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Machine Learning

Linear Methods For Classification

Interview questions on Linear Methods For Classification.

3 questions

All subtopicsGeneral ConceptsOdds and Log-oddsThe SigmoidTruly Understanding Logistic RegressionThe Logit Function and Entropy

The Sigmoid

Q1. Compute the derivative of the natural sigmoid function:$$

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\sigma(x) = \frac{1}{1+e^{-x}}; \quad \epsilon (0, 1)

The Sigmoid

Q2. Characterize the sigmoid function when its argument approaches $0 $,$∞$ and $-∞$.

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The Sigmoid

Q3. Remember that in logistic regression, the hypothesis function for some parameter vector $β$ and measurement vector $x$ is defined as:$$ h_\beta(x) = g(\beta^Tx) = \frac{1}{1+e^{-\beta^Tx}}\\ = P(y = 1|x;\beta)$$

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where y holds the hypothesis value. Suppose the coefficients of a logistic regression model with independent variables are as follows: β0=−1.5\beta_0 = -1.5 ,β1=3\beta_1 = 3 ,β2=−0.5\beta_2 = -0.5 . Assume additionally, that we have an observation with the following values for the independent variables:x1=1x_1 = 1,x2=5 x_2 = 5. As a result, the logit equation becomes: logit=β0+β1x1+β2x2\text{logit} = \beta_0 + \beta_1x_1 + \beta_2x_2 1. What is the value of the logit for this observation? 2. What is the value of the odds for this observation? 3. What is the value of P(y=1)P(y = 1) for this observation?