ISYE 6525 HIGH DIMENSIONAL DATA
ANALYTICS EXAM 1 WORKED SOLUTIONS
(SUMMER 2026) – FULL QUESTIONS AND
CORRECT ANSWERS (VERIFIED ANSWERS)
PLUS RATIONALES 2026 Q&A | INSTANT
DOWNLOAD PDF
Core Domains
• Functional Data Analysis and Basis Expansions
• Image Processing and Feature Extraction
• Multilinear Algebra and Tensor Decompositions
• Regularization in High-Dimensional Regression
• Optimization Methods for Statistical Modeling
• Sparse Learning and Low-Rank Methods
• Dimensionality Reduction and Principal Component Analysis
• Matrix and Tensor Completion
• Kernel Methods and Feature Spaces
• Model Selection and Information Criteria
Introduction
This comprehensive examination is designed to assess mastery of high-
dimensional data analytics concepts as taught in ISyE 6525 at the Georgia
Institute of Technology. The assessment covers functional data analysis, image
and hyperspectral data processing, multilinear algebra and tensor
decompositions, regularization techniques for high-dimensional regression,
sparse and low-rank learning, optimization methods, and dimensionality
,reduction techniques. The multiple-choice format challenges students to apply
theoretical knowledge to practical problems involving structured high-
dimensional data. Emphasis is placed on understanding the mathematical
foundations, algorithmic implementations, and real-world applications of
these advanced analytical techniques. This exam prepares students for
rigorous quantitative analysis of complex data structures encountered in
modern industrial and systems engineering applications.
SECTION ONE: QUESTIONS 1–100
Question 1
Which of the following best defines functional data analysis (FDA)?
A. Analyzing data where each observation is a single scalar value
B. Analyzing data where each observation is a function or curve rather than a
finite-dimensional vector
C. Analyzing data with more features than observations
D. Analyzing categorical data using logistic regression
B. Analyzing data where each observation is a function or curve rather
than a finite-dimensional vector
RATIONALE: Functional data analysis treats each observation as a
continuous function or curve, such as growth trajectories or spectral curves.
Option A describes standard scalar data, option C describes the high-
dimensional "p > n" problem, and option D describes categorical data
analysis.
Question 2
In functional data analysis, what is the primary purpose of basis expansion?
A. To reduce the number of observations
B. To represent functional data using a linear combination of basis functions
C. To eliminate outliers from the dataset
D. To transform categorical variables into continuous variables
, B. To represent functional data using a linear combination of basis
functions
RATIONALE: Basis expansion represents a function as a linear
combination of basis functions (e.g., B-splines, Fourier basis). This allows
functional data to be analyzed using multivariate techniques by working with
the basis coefficients.
Question 3
Which of the following is a common basis function used in functional data
analysis?
A. Radial basis function
B. B-spline
C. Sigmoid function
D. Softmax function
B. B-spline
RATIONALE: B-splines are commonly used as basis functions in
functional data analysis due to their local support and smoothness properties.
Radial basis functions are used in interpolation and neural networks, while
sigmoid and softmax are activation functions.
Question 4
What is the fundamental challenge in high-dimensional regression when p >
n (more predictors than observations)?
A. The model is overidentified
B. The ordinary least squares solution is not unique
C. The model has too few parameters
D. The data cannot be standardized
B. The ordinary least squares solution is not unique
, RATIONALE: When p > n, the design matrix X is not full rank, leading to
infinitely many least squares solutions. Regularization techniques are
required to obtain a unique solution.
Question 5
Which regularization method adds an L1 penalty to the regression objective
function?
A. Ridge regression
B. Lasso regression
C. Elastic net
D. Principal component regression
B. Lasso regression
RATIONALE: Lasso (Least Absolute Shrinkage and Selection Operator)
adds an L1 penalty (sum of absolute values of coefficients) to the least squares
objective. Ridge adds an L2 penalty, and elastic net combines L1 and L2
penalties.
Question 6
What property of the Lasso penalty makes it useful for feature selection?
A. It shrinks all coefficients toward zero equally
B. It forces some coefficients to be exactly zero
C. It is computationally faster than Ridge
D. It is insensitive to outliers
B. It forces some coefficients to be exactly zero
RATIONALE: The L1 penalty in Lasso has the property of producing
sparse solutions by driving some coefficients exactly to zero, effectively
performing feature selection. Ridge regression shrinks coefficients but does
not set them to zero.
ANALYTICS EXAM 1 WORKED SOLUTIONS
(SUMMER 2026) – FULL QUESTIONS AND
CORRECT ANSWERS (VERIFIED ANSWERS)
PLUS RATIONALES 2026 Q&A | INSTANT
DOWNLOAD PDF
Core Domains
• Functional Data Analysis and Basis Expansions
• Image Processing and Feature Extraction
• Multilinear Algebra and Tensor Decompositions
• Regularization in High-Dimensional Regression
• Optimization Methods for Statistical Modeling
• Sparse Learning and Low-Rank Methods
• Dimensionality Reduction and Principal Component Analysis
• Matrix and Tensor Completion
• Kernel Methods and Feature Spaces
• Model Selection and Information Criteria
Introduction
This comprehensive examination is designed to assess mastery of high-
dimensional data analytics concepts as taught in ISyE 6525 at the Georgia
Institute of Technology. The assessment covers functional data analysis, image
and hyperspectral data processing, multilinear algebra and tensor
decompositions, regularization techniques for high-dimensional regression,
sparse and low-rank learning, optimization methods, and dimensionality
,reduction techniques. The multiple-choice format challenges students to apply
theoretical knowledge to practical problems involving structured high-
dimensional data. Emphasis is placed on understanding the mathematical
foundations, algorithmic implementations, and real-world applications of
these advanced analytical techniques. This exam prepares students for
rigorous quantitative analysis of complex data structures encountered in
modern industrial and systems engineering applications.
SECTION ONE: QUESTIONS 1–100
Question 1
Which of the following best defines functional data analysis (FDA)?
A. Analyzing data where each observation is a single scalar value
B. Analyzing data where each observation is a function or curve rather than a
finite-dimensional vector
C. Analyzing data with more features than observations
D. Analyzing categorical data using logistic regression
B. Analyzing data where each observation is a function or curve rather
than a finite-dimensional vector
RATIONALE: Functional data analysis treats each observation as a
continuous function or curve, such as growth trajectories or spectral curves.
Option A describes standard scalar data, option C describes the high-
dimensional "p > n" problem, and option D describes categorical data
analysis.
Question 2
In functional data analysis, what is the primary purpose of basis expansion?
A. To reduce the number of observations
B. To represent functional data using a linear combination of basis functions
C. To eliminate outliers from the dataset
D. To transform categorical variables into continuous variables
, B. To represent functional data using a linear combination of basis
functions
RATIONALE: Basis expansion represents a function as a linear
combination of basis functions (e.g., B-splines, Fourier basis). This allows
functional data to be analyzed using multivariate techniques by working with
the basis coefficients.
Question 3
Which of the following is a common basis function used in functional data
analysis?
A. Radial basis function
B. B-spline
C. Sigmoid function
D. Softmax function
B. B-spline
RATIONALE: B-splines are commonly used as basis functions in
functional data analysis due to their local support and smoothness properties.
Radial basis functions are used in interpolation and neural networks, while
sigmoid and softmax are activation functions.
Question 4
What is the fundamental challenge in high-dimensional regression when p >
n (more predictors than observations)?
A. The model is overidentified
B. The ordinary least squares solution is not unique
C. The model has too few parameters
D. The data cannot be standardized
B. The ordinary least squares solution is not unique
, RATIONALE: When p > n, the design matrix X is not full rank, leading to
infinitely many least squares solutions. Regularization techniques are
required to obtain a unique solution.
Question 5
Which regularization method adds an L1 penalty to the regression objective
function?
A. Ridge regression
B. Lasso regression
C. Elastic net
D. Principal component regression
B. Lasso regression
RATIONALE: Lasso (Least Absolute Shrinkage and Selection Operator)
adds an L1 penalty (sum of absolute values of coefficients) to the least squares
objective. Ridge adds an L2 penalty, and elastic net combines L1 and L2
penalties.
Question 6
What property of the Lasso penalty makes it useful for feature selection?
A. It shrinks all coefficients toward zero equally
B. It forces some coefficients to be exactly zero
C. It is computationally faster than Ridge
D. It is insensitive to outliers
B. It forces some coefficients to be exactly zero
RATIONALE: The L1 penalty in Lasso has the property of producing
sparse solutions by driving some coefficients exactly to zero, effectively
performing feature selection. Ridge regression shrinks coefficients but does
not set them to zero.
