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Question & Answer: Consider a concept learning problem where the data D, which concerns ancient Egyptian vases discovered in archeological excav…..

5. Candidate Elimination Algorithm (CEA) Consider a concept learning problem where the data D, which concerns ancient Egyptian vases discovered in archeological excavations, is expressed as tuples of five attributes: damaged, color, material, kingdom, markings. Examples are classified as either valuable (+) or not valuable (-), and D consists of the following Number Example Class <no, brown, marble, middle, hieroglyphics> <no, white, sandstone, olod, <no, white, marble, new, hieroglyphics> <yes, grey, slate, <no, brown, granite, middle, hieroglyphics> none> 4 middle, hieroglyphics> Assume that all possible values of each attribute are represented in D above. (a) What is the size of the hypothesis space searched by the candidate elimination algorithm (CEA) using the data D given above? (b) Suppose the CEA has seen examples 1 and 2 only so far. Show its current specific boundary S2 and general boundary G2 for the version space. (c) Show S; and G3 after the CEA also sees example 3 (d) Show S5 and Gs after the CEA also sees the final two examples 4 and 5.

Consider a concept learning problem where the data D, which concerns ancient Egyptian vases discovered in archeological excavations, is expressed as tuples of five attributes: damaged, color, material, kingdom, markings. Examples are classified as either valuable (+) or not valuable (-), and D consists of the following: Assume that all possible values of each attribute are represented in D above. (a) What is the size of the hypothesis space searched by the candidate elimination algorithm (CEA) using the data D given above? (b) Suppose the CEA has seen examples 1 and 2 only so far. Show its current specific boundary S_2 and general boundary G_2 for the version space. (c) Show S_3 and G_3 after the CEA also sees example 3. (d) Show S_5 and G_5 after the CEA also sees the final two examples 4 and 5.

Expert Answer

 

  1. Initialize tex2html_wrap8323 to the set of maximally general hypotheses in tex2html_wrap8253
  2. Initialize tex2html_wrap8328 to the set of maximally specific hypotheses in tex2html_wrap8253
  3. For each training example tex2html_wrap8347 , do
    • If tex2html_wrap8347 is a positive example
      • Remove from tex2html_wrap8323 any hypothesis inconsistent with tex2html_wrap8347
      • For each hypothesis tex2html_wrap8351 in tex2html_wrap8328 that is not consistent with tex2html_wrap8347
        • Remove tex2html_wrap8351 from tex2html_wrap8328
        • Add to tex2html_wrap8328 all minimal generalizations tex2html_wrap8260 of tex2html_wrap8351 such that
          • tex2html_wrap8260 is consistent with tex2html_wrap8347 , and some member of tex2html_wrap8323 is more general than tex2html_wrap8260
        • Remove from tex2html_wrap8328 any hypothesis that is more general than another hypothesis is tex2html_wrap8328
    • If tex2html_wrap8347 is a negative example
      • Remove from tex2html_wrap8328 any hypothesis inconsistent with tex2html_wrap8347
      • For each hypothesis tex2html_wrap8368 in tex2html_wrap8323 that is not consistent with tex2html_wrap8347
        • Remove tex2html_wrap8368 from tex2html_wrap8323
        • Add to tex2html_wrap8323 all minimal specializations tex2html_wrap8260 of tex2html_wrap8368 such that
          • tex2html_wrap8260 is consistent with tex2html_wrap8347 , and some member of tex2html_wrap8328 is more specific than tex2html_wrap8260
        • Remove from tex2html_wrap8323 any hypothesis that is less general than another hypothesis is tex2html_wrap8323
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