NPTEL Data Science for Engineers Assignment 5 Answers 2023

Hello Learners, In this Post, you will find NPTEL Data Science for Engineers Assignment 5 Week 5 Answers 2023. All the Answers are provided below to help the students as a reference don’t straight away look for the solutions.

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NPTEL Data Science for Engineers Assignment 5 Answers 2023:

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Q.1. Which of the following statements is/are not TRUE with respect to the multi variate optimization?

I – The gradient of a function at a point is parallel to the contours II – Gradient points in the direction of greatest increase of the function III – Negative gradient points in the direction of the greatest decrease of the function IV – Hessian is a non-symmetric matrix

• I
• II and III
• I and IV
• III and IV

Q.2. The solution to an unconstrained optimization problem is always the same as the solution to the constrained one.

• True
• False

Q.3. Gradient based algorithm methods compute

• only step length at each iteration
• both direction and step length at each iteration
• only direction at each iteration
• none of the above

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Q.4. For an unconstrained multivariate optimization given f(x¯¯¯), the necessary second order condition for x¯¯¯∗ to be the minimizer of f(x) is

• ∇2f(x¯¯¯∗) must be negative definite.
• ∇2f(x¯¯¯∗) must be positive definite.
• ∇f(x¯¯¯∗)=0
• f”(x¯¯¯∗)>0

Use the following information to answer Q5, 6, 7 and 8

minx1,x2∈R f(x1,x2)=x21+4×22−2×1+8×2.

Q.5. Which among the following is the stationary point for f(x1,x2)?

• (0,0)
• (1,−1)
• (−1,−1)
• (−1,1)

Q.6. Find the eigen values corresponding to Hessian matrix of f.

• 1,−1
• 1,1
• 2,8
• 0,2

Q.7. Find the minimum value of f.

• 0
• -5
• -1
• 1

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Q.8. What is the minimum value of f(x1,x2) subject to the constraint x1+2×2=7?

• -5
• -1
• 27
• 0

Q.9. Find the maximum value of f(x,y)=49−x2−y2 subject to the constraint x+3y=10.

• 49
• 46
• 59
• 39

Q.10. Consider an optimization problem minx1,x2 x2−xy+y2 subject to the constraints

2x+y≤1x+2y≥2x≥−1

• Answer: C

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Disclaimer: This answer is provided by us only for discussion purpose if any answer will be getting wrong don’t blame us. If any doubt or suggestions regarding any question kindly comment. The solution is provided by Brokenprogrammers. This tutorial is only for Discussion and Learning purpose.

About NPTEL Data Science for Engineers Course:

Learning Objectives :

1. Introduce R as a programming language 
2. Introduce the mathematical foundations required for data science 
3. Introduce the first level data science algorithms 
4. Introduce a data analytics problem solving framework
5. Introduce a practical capstone case study

Learning Outcomes:

1. Describe a flow process for data science problems (Remembering) 
2. Classify data science problems into standard typology (Comprehension)
3. Develop R codes for data science solutions (Application) 
4. Correlate results to the solution approach followed (Analysis)
5. Assess the solution approach (Evaluation) 
6. Construct use cases to validate approach and identify modifications required (Creating) 

Course Layout:

• Week 1:  Course philosophy and introduction to R  
• Week 2:  Linear algebra for data science 
•                 1. Algebraic view – vectors, matrices, product of matrix & vector, rank, null space, solution of over-determined set of equations and pseudo-inverse) 
•                 2. Geometric view – vectors, distance, projections, eigenvalue decomposition
• Week 3:  Statistics (descriptive statistics, notion of probability, distributions, mean, variance, covariance, covariance matrix, understanding univariate and multivariate normal distributions, introduction to hypothesis testing, confidence                        interval for estimates)  
• Week 4:  Optimization
• Week 5:  1. Optimization
• 2. Typology of data science problems and a solution framework
• Week 6:  1. Simple linear regression and verifying assumptions used in linear regression 
• 2. Multivariate linear regression, model assessment, assessing importance of different variables, subset selection
• Week 7:  Classification using logistic regression
• Week 8:  Classification using kNN and k-means clustering

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.

If you have not registered for exam kindly register Through https://examform.nptel.ac.in/