IIT M DIPLOMA FN EXAM QDD1 13 Apr 2025 - 13 Apr 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, principles, and equations essential for the exam, followed by Mermaid knowledge graphs to visualize relationships.

Core Topics & Concepts

1. Data Preprocessing

Key Concepts:

• Scaling/Normalization:

  • MinMaxScaler: Scales features to [0, 1] range.

• StandardScaler: Standardizes features to mean=0, variance=1.

• Encoding Categorical Data:

  • OneHotEncoder: Converts categorical features into binary columns.
  • LabelEncoder: Converts categorical labels into numerical values (e.g., ["Yes", "No"] → [1, 0]).

• Polynomial Features:

  • PolynomialFeatures(degree=n): Generates polynomial/combination features (e.g., $x_1, x_2, x_1^2, x_1x_2$).

• Pipeline & ColumnTransformer:

  • Pipeline: Sequentially applies transformations/estimators.
  • ColumnTransformer: Applies different transformations to different columns.

Key Equations:

2. Model Training & Evaluation

Key Concepts:

• Dummy Regressor/Classifier:

  • strategy="median": Always predicts the median of y_train.
  • strategy="most_frequent": Always predicts the most frequent class.

• K-Nearest Neighbors (KNN):

  • Bottleneck: Prediction time (searches entire training set).
  • Distance Metrics: Euclidean, Manhattan, Minkowski.
  • Hyperparameters: n_neighbors, p (for Minkowski), weights (uniform/distance).

• Naïve Bayes:

  • Assumes feature independence given the class.
  • Variants: Gaussian (continuous data), Multinomial (text), Bernoulli (binary features).

• Support Vector Machines (SVM):

  • Kernels: Linear, RBF, Polynomial, Sigmoid.
  • Hyperparameters: C (regularization), gamma (RBF kernel width).

• Decision Trees & Random Forest:

  • max_depth, min_samples_split, bootstrap, oob_score.
  • Random Forest: Ensemble of decision trees with bagging.

• Stochastic Gradient Descent (SGD):

  • learning_rate="adaptive", penalty="l2" (Ridge), early_stopping.
  • Loss functions: log_loss (classification), squared_error (regression).

• Neural Networks (MLP):

  • Activation functions: ReLU, Sigmoid, Tanh.
  • Solvers: adam, sgd, lbfgs.
  • Critical Preprocessing: Feature scaling (e.g., StandardScaler).

• Model Evaluation:

  • Confusion Matrix:

    • Recall (Sensitivity): $\frac{TP}{TP + FN}$
    • Precision: $\frac{TP}{TP + FP}$
    • F1-Score: $2 \times \frac{\text{Precision} \times \text{Recall}}{\text{Precision} + \text{Recall}}$
  • Classification Report: Precision, recall, F1-score per class.

  • Overfitting Mitigation:

    • Regularization (L1/L2), early stopping, reducing model complexity.

Key Equations:

3. Hyperparameter Tuning

Key Concepts:

• GridSearchCV: Exhaustive search over specified parameter values.
• RandomizedSearchCV: Randomly samples parameter combinations.
• Cross-Validation: Splits data into k folds to evaluate generalization.

• Common Hyperparameters:

  • C (SVM/Logistic Regression), alpha (Ridge/Lasso), n_estimators (Random Forest).

4. Clustering

Key Concepts:

• Hierarchical Clustering:

  • Agglomerative (Bottom-Up): Starts with individual points, merges closest clusters.
  • Divisive (Top-Down): Starts with one cluster, recursively splits.
  • Distance Metrics: Euclidean, Manhattan, Cosine, Jaccard.

• K-Means:

  • Requires predefined k (number of clusters).
  • Sensitive to initialization (use k-means++).

5. Dimensionality Reduction

Key Concepts:

• Principal Component Analysis (PCA):

  • Transforms features into orthogonal components (ordered by variance).
  • n_components: Number of principal components to retain.

• Feature Union:

  • Combines multiple feature transformations (e.g., PolynomialFeatures + PCA).

Key Equations:

6. Pandas & Data Handling

Key Concepts:

• DataFrame Slicing:

  • loc: Label-based indexing (inclusive of both start/end).
  • iloc: Position-based indexing (exclusive of end).

• Handling Missing Data:

  • dropna(), fillna(), or ignore in OneHotEncoder (handle_unknown="ignore").

• Aggregation:

  • groupby(), apply(), sum(), mean().

Example Code Snippets:

### loc vs iloc
df.loc[23:25, 'Marks':'History']  # Labels 23-25, columns 'Marks' to 'History'
df.iloc[2:4, 1:3]                 # Rows 2-3 (0-based), columns 1-2

7. Imbalanced Data & Metrics

Key Concepts:

• Accuracy Paradox: High accuracy can be misleading if classes are imbalanced.

• Better Metrics:

  • Precision-Recall Curve, ROC-AUC, F1-Score.
  • class_weight in models (e.g., RandomForestClassifier).

• Resampling:

  • Oversampling (SMOTE), undersampling.

Graph 2: Model Evaluation Metrics

Graph 3: Hyperparameter Tuning

Graph 4: Neural Networks (MLP)

Graph 5: Clustering Algorithms

Graph 6: SVM Kernels

Graph 7: Handling Imbalanced Data

Key Equations Summary