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

The video tutorial explains logistic regression using maximum likelihood estimation on Bernoulli random variables. It begins with an introduction to Bernoulli variables and binary classification, followed by a transformation of feature vectors. The tutorial then models the probability of success using a sigmoid function, which is central to logistic regression. Finally, it discusses the application of maximum likelihood estimation and the use of log likelihood for optimization.

What is the purpose of adding a bias term to the feature vector in logistic regression?

• To increase the dimensionality of the data

• To simplify the model by reducing parameters

• To make the model non-linear

• To absorb the bias into the feature vector

In a Bernoulli trial, what does the probability of success represent in the context of binary classification?

• The overall accuracy of the model

• The likelihood of the model being incorrect

• The chance of a data point being classified as class 0

• The probability of a data point being classified as class 1

Why is the sigmoid function used in logistic regression?

• It is a linear function that simplifies calculations

• It reduces the dimensionality of the data

• It maps any real-valued number into the range of 0 to 1

• It is the only function that can model probabilities

What is the primary reason logistic regression is named as such?

• Due to its application in logistics and supply chain

• Because it is a linear regression model

• Due to its use of the logistic function or sigmoid function

• Because it uses a logistic growth model

What is the role of the likelihood function in maximum likelihood estimation?

• To ensure the data is normally distributed

• To reduce the complexity of the model

• To find the parameter values that maximize the probability of observing the data

• To minimize the error in predictions

Why is the log of the likelihood function used in optimization?

• Because it reduces the number of parameters

• Because it is monotonically increasing, preserving the location of maxima

• Because it is easier to differentiate

• Because it simplifies the calculations

What assumption is made about the dataset in maximum likelihood estimation?

• The dataset is independent and identically distributed (IID)

• The dataset is normally distributed

• The dataset is linearly separable

• The dataset contains no outliers