IIT M DIPLOMA AN EXAM QDD2 26 Oct 2025 - 26 Oct 2025

Concepts this paper tests

Auto-generated summary from the source site. Handy as a checklist; the lessons above explain each idea from scratch.

Here’s a structured summary of core topics, concepts, and equations for the Diploma-Level Machine Learning Foundations exam, along with Mermaid knowledge graphs to visualize relationships.

1. Core Topics & Concepts

A. Machine Learning Fundamentals

1. Supervised Learning:

   • Classification (e.g., loan approval: Yes/No).

     • Algorithms: Logistic Regression, Decision Trees, SVM.

   • Regression (predicting continuous values).

     • Algorithms: Linear Regression, Polynomial Regression.

   • Loss Functions:

     • Squared Loss (MSE) for regression: $L(y, \hat{y}) = \frac{1}{n} \sum_{i=1}^n (y_i - \hat{y}_i)^2$.
     • Log Loss (Cross-Entropy) for classification: $L(y, \hat{y}) = -\sum_{i=1}^n y_i \log(\hat{y}_i)$.

1. Unsupervised Learning:

   • Clustering (e.g., K-Means, Hierarchical Clustering).
   • Dimensionality Reduction (e.g., PCA, t-SNE).

1. Model Evaluation:

   • Overfitting/underfitting, bias-variance tradeoff.
   • Train/test split, cross-validation.

B. Linear Algebra (Critical for ML)

1. Matrix Basics:

   • Row Space: Span of row vectors of a matrix $A$.

   • Basis: Linearly independent vectors spanning a space.

     • Example: For $A \in \mathbb{R}^{m \times n}$, row space basis has rank $r \leq \min(m, n)$.
   • Rank: Number of linearly independent rows/columns.

1. Special Matrices:

   • Orthogonal Matrix: $A^T A = I$ (columns are orthonormal).
   • Symmetric Matrix: $A = A^T$.
   • Invertible Matrix: $\det(A) \neq 0$, $AA^{-1} = I$.

1. Eigenvalues/Eigenvectors:

   • For matrix $A$, solve $A \mathbf{v} = \lambda \mathbf{v}$.
   • Real Symmetric Matrices: All eigenvalues are real.

   • Diagonalizable Matrix: $A = PDP^{-1}$ (requires $n$ linearly independent eigenvectors).

     • Not all diagonalizable matrices are invertible (e.g., singular matrices with $\lambda = 0$).

1. Key Theorems:

   • A matrix is diagonalizable iff it has $n$ linearly independent eigenvectors (not necessarily distinct eigenvalues).
   • Spectral Theorem: Real symmetric matrices are diagonalizable.

C. Probability & Statistics (Implied in Questions)

1. Basics:

   • Expected value, variance, covariance.
   • Conditional probability (Bayes’ Theorem for classification).

1. Distributions:

   • Gaussian (Normal) distribution for regression.
   • Bernoulli distribution for binary classification.

D. Calculus (Optimization)

1. Gradient Descent:

   • Update rule: $\theta := \theta - \alpha \nabla J(\theta)$.
   • Used to minimize loss functions (e.g., MSE, log loss).

1. Partial Derivatives:

   • Critical for computing gradients in ML models.

2. Key Equations

Graph 2: Linear Algebra Concepts

Graph 3: Model Evaluation & Optimization

4. Exam Tips

1. Classification vs. Regression:

   • Use classification for categorical outputs (e.g., loan approval).
   • Use regression for continuous outputs (e.g., predicting house prices).

1. Linear Algebra:

   • Basis: Must be linearly independent and span the space.
   • Eigenvalues: Real symmetric matrices always have real eigenvalues.
   • Diagonalizable: Requires $n$ linearly independent eigenvectors (not necessarily distinct eigenvalues).

1. Loss Functions:

   • Squared Loss is for regression.
   • Log Loss is for classification.

1. True/False Questions:

   • A matrix is diagonalizable iff it has $n$ linearly independent eigenvectors (not necessarily distinct eigenvalues).
   • Real symmetric matrices always have real eigenvalues.
   • Orthogonal matrices satisfy $A^T A = I$.