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## NPTEL Introduction to Machine Learning Assignment 3 Answers 2023:

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#### Q.1. Which of the following is false about a logistic regression based classifier?

- The logistic function is non-linear in the weights
**The logistic function is linear in the weights****The decision boundary is non-linear in the weights**- The decision boundary is linear in the weights

#### Q.2. Consider the case where two classes follow Gaussian distribution which are cen- tered at (3, 9) and (âˆ’3, 3) and have identity covariance matrix. Which of the following is the separating decision boundary using LDA assuming the priors to be equal?

#### Q.3. Consider the following relation between a dependent variable and an independent variable identified by doing simple linear regression. Which among the following relations between the two variables does the graph indicate?

- as the independent variable increases, so does the dependent variable
- as the independent variable increases, the dependent variable decreases
- if an increase in the value of the dependent variable is observed, then the independent variable will show a corresponding increase
- if an increase in the value of the dependent variable is observed, then the independent variable will show a corresponding decrease
**the dependent variable in this graph does not actually depend on the independent variable**- none of the above

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#### Q.4. Given the following distribution of data points:

What method would you choose to perform Dimensionality Reduction?

**Linear Discriminant Analysis**- Principal Component Analysis

#### Q.5.** **In general, which of the following classification methods is the most resistant to gross outliers?

- Quadratic Discriminant Analysis (QDA)
- Linear Regression
**Logistic regression**- Linear Discriminant Analysis (LDA)

#### Q.6. Suppose that we have two variables, X and Y (the dependent variable). We wish to find the relation between them. An expert tells us that

relation between the two has the form Y=m+X2+c. Available to us are samples of the variables X and Y. Is it possible to apply linear regression to this data to estimate the values of m and c ?

**no**- yes
- insufficient information

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#### Q.7. In a binary classification scenario where x is the independent variable and y is the dependent variable, logistic regression assumes that the conditional distribution y|x follows a

#### Q.8. Consider the following data:

Assuming that you apply LDA to this data, what is the estimated covariance matrix?

**Answer: e. [3.251.16671.16672.375]**

#### Q.9. Given the following 3D input data, identify the principal component.

(Steps: center the data, calculate the sample covariance matrix, calculate the eigenvectors and eigenvalues, identify the principal component)

**Answer:****e. [0.8123 0.5774 0.0824]**

#### Q.10. For the data given in the previous question, find the transformed input along the first two principal components.

**Answer: C**

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**Disclaimer**: This answer is provided by us only for discussion purpose if any answer will be getting wrong donâ€™t blame us. If any doubt or suggestions regarding any question kindly comment. The solution is provided byÂ **Chase2learn**. This tutorial is only for Discussion andÂ LearningÂ purpose.

#### About NPTEL Introduction to Machine Learning Course:

With the increased availability of data from varied sources there has been increasing attention paid to the various data driven disciplines such as analytics and machine learning. In this course we intend to introduce some of the basic concepts of machine learning from a mathematically well motivated perspective. We will cover the different learning paradigms and some of the more popular algorithms and architectures used in each of these paradigms.

**Course Outcome:**

**Week 0:**Â Probability Theory, Linear Algebra, Convex Optimization â€“ (Recap)**Week 1:**Â Introduction: Statistical Decision Theory â€“ Regression, Classification, Bias Variance**Week 2:Â**Linear Regression, Multivariate Regression, Subset Selection, Shrinkage Methods, Principal Component Regression, Partial Least squares**Week 3:**Â Linear Classification, Logistic Regression, Linear Discriminant Analysis**Week 4:**Â Perceptron, Support Vector Machines**Week 5:**Â Neural Networks â€“ Introduction, Early Models, Perceptron Learning, Backpropagation, Initialization, Training & Validation, Parameter Estimation â€“ MLE, MAP, Bayesian Estimation**Week 6:Â**Decision Trees, Regression Trees, Stopping Criterion & Pruning loss functions, Categorical Attributes, Multiway Splits, Missing Values, Decision Trees â€“ Instability Evaluation Measures**Week 7:**Â Bootstrapping & Cross Validation, Class Evaluation Measures, ROC curve, MDL, Ensemble Methods â€“ Bagging, Committee Machines and Stacking, Boosting**Week 8:**Â Gradient Boosting, Random Forests, Multi-class Classification, Naive Bayes, Bayesian Networks**Week 9:**Â Undirected Graphical Models, HMM, Variable Elimination, Belief Propagation**Week 10:**Â Partitional Clustering, Hierarchical Clustering, Birch Algorithm, CURE Algorithm, Density-based Clustering**Week 11:**Â Gaussian Mixture Models, Expectation Maximization**Week 12:**Â Learning Theory, Introduction to Reinforcement Learning, Optional videos (RL framework, TD learning, Solution Methods, Applications)

**CRITERIA TO GET A CERTIFICATE**:

Average assignment score = 25% of average of best 8 assignments out of the total 12 assignments given in the course.

Exam score = 75% of the proctored certification exam score out of 100

Final score = Average assignment score + Exam score

**YOU WILL BE ELIGIBLE FOR A CERTIFICATE ONLY IF AVERAGE ASSIGNMENT SCORE >=10/25 AND EXAM SCORE >= 30/75. If one of the 2 criteria is not met, you will not get the certificate even if the Final score >= 40/100.**

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