Data Science and Machine Learning (Theory and Projects) A to Z - Mathematical Derivations for Math Lovers (Optional): Lo

The video tutorial explains logistic regression, focusing on the likelihood function and its optimization using the log likelihood. It discusses the relationship between log likelihood and cross entropy loss, and derives the error function. The tutorial concludes with the necessity of gradient descent for parameter estimation in logistic regression due to the absence of a closed form solution.

What is the primary function used in logistic regression to model probabilities?

• Exponential function

• Linear function

• Quadratic function

• Sigmoid function

In logistic regression, what type of random variable is used to model the likelihood function?

• Gaussian random variable

• Uniform random variable

• Bernoulli random variable

• Poisson random variable

What is the main advantage of using the log likelihood function over the likelihood function?

• It is more accurate

• It simplifies the product to a sum

• It requires less data

• It is faster to compute

What does the cross-entropy loss function aim to do in logistic regression?

• Maximize the likelihood

• Minimize the likelihood

• Maximize the error

• Minimize the error

How is the cross-entropy loss related to the log likelihood function?

• They are unrelated

• Cross-entropy loss is the square of the log likelihood

• Cross-entropy loss is the negative of the log likelihood

• Cross-entropy loss is the derivative of the log likelihood

What mathematical operation is used to simplify the error function in logistic regression?

• Integration

• Logarithmic transformation

• Matrix inversion

• Differentiation

What is the role of the sigmoid function in the error function derivation?

• It is used to calculate the gradient

• It is used to normalize the data

• It is used to scale the features

• It is used to compute probabilities

Why is gradient descent necessary in logistic regression?

• To increase computational efficiency

• To optimize the parameters due to lack of closed-form solution

• To handle non-linear data

• To find a closed-form solution

What is the main goal of applying gradient descent in logistic regression?

• To minimize the likelihood

• To minimize the error

• To maximize the error

• To maximize the likelihood

What is the relationship between the gradient and the direction of optimization in gradient descent?

• The gradient is unrelated to the direction of optimization

• The gradient is opposite to the direction of optimization

• The gradient is parallel to the direction of optimization

• The gradient is perpendicular to the direction of optimization