CS364: Machine Learning - Linear & Logistic Regressions
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Questions and Answers

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?

  • 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?

  • Gradient Ascent
  • Logistic Descent
  • Linear Regression
  • Gradient Descent (correct)

    • What is the purpose of Multiple Linear Regression?

    <p>To estimate the relationship between a quantitative dependent variable and two or more independent variables</p> Signup and view all the answers

    What is an example of an application of Multiple Linear Regression?

    <p>House prices prediction by given different attributes</p> Signup and view all the answers

    What is the purpose of Logistic Regression?

    <p>To predict a categorical dependent variable using a given set of independent features</p> Signup and view all the answers

    What is the main goal of regression analysis?

    <p>To predict the value of a dependent variable based on the value of at least one independent variable</p> Signup and view all the answers

    What is the primary objective of simple linear regression?

    <p>To model the relationship between one independent variable and a dependent variable</p> Signup and view all the answers

    What is the type of machine learning task addressed by regression analysis?

    <p>Regression</p> Signup and view all the answers

    What is the term for the variable being predicted or explained in regression analysis?

    <p>Dependent variable</p> Signup and view all the answers

    What is the purpose of the error term in simple linear regression?

    <p>To account for the random variation in the data</p> Signup and view all the answers

    What is an example of a regression task?

    <p>Weather forecasting</p> Signup and view all the answers

    What is the equation for a simple linear regression model?

    <p>Y = β0 + β1X + ε</p> Signup and view all the answers

    What is the term for the variable used to predict or explain the dependent variable?

    <p>Independent variable</p> Signup and view all the answers

    What is the estimated mean value of Y when the value of X is zero?

    <p>β0</p> Signup and view all the answers

    What is the goal of ML regression?

    <p>To find the best coefficients to predicate the actual value</p> Signup and view all the answers

    What is the purpose of the least square method?

    <p>To minimize the sum of the squared differences</p> Signup and view all the answers

    What does β1 represent in the regression equation?

    <p>The estimated change in the mean value of Y as a result of a one-unit increase in X</p> Signup and view all the answers

    What is the estimate of the population regression line?

    <p>Ŷi = b0 + b1Xi</p> Signup and view all the answers

    What is the purpose of finding the values of b0 and b1?

    <p>To minimize the sum of the squared differences</p> Signup and view all the answers

    What does the predicted value of Y represent?

    <p>The estimated value of Y for Xi</p> Signup and view all the answers

    What is the equation for finding the values of b0 and b1?

    <p>min ∑ (Yi - Ŷi) = min ∑ (Yi - (b0 + b1Xi))</p> Signup and view all the answers

    What is the purpose of modifying the cost/error minimization function in locally weighted regression?

    <p>To derive a local approximation of the target function</p> Signup and view all the answers

    What is the role of the query point 𝑥𝑞 in the error criterion 𝐸(𝑥𝑞)?

    <p>It is the point at which the error is being evaluated</p> Signup and view all the answers

    What is the advantage of criterion three over criterion two?

    <p>It has a computational cost independent of the total number of training examples</p> Signup and view all the answers

    What is the form of the linear function used to approximate the target function 𝑓 near 𝑥?

    <p>𝑓(𝑥) = 𝑤0 + 𝑤1 𝑎1 𝑥 + 𝑤2 𝑎2 𝑥 + ⋯ + 𝑤𝑛 𝑎𝑛 𝑥</p> Signup and view all the answers

    Why is criterion two not preferred despite being aesthetically pleasing?

    <p>It is computationally expensive and grows linearly with the number of training examples</p> Signup and view all the answers

    What is the purpose of the weighting function K in criterion two?

    <p>To weight the error of each training example by its distance from 𝑥𝑞</p> Signup and view all the answers

    What is the advantage of using the squared error in locally weighted regression?

    <p>It is a simple and intuitive measure of error</p> Signup and view all the answers

    What is the role of the number k of nearest neighbors in criterion three?

    <p>It is the number of nearest neighbors used to compute the error</p> Signup and view all the answers

    What does the equation 𝒉𝜽 = 𝝈(𝜽𝑻 𝒙) represent in the context of logistic regression?

    <p>The probability of the dependent variable being 1</p> Signup and view all the answers

    What is the purpose of the intercept term 𝜽𝟎 in the logistic regression model?

    <p>To account for the intercept or constant term in the model</p> Signup and view all the answers

    What is the maximum likelihood estimation method used for in logistic regression?

    <p>To find the optimal parameters for the logistic regression model</p> Signup and view all the answers

    What is the difference between the maximum likelihood estimation method used in logistic regression and the least square estimation method used in linear regression?

    <p>The maximum likelihood estimation method is used for logistic regression and the least square estimation method is used for linear regression</p> Signup and view all the answers

    What is the form of the logistic function 𝝈(𝒛) in the logistic regression model?

    <p>𝝈(𝒛) = 1 / (1 + 𝑒^(-𝒛))</p> Signup and view all the answers

    What is the significance of the term 𝒙𝟎 in the logistic regression model?

    <p>It is always equal to 1</p> Signup and view all the answers

    What is the relationship between the input features 𝒙 and the coefficients 𝜽 in the logistic regression model?

    <p>𝜽 and 𝒙 are linearly related</p> Signup and view all the answers

    What is the purpose of logistic regression in machine learning?

    <p>To predict a categorical dependent variable</p> Signup and view all the answers

    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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    Quiz Team

    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.

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