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Problem Solving

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Problem Solving

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    1. Problem Solving

    2. Definition of Machine Intelligence

    3. Models of Reasoning State Space Searching with Heuristics Rule Base Systems Evolution and adaptation

    5. Main feature of rules - acquisition

    7. Other aspects of Intelligence Researchers in AI have constructed models of other aspects of intelligence such as CBR Neural Networks Probably many more great ideas to be discovered. Swarm Intelligence, Ant Intelligence

    8. Problem Solving Logic Deductive Reasoning Inductive Reasoning Abductive Reasoning Analogical Reasoning

    9. Analogy and Experience

    10. Case-based Reasoning A type of analogical reasoning

    11. Underlying Model of CBR Humans are robust problem solvers Humans reason from cases in a wide variety of contexts Studies abound in how humans do this

    12. What is CBR? Case-based reasoning is [...] reasoning by remembering. A case-based reasoner solves new problems by adapting solutions that were used to solve old problems. Case-based reasoning is a recent approach to problem solving and learning Case-based reasoning is both the ways people use cases to solve problems and the ways we can make machines use them.

    13. Analogical Reasoning (CBR) Case-based reasoning (CBR) is a certain technique which was based on analogical reasoning. The main intention is to reuse previous experiences for actual problems. The difficulty arises when the actual situation is not identical to the previous one: There is an inexactness involved. Its main aspect is that CBR-techniques allow inexact (approximate) reasoning in a controlled manner. Here we will shortly describe its main features. Major applications include fault diagnosis, help desk systems, eCommerce

    14. Could be called Similarity Based Reasoning The central notion in CBR is the concept of similarity. The methods in CBR have been extended in a way which allows applications to other problems rather than reusing previous experiences: in electronic commerce e.g. to product selection. This is due to an abstract formulation of the similarity concept. In particular, the main algorithms of CBR can still be applied to these new situations. We will first describe the original technique informally and then proceed to the extensions.

    15. Research in CBR ECCBR 2010 - European Conference on Case-Based Reasoning ICCBR 2011 - International Conference on Case based Reasoning

    16. Case-Based Reasoning (CBR) Basic Ideas: Store previous experience (case) Solve new Problems by selecting and reusing cases Store new experience again Replaces 0-1-logic by approximation Is a well-founded technology: Mathematically Algorithmically With respect to software technology Supported by experiments and applications Business success Most successful recent branch of AI

    17. What is a Case ? A case has two parts: Description of a problem or a set of problems (generalized case) Description of the solution of this problem (formally or informally) Possibly additions like explanations, comments on the quality of the solution etc. Cases represent experiences : They record how a problem was solved in the past

    18. Different Case Representations

    19. Structured Case Representation Many different case representations are used Depend on requirements of domain and task Structure of already available case data Flat feature-value list Simple case structure is sometimes sufficient for problem solving Easy to store and retrieve in a CBR system Object-oriented representations Case: collection of objects (instances of classes) Required for complex and structured objects Genauer im Teil III. Genauer im Teil III.

    20. How to Use a Case

    21. How to Use a Case-Base A case base is a data base of cases If a new problem arises one will use a case from the case base in order to solve the problem If we have many cases then the chance is higher to find one with a suitable solution Because the given problem is usually not exactly in the base one wants to retrieve a case which solved a problem which is similar enough to be useful Hence, the notion of similarity is central to CBR The concept of similarity based retrieval is compared with data base retrieval

    22. Components of CBR

    23. The Classical CBR Algorithm

    24. Typical Problems Handled with CBR: Classification and Diagnosis A class is a certain subset of some universe and a classification assigns to each element one or more classes to which it belongs. In fault diagnosis the classification is only the first step:

    25. An Example Overview Typical Scenario: Call Center Technical Diagnosis of Car Faults: symptoms are observed (e.g., engine doesnt start) and values are measured (e.g., battery voltage = 6.3V) goal: Find the cause for the failure (e.g., battery empty) and a repair strategy (e.g., charge battery) Case-Based Diagnosis: a case describes a diagnostic situation and contains: description of the symptoms description of the failure and the cause description of a repair strategy store a collection of cases in a case base find case similar to current problem and reuse repair strategy

    26. A Simple Example (II) What does a Case Look Like? A case describes one particular diagnostic situation A case records several features and their specific values occurred in that situation ? A case is not a ( general) rule !!

    27. A Case Base With Two Cases Each case describes one particular situation All cases are independent of each other

    28. Solving a New Diagnostic Problem A new problem has to be solved We make several observations in the current situation Observations define a new problem Not all feature values have to be known Note: The new problem is a case without solution part

    29. You are required to identify between case 1 and case 2 the case that is most similar to to the problem case When are two cases similar? How to rank the cases according to their similarity? ? Similarity is the most important concept in CBR !! We can assess similarity based on the similarity of each feature Similarity of each feature depends on the feature value. BUT: Importance of different features may be different

    30. Class Exercise

    31. A similarity algorithm Assignment of similarities for features values. Express degree of similarity by a real number between 0 and 1 Examples: Feature: Problem Feature: Battery voltage (similarity depends on the difference) Different features have different importance (weights)! High importance: Problem, Battery voltage, State of light, ... Low importance: Car, Year, ...

    32. Compare Similarity Similarity computation by weighted average similarity(new,case 2) = 1/20 * [ 6*0.8 + 1*0.8 + 1*0.4 + 6*0.95 + 6*0 ] = 0.585 Case 1 is more similar: due to feature State of lights

    33. Assign similarity values to each feature pair and a weight to each feature Similarity computation by weighted average similarity(new,case 1) = 1/20 * [ 6*0.8 + 1*0.4 + 1*0.6 + 6*0.9 + 6* 1.0 ] = 0.86

    34. Case adaption algorithm

    35. New case inserted into the case library ??

    36. The Classical CBR R4-Cycle

    37. Retrieve: Modeling Similarity The similarity based retrieval realizes an inexact match which is still useful: Useful solutions from a case base Useful products from a product base Different approaches depending on case representation Similarity measures: Are functions to compare two cases sim: Case x Case [0..1] Local similarity measure: similarity on feature level Global similarity measure: similarity on case or object level

    38. Similarities (1) Similarities are described by measures with numerical values They operate on problem descriptions, demands, products ,...

    39. Similarities and Inexact Reasoning The similarity measure controls the utility when inexact solutions are employed or the desired product is not exactly as desired available.

    40. A Typical Similarity Measure

    41. Nearest Neighbor Problem: Should a person be granted a load or not (Ian Watson Slide) Depends on Monthly income and loan amount. The loan decisions will be clustered

    42. Retrieval: Finding The Nearest Neighbor For a new problem C the nearest neighbor in the case base is the case (D,L) for which problem D has the greatest similarity to C. Its solution L is intended to be most useful and is then the best solution the case base can offer (or best available product). Classical databases use always total similarity (i.e. equality). The access to data in databases is in similarity based systems replaced by the search for the nearest neighbor. It can be regarded as an optimization process.

    43. Thresholds The nearest neighbor (in the given case base) is not always sufficient for providing an acceptable solution. On the other hand, a case which is not the nearest neighbor may be sufficient enough. For this purpose one can introduce two thresholds a and b, 0 < a < b < 1 with the intention If sim(newproblem, caseproblem) < a then the case is not accepted; If sim(newproblem, caseproblem) > b then the case is accepted. This partitions this case base (for the actual problem into three parts: accepted cases, unaccepted cases and an uncertainty set. The same works for product bases.

    44. Retrieve: Efficiency Issues Efficient case retrieval is essential for large case bases and large product spaces. Different approaches depending on the representation complexity of similarity computation size of the base Organization of the base: Linear lists, only for small bases Index structures for large bases, e.g., kd-trees, How to store cases or products: Databases: for large bases or if shared with other applications Main memory: for small bases, not shared

    45. Reuse: How to Adapt the Solution No modification of the solution: just copy. Manual/interactive solution adaptation by the user. Automatic solution adaptation : Transformational Analogy: transformation of the solution Rules or operators to adjust solution w.r.t. differences in the problems Knowledge required about the impact of differences Compositional adaptation: combine several cases to a single solution

    46. Summary CBR is a technique for solving problems based on experience CBR problem solving involves four phases: Retrieve, Reuse, Revise, Retain CBR systems store knowledge in four containers: Vocabulary, Case Base, Similarity Concept, Solution Adaptation Large variety of techniques for: representing the knowledge, in particular, the cases realizing the different phases CBR has several advantages over traditional KBS The basic techniques of CBR can be extended to the needs of E-Commerce.

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