IIT M DIPLOMA AN EXAM QDD2 01 Dec 2024 - 01 Dec 2024

Concepts this paper tests

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

Summary of Core Topics, Concepts, Principles, and Equations

1. Machine Learning Models and Algorithms

• Ridge Regression

  • Concept: Linear regression with L2 regularization.
  • Equation: $\text{RSS} + \lambda \sum_{j=1}^{p} \beta_j^2$
  • Key Parameter: alpha (regularization strength).

• Stochastic Gradient Descent (SGD)

  • Concept: Optimization algorithm for training linear models.
  • Key Parameters: penalty, l1_ratio, alpha, tol.
  • Equation: $w = w - \eta \nabla Q_i(w)$

• Polynomial Regression

  • Concept: Extending linear regression by adding polynomial terms.
  • Equation: $y = \beta_0 + \beta_1 x + \beta_2 x^2 + \dots + \beta_n x^n$

• Support Vector Machines (SVM)

  • Concept: Supervised learning model for classification and regression.
  • Key Parameters: C (regularization), kernel (linear, rbf, sigmoid).
  • Equation: $\min_{w} \frac{1}{2} \|w\|^2 + C \sum_{i=1}^{n} \xi_i$

• Logistic Regression

  • Concept: Classification algorithm for binary and multiclass problems.
  • Equation: $\sigma(z) = \frac{1}{1 + e^{-z}}$
  • Key Parameters: penalty, C.

• K-Nearest Neighbors (KNN)

  • Concept: Non-parametric method for classification and regression.
  • Key Parameters: n_neighbors, metric, weights.
  • Equation: $\hat{y} = \frac{1}{k} \sum_{i=1}^{k} y_i$

• Gaussian Naive Bayes

  • Concept: Probabilistic classifier based on Bayes' theorem.
  • Equation: $P(y|X) = \frac{P(X|y)P(y)}{P(X)}$

• Perceptron

  • Concept: Linear classifier for binary classification.
  • Equation: $y = \text{sign}(w \cdot x + b)$

2. Model Evaluation Metrics

• Precision Score

  • Concept: Ratio of true positives to the sum of true and false positives.
  • Equation: $\text{Precision} = \frac{TP}{TP + FP}$

• Mean Squared Error (MSE)

  • Concept: Average squared difference between predicted and actual values.
  • Equation: $\text{MSE} = \frac{1}{n} \sum_{i=1}^{n} (y_i - \hat{y}_i)^2$

• R² Score

  • Concept: Coefficient of determination.
  • Equation: $R^2 = 1 - \frac{\text{SS}_{\text{res}}}{\text{SS}_{\text{tot}}}$

3. Data Preprocessing and Feature Engineering

• StandardScaler

  • Concept: Standardizes features by removing the mean and scaling to unit variance.
  • Equation: $z = \frac{x - \mu}{\sigma}$

• Polynomial Features

  • Concept: Generates polynomial and interaction features.
  • Equation: $x_1, x_2, x_1^2, x_1x_2, x_2^2, \dots$

• CountVectorizer

  • Concept: Converts text documents to a matrix of token counts.
  • Key Parameter: ngram_range.

4. Hyperparameter Tuning and Model Selection

• GridSearchCV

  • Concept: Exhaustive search over specified parameter values for a model.
  • Key Parameters: param_grid, cv, scoring.

• Pipeline

  • Concept: Sequentially applies a list of transforms and a final estimator.
  • Example: Pipeline([('scaler', StandardScaler()), ('classifier', SVC())])

5. Handling Missing Data

• KNNImputer

  • Concept: Imputes missing values using the K-Nearest Neighbors approach.
  • Key Parameters: n_neighbors, weights.