Logitic Regression cost function - what if ln(0)?












1












$begingroup$


I am building logistic regression from scrap.



The simplified cost function I am using is (from machine learning course on coursera):
enter image description here



in specific case during learning,
one observation in training set y is 0 - but the specific choice of betas in:



enter image description here



makes g(z) = h(x) = 1 , because e.g. z > 50.



in this case my right side od J is (1 - 0) * log(1 - 1) what is -inf (I am doing my calculations in python)



I understand that in this case value of cost function should be high because the probability of y = 1 is very big while the truth is that it actually is 0.



Is the problem approximation of g(50) being 1 instead of something like: 0.999999? Or there is some more fundametal error with my logic?



because this specific example the summation of cost of all observations is nan (not a number) in my code.






logistic-regression cost-function







share|improve this question









$endgroup$

















    1












    $begingroup$


    I am building logistic regression from scrap.



    The simplified cost function I am using is (from machine learning course on coursera):
    enter image description here



    in specific case during learning,
    one observation in training set y is 0 - but the specific choice of betas in:



    enter image description here



    makes g(z) = h(x) = 1 , because e.g. z > 50.



    in this case my right side od J is (1 - 0) * log(1 - 1) what is -inf (I am doing my calculations in python)



    I understand that in this case value of cost function should be high because the probability of y = 1 is very big while the truth is that it actually is 0.



    Is the problem approximation of g(50) being 1 instead of something like: 0.999999? Or there is some more fundametal error with my logic?



    because this specific example the summation of cost of all observations is nan (not a number) in my code.






    logistic-regression cost-function







    share|improve this question









    $endgroup$















      1












      1








      1





      $begingroup$


      I am building logistic regression from scrap.



      The simplified cost function I am using is (from machine learning course on coursera):
      enter image description here



      in specific case during learning,
      one observation in training set y is 0 - but the specific choice of betas in:



      enter image description here



      makes g(z) = h(x) = 1 , because e.g. z > 50.



      in this case my right side od J is (1 - 0) * log(1 - 1) what is -inf (I am doing my calculations in python)



      I understand that in this case value of cost function should be high because the probability of y = 1 is very big while the truth is that it actually is 0.



      Is the problem approximation of g(50) being 1 instead of something like: 0.999999? Or there is some more fundametal error with my logic?



      because this specific example the summation of cost of all observations is nan (not a number) in my code.






      logistic-regression cost-function







      share|improve this question









      $endgroup$




      I am building logistic regression from scrap.



      The simplified cost function I am using is (from machine learning course on coursera):
      enter image description here



      in specific case during learning,
      one observation in training set y is 0 - but the specific choice of betas in:



      enter image description here



      makes g(z) = h(x) = 1 , because e.g. z > 50.



      in this case my right side od J is (1 - 0) * log(1 - 1) what is -inf (I am doing my calculations in python)



      I understand that in this case value of cost function should be high because the probability of y = 1 is very big while the truth is that it actually is 0.



      Is the problem approximation of g(50) being 1 instead of something like: 0.999999? Or there is some more fundametal error with my logic?



      because this specific example the summation of cost of all observations is nan (not a number) in my code.






      logistic-regression cost-function




      logistic-regression cost-function






      share|improve this question













      share|improve this question











      share|improve this question




      share|improve this question










      asked yesterday









      Mateusz KonopelskiMateusz Konopelski

      1233




      1233






















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          $begingroup$

          In practice, an offset is used to avoid log explosion due to values close to zero. For example $hat{text{log}}(x)=text{log}(x + text{1e-6})$.






          share|improve this answer









          $endgroup$









          • 1




            $begingroup$
            Ha. Didn't think about it. Thanks!
            $endgroup$
            – Mateusz Konopelski
            yesterday











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          1 Answer
          1






          active

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          active

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          1












          $begingroup$

          In practice, an offset is used to avoid log explosion due to values close to zero. For example $hat{text{log}}(x)=text{log}(x + text{1e-6})$.






          share|improve this answer









          $endgroup$









          • 1




            $begingroup$
            Ha. Didn't think about it. Thanks!
            $endgroup$
            – Mateusz Konopelski
            yesterday
















          1












          $begingroup$

          In practice, an offset is used to avoid log explosion due to values close to zero. For example $hat{text{log}}(x)=text{log}(x + text{1e-6})$.






          share|improve this answer









          $endgroup$









          • 1




            $begingroup$
            Ha. Didn't think about it. Thanks!
            $endgroup$
            – Mateusz Konopelski
            yesterday














          1












          1








          1





          $begingroup$

          In practice, an offset is used to avoid log explosion due to values close to zero. For example $hat{text{log}}(x)=text{log}(x + text{1e-6})$.






          share|improve this answer









          $endgroup$



          In practice, an offset is used to avoid log explosion due to values close to zero. For example $hat{text{log}}(x)=text{log}(x + text{1e-6})$.







          share|improve this answer












          share|improve this answer



          share|improve this answer










          answered yesterday









          EsmailianEsmailian

          1,536113




          1,536113








          • 1




            $begingroup$
            Ha. Didn't think about it. Thanks!
            $endgroup$
            – Mateusz Konopelski
            yesterday














          • 1




            $begingroup$
            Ha. Didn't think about it. Thanks!
            $endgroup$
            – Mateusz Konopelski
            yesterday








          1




          1




          $begingroup$
          Ha. Didn't think about it. Thanks!
          $endgroup$
          – Mateusz Konopelski
          yesterday




          $begingroup$
          Ha. Didn't think about it. Thanks!
          $endgroup$
          – Mateusz Konopelski
          yesterday


















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