ISYE 6525 HIGH DIMENSIONAL DATA ANALYTICS EXAM 1 QUESTIONS COMPLETE WITH 100% VERIFIED ANSWERS

ISYE 6525 HIGH DIMENSIONAL DATA ANALYTICS EXAM 1
QUESTIONS COMPLETE WITH 100% VERIFIED ANSWERS




CORE DOMAINS COVERED

• FUNCTIONAL DATA ANALYSIS AND BASIS EXPANSIONS

• IMAGE PROCESSING AND FEATURE EXTRACTION

• MULTILINEAR ALGEBRA AND TENSOR D ECOMPOSITIONS

• 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

,Question 1
What is the primary distinction between functional data analysis and multivariate
data analysis?
A. FDA analyzes data where variables are independent while multivariate assumes
dependence
B. FDA treats each observation as a function while multivariate treats observations
as vectors
C. FDA requires normally distributed data while multivariate does not
D. FDA only works with time series data while multivariate works with any data
type
B. FDA treats each observation as a function while multivariate treats observations
as vectors
RATIONALE: Functional data analysis views each observation as a continuous
function or curve defined over some continuum, whereas traditional multivariate
analysis treats each observation as a finite-dimensional vector of measurements
at discrete points.


Question 2
In functional principal component analysis (FPCA), what is the key difference from
standard PCA?
A. FPCA uses covariance operators instead of covariance matrices
B. FPCA requires categorical variables
C. FPCA produces fewer components than standard PCA
D. FPCA cannot handle missing data
A. FPCA uses covariance operators instead of covariance matrices
RATIONALE: In FPCA, the data are functions, so the covariance structure is
represented by a covariance operator (integral operator) rather than a finite
covariance matrix. The eigenfunctions of this operator serve as the functional
principal components.

,Question 3
Which basis function system is most appropriate for periodic functional data?
A. B-splines
B. Fourier basis
C. Polynomial basis
D. Wavelet basis
B. Fourier basis
RATIONALE: Fourier basis functions (sine and cosine functions) are ideal for
periodic data because they naturally capture cyclic patterns and periodic behavior.
B-splines and wavelets are better suited for non-periodic data with local features.


Question 4
What is the roughness penalty approach in functional data analysis?
A. A method to remove outliers from functional data
B. A regularization technique that penalizes the curvature of fitted functions
C. A technique to increase the number of basis functions
D. A method to transform functional data to scalar values
B. A regularization technique that penalizes the curvature of fitted functions
RATIONALE: The roughness penalty approach adds a penalty term to the fitting
criterion that penalizes the integrated squared second derivative (or higher
derivatives) of the function, thereby controlling the smoothness of the estimated
function and preventing overfitting.


Question 5
What does the smoothing parameter λ control in penalized spline regression?
A. The number of basis functions
B. The trade-off between data fit and smoothness

, C. The convergence rate of the algorithm
D. The variance of the error term
B. The trade-off between data fit and smoothness
RATIONALE: The smoothing parameter λ controls the balance between fitting the
data well (small λ) and producing a smooth function (large λ). As λ increases, the
penalty on roughness becomes stronger, resulting in smoother estimates.


Question 6
Which of the following is a property of B-spline basis functions?
A. They are globally supported functions
B. They have compact local support
C. They are orthogonal to each other
D. They are only defined on bounded intervals
B. They have compact local support
RATIONALE: B-splines have compact local support, meaning each basis function is
nonzero only over a limited interval. This property makes them computationally
efficient and allows for flexible local control of the fitted function.


Question 7
In functional linear regression, what is the role of the coefficient function β(t)?
A. It represents the mean function of the response
B. It represents the effect of the predictor function at each point t
C. It represents the variance function of the predictors
D. It represents the intercept term only
B. It represents the effect of the predictor function at each point t
RATIONALE: In functional linear regression Y = α + ∫β(t)X(t)dt + ε, the coefficient
function β(t) quantifies how the response Y changes with respect to the predictor
function X at each time point t.