or known are not forgotten, i.e., decision-maker has perfect recall. This assumption translates into the existence of a linear ordering of these decisions and uncertainties such that;
di is made prior to making dj if and only if di comes before dj in the ordering
di is made prior to knowing uj if and only if di comes before uj in the ordering
di is made after knowing uj if and only if di comes after uj in the ordering
Consider the case where the decision-maker is enabled to know the outcome of some additional uncertainties earlier in his/her decision situation, i.e., some ui are moved to appear earlier in the ordering. In such case, VoC is quantified as the highest price which the decision-maker is willing to pay for all those moves.
[edit] Generalized
The standard definition is further generalized in team decision analysis framework where there is typically incomplete sharing of information among team members under the same decision situation. In such case, what is made or known might not be known in later decisions belonging to different team members, i.e., there might not exist linear ordering of decisions and uncertainties satisfying perfect recall assumption. VoC thus captures the value of being able to know "not only additional uncertainties but also additional decisions already made by other team members" before making some other decisions in the team decision situation.
[edit] Characteristics
There are two extremely important characteristics of VoI that always hold for any decision situation;
Value of information can never be less than zero since the decision-maker can always ignore the additional information and makes decision as if such information is not available.
No other information gathering/sharing activities can be more valuable than that quantified by value of clairvoyance.
[edit] Computation
VoC is derived strictly following its definition as the monetary amount that is big enough to just offset additional benefit of getting more information. In other words; VoC is calculated iteratively until;
"value of decision situation with perfect information while paying VoC" = "value of current decision situation".
A special case is when the decision-maker is risk neutral where VoC can be simply computed as;
VoC = "value of decision situation with perfect information" - "value of current decision situation"
This special case is how expected value of perfect information and expected value of sample information are calculated where risk neutrality is implicitly assumed. For cases where decision-maker is risk averse or risk seeking, this simple calculation does not necessary yield correct result, and iterative calculation is the only way to ensure correctness.
Decision tree and influence diagram are most commonly used in representing and solving decision situation as well as associated VoC calculation. Influence diagram, in particular, is structured to accommodate team decision situation where incomplete sharing of information among team members can be represented and solved very efficiently. While decision tree is not designed to accommodate team decision situation, it can do so by augmenting it with information set widely used in game tree.
[edit] Notes
Special care is needed when the choice being made for a decision can influence how an uncertainty resolves in the future. Having a perfect or imperfect information on such uncertainty implies that the choice to be made can be inferred prior to making such choice. This circular logic is against free will principle and thus extra works are needed to represent and solve for VoI properly.
[edit] Bibliography
Detwarasiti, A. (2005). Team decision analysis and influence diagrams. Ph.D. Dissertation, Department of Management Science and Engineering, Stanford University.
Howard, R.A. (1966). Information value theory. IEEE Transactions on Systems Science and Cybernetics (SSC-2), 22-26.
Howard, R.A. and J.E. Matheson, "Influence diagram" (1981), in Readings on the Principles and Applications of Decision Analysis, eds. R.A. Howard and J.E. Matheson, Vol. II (1984), Menlo Park CA: Strategic Decisions Group.
Kuhn, H.W. (1953). Extensive games and the problem of information. Contributions to the Theory of Games II, eds. H.W. Kuhn and A.W. Tucker, 193-216.
Stratonovich, R. L. (1965). On value of information. Izvestiya of USSR Academy of Sciences, Technical Cybernetics 5, 3–12. In Russian.
Source
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