Problem 1
Consider the simplified logistic regression with one variable (without intercept)???
Hypothesis: ?????????=????(????????)=
????1Cost Function: ????????=?????=1?????????log??????????????
????
????????1Gradients: ????????=?????=1?????????(????)?????(????)????(????)
????????????
11+?????????x????
1?????
log(1??????(????(????)))
Please solve the following problem:
1.Suppose initially ????=0.5, for a test sample ????=2, please calculate ????(????=
1|????=2;????=0.5)
2.Please perform one iteration of gradient descent using the following training data with initial ????=0.5and learning rate as ????=2. What’s the new ?????
????????103. Please recalculate ????(????=1|????=2;????)using the new ????you get from 2
4. Please compare the cost function before and after the gradient descent. Does it decrease?
SocialMediaMiningMachine Learning for Data Analytics0101
2????
Measures andMetricsQuiz 11
Problem 1
Consider the simplified logistic regression (without intercept)???
Hypothesis: ?????????=????(????????)=
????1Cost Function: ????????=?????=1?????????log??????????????
????????????1Gradients: ????????=?????=1?????????(????)?????(????)????(????)
????????????
11+?????????x????
1?????
log(1??????(????(????)))
Please solve the following problem:
1.Suppose initially ????=0.5, for a test sample ????=2, please calculate ????(????=
1|????=2;????=0.5)
11????????=1????=2;????=0.5=?????????===0.73?0.5×2?11+????1+????SocialMediaMiningMachine Learning for Data AnalyticsMeasures andMetricsQuiz 12
Problem 1
Consider the simplified logistic regression (without intercept)??
Hypothesis: ?????????=????(????1????1)=????Gradients: ????
????????????
????1?????=1????
11+?????????x2. Please perform one iteration of gradient descent using the following training data with initial ????=0.5and learning rate as ????=2. What’s the new ?????
????01????
????=
?????????(????)?????(????)????(????)????1001
2????
????11(????)(????)(????)
?????????????????=??????????=[?????0?1×0+?????1?0×1]
????????????211=?0×1=0.311?0.521+????????????????????????=1SocialMediaMiningMachine Learning for Data Analytics????=?????????????=0.5?2?0.311=?0.122Measures andMetricsQuiz 13
Problem 1
Consider the simplified logistic regression (without intercept)??
Hypothesis: ?????????=????(????1????1)=????Gradients: ????
????????????
????1?????=1????
11+?????????x3. Please recalculate ????(????=1|????=2;????)using the new ????you get from 2
11==0.4390.2441+????????=
?????????(????)?????(????)????(????)
????????=1????=2;????=?0.122=?????????=?
?
Initially, ????=0.5, we have ????????=1????=2;????=0.5=0.73, predict as 1After one integration of gradient descent, ????=?0.122, and ????????=1????=2;????=?0.122=0.439, predict as 0
0
1
2
????
4
1+????0.122×2SocialMediaMiningMachine Learning for Data AnalyticsMeasures andMetricsQuiz 1Problem 1
Consider the simplified logistic regression (without intercept)??
Hypothesis: ?????????=????(????????)=Cost Function: ????????=
????1?????=1?????????????
11+?????????x????
????
4. Please compare the cost function before and after the gradient descent. Does it decrease?When ????=0.5
11????0.5=?log?????0?1?1log1??????0+[?0×log?????1?1?0log(1??????(1))]
2211111)=0.362=?log?????0?log(1??????(1))=?log0.5?log(1??0.5221+????22log??????????1?????
log(1??????(????(????)))
11111)=0.288?????0.122=?log?????0?log(1??????(1))=?log0.5?log(1?0.122221+????22When ????=?0.122
????01????10SocialMediaMiningMachine Learning for Data AnalyticsMeasures andMetricsQuiz 15
Quiz 2 - 图文
