Podcast
Questions and Answers
What is the purpose of an optimization algorithm in machine learning?
What is the purpose of an optimization algorithm in machine learning?
- To find the local minima of estimated errors (correct)
- To predict the dependent variable directly
- To find the global maximum of estimated errors
- To estimate the relationship between dependent and independent variables
What type of regression is used to predict a categorical dependent variable?
What type of regression is used to predict a categorical dependent variable?
- Simple Linear Regression
- Logistic Regression (correct)
- Multiple Linear Regression
- Polynomial Regression
What is the name of the iterative first-order optimization algorithm used to find a local minimum/maximum of a given function?
What is the name of the iterative first-order optimization algorithm used to find a local minimum/maximum of a given function?
- Gradient Ascent
- Logistic Descent
- Linear Regression
- Gradient Descent (correct)
What is the purpose of Multiple Linear Regression?
What is the purpose of Multiple Linear Regression?
What is an example of an application of Multiple Linear Regression?
What is an example of an application of Multiple Linear Regression?
What is the purpose of Logistic Regression?
What is the purpose of Logistic Regression?
What is the main goal of regression analysis?
What is the main goal of regression analysis?
What is the primary objective of simple linear regression?
What is the primary objective of simple linear regression?
What is the type of machine learning task addressed by regression analysis?
What is the type of machine learning task addressed by regression analysis?
What is the term for the variable being predicted or explained in regression analysis?
What is the term for the variable being predicted or explained in regression analysis?
What is the purpose of the error term in simple linear regression?
What is the purpose of the error term in simple linear regression?
What is an example of a regression task?
What is an example of a regression task?
What is the equation for a simple linear regression model?
What is the equation for a simple linear regression model?
What is the term for the variable used to predict or explain the dependent variable?
What is the term for the variable used to predict or explain the dependent variable?
What is the estimated mean value of Y when the value of X is zero?
What is the estimated mean value of Y when the value of X is zero?
What is the goal of ML regression?
What is the goal of ML regression?
What is the purpose of the least square method?
What is the purpose of the least square method?
What does β1 represent in the regression equation?
What does β1 represent in the regression equation?
What is the estimate of the population regression line?
What is the estimate of the population regression line?
What is the purpose of finding the values of b0 and b1?
What is the purpose of finding the values of b0 and b1?
What does the predicted value of Y represent?
What does the predicted value of Y represent?
What is the equation for finding the values of b0 and b1?
What is the equation for finding the values of b0 and b1?
What is the purpose of modifying the cost/error minimization function in locally weighted regression?
What is the purpose of modifying the cost/error minimization function in locally weighted regression?
What is the role of the query point 𝑥𝑞 in the error criterion 𝐸(𝑥𝑞)?
What is the role of the query point 𝑥𝑞 in the error criterion 𝐸(𝑥𝑞)?
What is the advantage of criterion three over criterion two?
What is the advantage of criterion three over criterion two?
What is the form of the linear function used to approximate the target function 𝑓 near 𝑥?
What is the form of the linear function used to approximate the target function 𝑓 near 𝑥?
Why is criterion two not preferred despite being aesthetically pleasing?
Why is criterion two not preferred despite being aesthetically pleasing?
What is the purpose of the weighting function K in criterion two?
What is the purpose of the weighting function K in criterion two?
What is the advantage of using the squared error in locally weighted regression?
What is the advantage of using the squared error in locally weighted regression?
What is the role of the number k of nearest neighbors in criterion three?
What is the role of the number k of nearest neighbors in criterion three?
What does the equation 𝒉𝜽 = 𝝈(𝜽𝑻 𝒙) represent in the context of logistic regression?
What does the equation 𝒉𝜽 = 𝝈(𝜽𝑻 𝒙) represent in the context of logistic regression?
What is the purpose of the intercept term 𝜽𝟎 in the logistic regression model?
What is the purpose of the intercept term 𝜽𝟎 in the logistic regression model?
What is the maximum likelihood estimation method used for in logistic regression?
What is the maximum likelihood estimation method used for in logistic regression?
What is the difference between the maximum likelihood estimation method used in logistic regression and the least square estimation method used in linear regression?
What is the difference between the maximum likelihood estimation method used in logistic regression and the least square estimation method used in linear regression?
What is the form of the logistic function 𝝈(𝒛) in the logistic regression model?
What is the form of the logistic function 𝝈(𝒛) in the logistic regression model?
What is the significance of the term 𝒙𝟎 in the logistic regression model?
What is the significance of the term 𝒙𝟎 in the logistic regression model?
What is the relationship between the input features 𝒙 and the coefficients 𝜽 in the logistic regression model?
What is the relationship between the input features 𝒙 and the coefficients 𝜽 in the logistic regression model?
What is the purpose of logistic regression in machine learning?
What is the purpose of logistic regression in machine learning?
Study Notes
Regression Analysis
- Aims to solve a Machine Learning problem by approximating a real-valued function 𝑓 𝑥 ∈ ℝ (i.e., predicting a continuous output)
- Examples of regression tasks: house prices prediction, weather forecasting, stocks market prediction, spread of viral disease, estimating salaries
Simple Linear Regression Model
- Only one independent variable, X
- Relationship between X and Y is described by a linear function 𝒇(𝒙) = 𝒚
- Changes in Y are assumed to be related to changes in X
- Equation: Yi = β0 + β1Xi + ε i
- Intercept = β0, Slope = β1
Predication Line in Regression Equation
- Estimated regression line provides an estimate of the population regression line
- b0 is the estimated mean value of Y when the value of X is zero
- b1 is the estimated change in the mean value of Y as a result of a one-unit increase in X
The Least Square Method
- b0 and b1 are obtained by finding the values that minimize the sum of the squared differences between 𝑌 (real value) and 𝑌 (estimated value)
Finding Best Weights/Coefficients
- Goal is to find the best coefficients to predicate the actual value
- Optimization algorithm is applied to find the best values of these coefficients by finding the local minima of estimated errors
- Example of optimization algorithm: Gradient Descent (GD)
Regression Models: Other Types
- Multiple Linear Regression: estimates the relationship between a quantitative dependent variable and two or more independent variables
- Logistic Regression: used to predict dependent variable (as categorical or class) using a given set of independent feature
Multiple Linear Regression
- Hypothesis function of linear regression: 𝑓(𝑥) = 𝑤0 + 𝑤1 𝑎1 𝑥 + 𝑤2 𝑎2 𝑥 + ⋯ + 𝑤𝑛 𝑎𝑛 𝑥
Locally Weighted Regression
- Modify the error criterion E to emphasize fitting the local training examples
- Minimize the squared error over just the k nearest neighbors
- Combine 1 and 2 for a good approximation
Logistic Regression
- Used to predict dependent variable (as categorical or class) using a given set of independent feature
- Equation: 𝒉𝜽 = 𝝈(𝜽𝑻 𝒙)
- Model: 𝝈 𝒛 = 1+𝑒 −𝒛
Optimizing Logistic Regression
- Use Maximum likelihood estimation (MLE) method for estimation of accuracy (finding best parameters/weights for the logistic regression model)
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Description
This quiz covers linear and logistic regression concepts in machine learning, including simple and multiple linear regression, locally weighted regression, and logistic regression for classification. It is part of the CS364 course in Machine Learning.
