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Advanced Data Science Principles

Data Science

A collection of technical questions covering statistical theory, machine learning algorithms, and information theory.

statistics machine-learning information-theory

15 Questions Hard Ages 18+ Aug 29, 2026

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About this Study Set

This study set covers Data Science through 15 practice questions. A collection of technical questions covering statistical theory, machine learning algorithms, and information theory. Every question includes the correct answer so you can learn as you go — pick any format above to get started.

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1 In the context of the Bias-Variance Tradeoff, what does the 'irreducible error' represent?

A The error caused by high-bias models
B The variance component of the mean squared error
C The noise term in the true data-generating process
D The bias introduced by feature selection

2 Which theorem states that for any optimization algorithm, every representation of all possible problems will have the same performance when averaged over all possible problems?

A The No Free Lunch Theorem
B The Central Limit Theorem
C The Gauss-Markov Theorem
D The Stone-Weierstrass Theorem

3 In Information Theory, what is the mathematical definition of Kullback-Leibler (KL) divergence?

A A symmetric measure of distance between two probability distributions
B The entropy of a joint distribution minus the entropy of marginals
C A measure of how one probability distribution differs from a second, reference distribution
D The log-likelihood ratio of two nested models

4 Which regularization technique adds a penalty equal to the sum of the absolute values of the coefficients?

A Ridge Regression (L2)
B Lasso Regression (L1)
C Elastic Net
D Elastic Dropout

5 In the context of Support Vector Machines (SVM), what is the function of the 'kernel trick'?

A To normalize input data to a mean of zero
B To map input features into a higher-dimensional space to allow linear separation
C To reduce the number of support vectors for faster computation
D To optimize the selection of the hyperparameter C

6 What is the primary condition required for the Gauss-Markov Theorem to hold regarding Ordinary Least Squares (OLS) estimators?

A Errors must follow a non-parametric distribution
B Errors must be homoscedastic and uncorrelated with mean zero
C The number of predictors must exceed the number of observations
D The model must include an interaction term

7 In Gradient Boosting, what does the 'learning rate' (or shrinkage) parameter fundamentally control?

A The depth of the individual decision trees
B The contribution of each successive tree to the final prediction
C The threshold for pruning leaf nodes
D The size of the initial bootstrap sample

8 Which property of a stationary time series implies that the joint distribution of the series is invariant to time shifts?

A Weak stationarity
B Strict stationarity
C Cyclostationarity
D Non-ergodicity

9 What is the 'Curse of Dimensionality' in the context of Euclidean distance?

A The computational complexity grows exponentially with the number of samples
B The ratio of the distance to the nearest and farthest neighbor tends toward one in high dimensions
C The model becomes increasingly biased as dimensions increase
D The variance of the model decreases as features are added

10 In Bayesian inference, what is the term for the distribution representing prior beliefs updated with observed data?

A Likelihood function
B Marginal distribution
C Posterior distribution
D Conjugate prior

11 Which activation function is defined as f(x) = ln(1 + e^x) and is known as the smooth approximation of the ReLU function?

A Sigmoid
B Softplus
C Tanh
D Leaky ReLU

12 In cluster analysis, what is the objective function minimized by the K-Means algorithm?

A Within-cluster sum of squares (WCSS)
B Between-cluster variance
C The Silhouette coefficient
D The Calinski-Harabasz index

13 Which statistical method is specifically designed to handle multicollinearity by transforming variables into uncorrelated components?

A Principal Component Regression (PCR)
B Stepwise Regression
C Ordinary Least Squares
D Lasso Regression

14 What does the Vapnik-Chervonenkis (VC) dimension measure in statistical learning theory?

A The computational speed of an algorithm
B The capacity (complexity) of a statistical classification algorithm
C The minimum number of samples needed to achieve zero bias
D The variance of an estimator in high dimensions

15 In a hidden Markov model, what does the Viterbi algorithm compute?

A The probability of a specific observation sequence
B The most likely sequence of hidden states given an observation sequence
C The parameters that maximize the probability of the observations
D The stationary distribution of the Markov chain

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