ML MASTERS

What is the primary conceptual difference between a deterministic function and a non-deterministic function in supervised learning?

"In a non-deterministic function

"When deriving a Maximum Likelihood (ML) hypothesis for binary non-deterministic data ($0$ or $1$)

what type of error function is typically used instead of sum of squared errors?"

How does a standard neural network using sum of squared errors behave when trained on non-deterministic data where the same $x$ has different $y$ values?

"The network will attempt to predict the mean value of $y$ for each $x$

What is the structural limitation of a single-layer perceptron regarding boolean functions like XOR ($A \oplus B$)?

A single-layer perceptron can only implement linearly separable functions and cannot solve XOR because no single line can separate the outputs.

What is a major advantage of the gradient descent training rule over the perceptron training rule for neural networks?

Gradient descent allows for training multi-layer networks by utilizing differentiable error functions and the chain rule for backpropagation.

"In decision tree regression using squared error

what value is predicted at a leaf node?"

How does a 'lazy' version of the ID3 decision tree algorithm differ from the standard 'eager' version?

"The lazy algorithm delays building the tree until a prediction is needed for a specific test instance

"Between Decision Trees and Nearest-Neighbor learning

which is generally more efficient for a target function defined by a diagonal line in a 2D plane?"

What is the VC dimension of an origin-centered circle in a 2D plane?

The VC dimension is 2 because it can shatter any 2 points but fails on 3 points if the inner two are positive and the outer one is negative.

How is entropy defined in the context of information theory?

Entropy is a measure of the average uncertainty or randomness associated with a random variable's possible outcomes.

Under what condition is the K-means clustering procedure considered a special case of the Expectation-Maximization (EM) algorithm?

"K-means is a special case of EM when the model assumes a mixture of Gaussians with equal

What does the first Principal Component in PCA represent in terms of data variance?

The first Principal Component is the direction in the feature space along which the data exhibits the maximum possible variance.

Which hierarchical clustering linkage method is most likely to produce 'chaining' effects where clusters are merged based on single close points?

Single-link clustering is most prone to chaining because it defines distance as the minimum distance between any two points in different clusters.

"In Markov Decision Processes (MDPs)

what is the core purpose of the Bellman Equation?"

What distinguishes Policy Iteration from Value Iteration in Reinforcement Learning?

"Policy Iteration alternates between explicitly evaluating a fixed policy and improving it

What is the conceptual definition of a Nash Equilibrium in game theory?

It is a strategy profile where no player can increase their payoff by unilaterally changing their own strategy while others keep theirs fixed.

Why is pruning applied to decision trees during the training process?

"Pruning is used to reduce overfitting by removing branches that offer little predictive power

What is a primary goal of cross-validation in regression analysis?

Cross-validation is used to estimate the generalization performance of the model and assist in hyperparameter tuning.

"In neural network training

what does the 'vanishing gradient problem' refer to?"

What characteristic makes instance-based learning (like KNN) sensitive to irrelevant features?

"Because it relies on similarity measures in the full feature space

How do ensemble methods like Random Forests or Boosting improve model generalization?

"They combine multiple diverse models to mitigate individual model weaknesses

What is the 'kernel trick' in Support Vector Machines (SVMs)?

The kernel trick implicitly maps data into a higher-dimensional space to find a linear separating hyperplane for non-linearly separable data.

"In the PAC learning framework

what does the 'confidence parameter' represent?"

What is the relationship between a model's VC dimension and its potential to overfit?

"A high VC dimension indicates a more complex hypothesis class with a greater capacity to fit noise

How can randomized optimization algorithms escape local optima?

They introduce probabilistic or random moves that allow the search to transition to inferior states temporarily to find better global solutions.

What is the primary innovation of AdamW compared to the standard Adam optimizer?

AdamW decouples weight decay from the gradient-based adaptive update to ensure the regularization effect remains consistent regardless of the learning rate.

"According to Information Theory

how does the probability of an event relate to the information it carries?"

What does the 'likelihood' represent in Bayesian Learning?

The likelihood quantifies the probability of observing the specific training data given that a particular hypothesis is true.

Why is Bayesian inference considered a 'principled' way to update beliefs?

It uses probability theory to mathematically integrate prior knowledge with new evidence to form a posterior probability distribution.

Why is feature scaling critical for K-Means clustering?

"K-Means uses distance calculations (like Euclidean distance)

What is a significant risk when performing feature selection using a simple filter method?

Filter methods may discard features that appear irrelevant individually but are highly predictive when combined with other features.

How does UMAP differ from t-SNE in its approach to manifold learning?

"UMAP better preserves global structure and provides a faster

"In feature transformation

how does Independent Component Analysis (ICA) differ from PCA?"

What is the definition of a 'greedy' policy in Reinforcement Learning?

A greedy policy is one where the agent always selects the action that maximizes the immediate expected reward or state-action value.

"In MDPs

what does a discount factor ($\gamma$) near 0 imply about the agent's behavior?"

What is the purpose of the 'Experience Replay' buffer in Deep Q-Networks (DQN)?

"It stores past transitions to allow the model to sample randomly

How do Dueling Networks improve the architecture of a standard DQN?

"They split the network into two streams to separately estimate the state value and the advantage of each action

What is the function of 'NoisyNets' in the Rainbow DQN framework?

NoisyNets inject learned noise into the network weights to encourage state-dependent exploration without relying on a fixed $\epsilon$-greedy schedule.

Why might a general-sum stochastic game lack a unique $Q^*$ solution?

"Unlike zero-sum games

"In the context of clustering

what is the 'complete link' criteria?"

What does Mutual Information measure between two random variables?

"It measures the amount of information obtained about one random variable by observing the other

How does prioritized experience replay change the sampling process in reinforcement learning?

"It samples transitions with high temporal-difference (TD) error more frequently

What is the 'out-of-sample mapping' problem in manifold learning?

It is the difficulty of determining where a new data point should be placed in a low-dimensional embedding without re-running the entire algorithm.

"In Bayesian Learning

what is the Maximum A Posteriori (MAP) hypothesis?"

What is 'Sample Complexity' in Computational Learning Theory?

Sample complexity is the number of training examples required for a learning algorithm to achieve a specified level of accuracy with high confidence.

Why can Decision Trees be used for classification even if they are 'axis-aligned'?

"They can approximate complex boundaries by creating a large number of hierarchical

What is the 'Advantage' function in Dueling DQN architectures?

The advantage function measures the relative importance of a specific action compared to the average value of all actions in that state.

"In K-Means clustering

what does 'proper initialization' help to avoid?"

How does 'weight decay' act as a form of regularization in neural networks?

"It penalizes large weights by adding their magnitude to the loss function

What is the primary conceptual use of KL Divergence in machine learning?

"KL Divergence is used to measure the difference or 'distance' between two probability distributions

What is the primary function of elitism in Genetic Algorithms (GAs)?

It copies the top performing individuals unchanged to the next generation to preserve the best-found fitness.

"In Genetic Algorithms

what is a potential consequence of excessive selection pressure?"

True or False: Genetic Algorithms are strictly limited to binary encodings.

False; real-valued representations are valid and frequently used in GA implementations.

How does the MIMIC algorithm learn to generate new candidate solutions?

It fits a probabilistic model (often a tree-structured distribution) to a selected set of elite samples.

Under what condition does the MIMIC algorithm reduce to an Estimation of Distribution Algorithm (EDA) with factorized marginals?

This occurs when full independence across all variables is assumed.

"In Simulated Annealing

what is the acceptance probability for a 'downhill' move that decreases cost ($\Delta E < 0$)?"

How does the temperature $T$ in Simulated Annealing influence the acceptance of 'uphill' moves?

"High temperatures increase the probability of accepting uphill moves to encourage exploration

What is a key conceptual difference between Heavy-ball momentum and Nesterov Accelerated Gradient (NAG)?

"Heavy-ball uses the current gradient

Why is 'bias correction' used in the Adam optimizer?

It counters the zero-initialization bias of the first and second moment moving averages during early training steps.

How does AdamW differ from standard Adam regarding weight decay?

AdamW decouples weight decay from the adaptive gradient updates to ensure it behaves consistently regardless of the learning rate.

"In Information Theory

how does the entropy of a biased coin compare to that of a fair coin?"

Under what condition does the mutual information $I(X; Y)$ in a Binary Symmetric Channel become zero?

It becomes zero when the bit-flip probability $\epsilon$ is exactly 0.5 and $X$ is uniform.

"In Bayesian Learning

what occurs to the Maximum A Posteriori (MAP) estimate if the prior $P(h)$ is uniform over all hypotheses?"

What defines the Bayes-optimal decision boundary when class-conditional distributions are Gaussians with a shared covariance matrix?

The resulting decision boundary is linear in the feature space $x$.

How does increasing the prior probability $P(y=1)$ for a class affect its posterior probability $P(y=1 | x)$?

The posterior probability increases monotonically as the prior for that class increases.

What is the core assumption of the Naive Bayes classifier regarding features?

It assumes all features are conditionally independent given the class label.

"In a Markov Decision Process (MDP)

what does the transition function $P(s' | s

What is a primary advantage of model-based reinforcement learning over model-free methods?

Model-based methods are generally more sample efficient because they can plan using a learned model of the environment.

Why might a model-based RL agent perform poorly compared to a model-free agent in a complex environment?

Its performance is strictly limited by the accuracy of its learned internal model of the environment.

How do SARSA and Q-Learning differ in their update rules?

"SARSA is on-policy (updates based on the actual next action)

What is the 'Folk Theorem' in repeated games?

"It suggests that many outcomes

"In Game Theory

how does a 'Grim Trigger' strategy function?"

"What is the 'Pavlov' (Win-Stay

Lose-Shift) strategy in a repeated game?"

"In the ID3 algorithm

what does a leaf node with zero entropy signify?"

How does L2 regularization (Ridge Regression) help mitigate multicollinearity?

"It penalizes large weights

"In classification

why is accuracy often a misleading metric for imbalanced datasets?"

What is the conceptual relationship between $k$ in $k$-Nearest Neighbors and model bias/variance?

"Small $k$ values result in low bias but high variance

Why can a single-layer perceptron not solve the XOR problem?

"The XOR function is not linearly separable

What is required in a neural network to represent non-linear functions like XOR?

The network must have at least one hidden layer with a non-linear activation function.

What does PAC (Probably Approximately Correct) learning guarantee with probability $1 - \delta$?

It guarantees that the learned hypothesis will have an error of at most $\epsilon$.

How does the expressiveness of a hypothesis class $\mathcal{H}$ affect sample complexity in PAC learning?

More expressive hypothesis classes (larger $|\mathcal{H}|$ or higher VC dimension) require more training samples to achieve the same error bounds.

What is the VC dimension of a hypothesis class?

It is the size of the largest set of points that can be 'shattered' (perfectly classified in all possible ways) by the class.

Why might K-Means clustering be biased toward larger clusters?

"It uses Euclidean distance and minimizes the sum-of-squares

How do Gaussian Mixture Models (GMMs) handle cluster sizes better than K-Means?

"GMMs learn separate covariance structures and mixing coefficients

What is the 'chaining' property in single-linkage hierarchical clustering?

"It refers to the tendency of the algorithm to merge clusters that are connected by a series of points

"In feature selection

what is the difference between 'relevance' and 'usefulness'?"

Compare 'Filter' and 'Wrapper' methods for feature selection.

"Filters rank features based on statistical properties (fast)

What is a significant risk of using 'Wrapper' methods on small datasets?

They are highly prone to overfitting because they optimize the feature subset specifically for the training/validation performance.

What is the primary goal of Principal Component Analysis (PCA)?

To reduce dimensionality by transforming data into orthogonal components that capture the maximum variance.

How does Independent Component Analysis (ICA) differ from PCA in terms of the components it seeks?

"PCA seeks orthogonal components that maximize variance

"In manifold learning

how does Isomap approximate 'geodesic' distance?"

Why is t-SNE generally considered poor for quantitative retrieval tasks in production?

"It distorts global geometry and cluster areas

What is a major conceptual advantage of UMAP over t-SNE?

UMAP generally preserves more of the global structure and is theoretically more grounded in manifold topology.

What does 'subgame perfection' require in a multi-stage game?

"It requires that the strategy forms a Nash equilibrium in every possible subgame

"In the context of AdamW

why is 'weight decay' applied directly to the weights rather than the gradient?"

How does the 'epsilon' parameter in RMSprop/Adam affect the update when placed outside the square root?

Placing it outside helps stabilize the step size when the squared gradient accumulator $v_t$ is very small.

"In PAC learning

what is the impact of reducing the confidence parameter $\delta$ (delta)?"

What is the VC dimension of linear hyperplanes in $\mathbb{R}^{10}$?

"The VC dimension is $d + 1$

Why might density-based clustering like DBSCAN fail on datasets with clusters of varying densities?

"DBSCAN uses a global density threshold (epsilon and MinPts)

What is 'embedded' feature selection?

"Feature selection that occurs automatically during the model training process