AI/ML Engineering Foundations

Describe key probability distributions (Gaussian, Bernoulli, Categorical) and explain their roles in ML modeling.

Apply Bayes' theorem to update prior beliefs with observed data in a classification context.

Compute gradients of multivariable functions and apply the chain rule to composite functions relevant to ML optimization.

Apply eigenvalue decomposition to covariance matrices and interpret its geometric meaning for data analysis.

Explain Maximum Likelihood Estimation (MLE) as a general principle for fitting probabilistic models.

Explain the principle of Empirical Risk Minimization as the theoretical foundation of learning from data.

Define machine learning and contrast it with traditional rule-based programming using real-world examples.

Distinguish between supervised, unsupervised, and reinforcement learning paradigms with illustrative examples.

Define hypothesis spaces, model parameters, and hyperparameters in the context of model selection.

Derive the ordinary least squares solution for linear regression from the normal equations.

Derive logistic regression from the sigmoid function and the principle of maximum likelihood estimation.

Explain the cross-entropy loss function and its information-theoretic interpretation for classification.

Define and compare common loss functions for regression (MSE, MAE) and classification (Cross-Entropy).

Apply gradient descent to iteratively minimize a loss function, explaining the role of learning rate and convergence criteria.

Distinguish between convex and non-convex optimization problems and their implications for finding global minima.

Derive L1 (Lasso) and L2 (Ridge) regularization as constrained optimization problems and explain their effects on model weights.

Explain the bias-variance tradeoff and its relationship to model complexity and regularization.

Explain polynomial regression as a method to increase model expressiveness and the associated risk of overfitting.

Explain the train/validation/test split methodology and its importance for unbiased performance estimation.

Identify overfitting and underfitting by interpreting the behavior of training and validation learning curves.

Apply k-fold cross-validation to obtain a robust estimate of model generalization performance.

Construct a confusion matrix for a classification problem and define accuracy, precision, and recall.

Compute and interpret F1-score as the harmonic mean of precision and recall.

Explain the Receiver Operating Characteristic (ROC) curve and interpret the Area Under the Curve (AUC) metric.

Explain the decision tree algorithm using information gain or Gini impurity as splitting criteria.

Derive the bagging principle and explain how Random Forests reduce variance over individual trees.

Describe the boosting framework and contrast the mechanisms of AdaBoost and Gradient Boosting.

Compare Random Forests and Gradient Boosting in terms of their bias-variance characteristics and training procedures.

Derive the maximum-margin classification principle behind Support Vector Machines (SVMs).

Explain the kernel trick and how it enables non-linear classification in SVMs without explicit feature transformation.

Explain the K-means clustering algorithm, its objective function, and its iterative optimization process.

Derive Principal Component Analysis (PCA) as the eigenvalue decomposition of the data covariance matrix.

Interpret explained variance ratios in PCA to guide dimensionality selection for a dataset.

Explain Gaussian Mixture Models (GMMs) for density estimation and contrast their probabilistic approach with K-means.

Derive the Expectation-Maximization (EM) algorithm as a general method for latent variable models, using GMMs as an example.

Describe the objective of t-SNE for high-dimensional data visualization and explain its primary use cases and limitations.

Describe the perceptron model and demonstrate its limitation to linearly separable problems.

Explain the role of non-linear activation functions (e.g., Sigmoid, Tanh, ReLU) in enabling deep networks to learn complex patterns.

Construct a feedforward neural network and define its forward propagation mechanism mathematically.

Apply the chain rule recursively to derive the gradient of the loss with respect to network parameters (the backpropagation algorithm).

Explain the vanishing and exploding gradient problems and their causes in deep feedforward networks.

Describe weight initialization strategies (e.g., Xavier/Glorot, He) and their theoretical justification for stable gradient flow.

Derive stochastic gradient descent (SGD) and explain its computational advantages over batch gradient descent.

Explain momentum-based optimization and its physical analogy for accelerating convergence.

Describe how RMSProp and Adam function as adaptive learning rate methods, and compare their tradeoffs.

Explain dropout as a regularization technique and its theoretical interpretation as a form of model ensemble approximation.

Explain batch normalization, the problem of internal covariate shift it addresses, and its distinct behaviors during training and inference.

Analyze the role of loss surfaces, local minima, and saddle points in the context of deep learning optimization.

Explain the convolution operation and how parameter sharing in CNNs exploits spatial hierarchies in data like images.

Describe the function of pooling layers, stride, and padding in a convolutional neural network.

Explain the vanilla Recurrent Neural Network (RNN) architecture, its weight sharing mechanism, and the process of unrolling for sequence processing.

Derive the backpropagation through time (BPTT) algorithm and use it to explain the long-range dependency problem in RNNs.

Describe how the gating mechanism in LSTMs (and GRUs) addresses the vanishing gradient problem.

Explain the encoder-decoder architecture for sequence-to-sequence tasks and identify its information bottleneck limitation.

Explain the conceptual motivation for the attention mechanism in overcoming the seq2seq information bottleneck.

Derive scaled dot-product attention mathematically.

Explain self-attention and how it enables the modeling of long-range dependencies without recurrence.

Derive multi-head attention and explain its role in capturing diverse feature representations from different subspaces.

Describe the high-level Transformer encoder-decoder architecture, including the role of positional encodings.

Detail the components of a Transformer block: multi-head attention, feed-forward networks, residual connections, and layer normalization.

Explain the pre-training and fine-tuning paradigm and its significance for transfer learning in modern NLP.

Contrast the architectures of BERT (encoder-only) and GPT (decoder-only) and their respective pre-training objectives.

Explain the architecture and reconstruction objective of a standard autoencoder for dimensionality reduction.

Derive the Variational Autoencoder (VAE), explaining the evidence lower bound (ELBO) and the reparameterization trick.

Describe the Generative Adversarial Network (GAN) framework, including the generator, discriminator, and minimax objective function.

Explain the core concept of diffusion models as a process of iterative denoising to generate data.

Define the core components of the Reinforcement Learning framework: agent, environment, state, action, and reward.

Derive the Bellman equation and explain its role in defining optimal value functions.

Describe Q-learning as a canonical value-based, off-policy reinforcement learning method.

Describe the core idea of policy gradient methods and how they differ from value-based methods.

Explain the theoretical principles of an MLOps pipeline, including experiment tracking, model versioning, and registries.

Describe model serving strategies (e.g., batch vs. real-time) and their architectural tradeoffs.

Explain the concepts of data drift and model drift and the importance of production monitoring.

Contrast CI/CD for ML systems with traditional software CI/CD, highlighting the role of data and model validation.