IIT M DIPLOMA AN EXAM QDD3 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, std=1.

• Encoding Categorical Data:

  • OneHotEncoder: Converts categories into binary columns.
  • LabelEncoder: Converts categories into integers (ordinal).

• Polynomial Features:

  • Generates interaction terms/non-linear features (e.g., $x_1^2, x_1x_2$).
  • Number of features for degree d and n original features:

• PCA (Principal Component Analysis):

  • Reduces dimensionality by projecting data onto orthogonal axes (principal components).
  • n_components: Number of PCs to retain.

Code Snippets:

from sklearn.preprocessing import MinMaxScaler, StandardScaler, OneHotEncoder, PolynomialFeatures
from sklearn.decomposition import PCA

### Example: Polynomial + PCA
poly = PolynomialFeatures(degree=2, include_bias=False)
pca = PCA(n_components=5)

2. Model Training & Evaluation

Key Concepts:

• Dummy Regressor/Classifier:

  • strategy="mean": Predicts the mean of y (regression).
  • strategy="most_frequent": Predicts the mode of y (classification).

• K-Nearest Neighbors (KNN):

  • Bottleneck: Prediction time (searches entire training set).
  • Distance Metrics: Euclidean, Manhattan (p=1 in Minkowski), etc.
  • effective_metric_: Returns the actual metric used (e.g., "manhattan").

• Naïve Bayes:

  • Assumes feature independence given the class.

  • Variants:

    • GaussianNB: Continuous data (assumes Gaussian distribution).
    • BernoulliNB: Binary features.
    • MultinomialNB: Discrete counts (e.g., text data).
  • Outputs posterior probabilities (predict_proba).

• Logistic Regression:

  • Solvers: liblinear, lbfgs, saga (for small/large datasets).
  • Regularization: Controlled by C (inverse of strength; smaller C = stronger regularization).
  • Multi-class: Uses ovr (one-vs-rest) or multinomial (softmax).

• Support Vector Machines (SVM):

  • Kernels: linear, poly, rbf, sigmoid.
  • Regularization: C (trade-off between margin width and classification error).
  • degree: Only used for kernel="poly".

• Random Forest:

  • Randomness Sources:

    • Bootstrapping (bootstrap=True).
    • Feature subset selection (max_features < n_features).
  • Out-of-Bag (OOB) Score: Estimates generalization error when bootstrap=True.
  • class_weight: Handles class imbalance.

• AdaBoost:

  • Overfitting Mitigation: Reduce learning_rate or n_estimators.

• Stochastic Gradient Descent (SGD):

  • Learning Rate Schedules:

    • constant: Fixed rate (eta0).
    • invscaling: Decays with power_t.

• adaptive: Adjusts based on loss.

  • Penalties: l1 (Lasso), l2 (Ridge), elasticnet.
  • Early Stopping: Stops if validation score doesn’t improve by tol for n_iter_no_change iterations.
  • Hyperparameter Tuning:
  • GridSearchCV: Exhaustive search over a parameter grid.
  • RandomizedSearchCV: Random sampling from a distribution.

Evaluation Metrics:

• Confusion Matrix:

  • Recall (Sensitivity):

• Precision:

• F1-Score: Harmonic mean of precision and recall.

  • Imbalanced Data: Accuracy can be misleading; use precision-recall curves or F1-score.

3. Clustering

Key Concepts:

• K-Means:

  • Initialization: k-means++ spreads centroids to avoid poor clusters.

  • Optimal k:

    • Elbow Method: Plot inertia (within-cluster sum of squares) vs. k.
    • Silhouette Score: Measures cohesion/separation.

• Hierarchical Clustering:

  • Linkage Metrics: Euclidean, Manhattan, centroid, etc.
  • Agglomerative: Bottom-up merging of clusters.

4. Neural Networks (MLP)

Key Concepts:

• MLPRegressor/Classifier:

  • hidden_layer_sizes: Tuple specifying layers (e.g., (100, 50)).
  • activation: relu, logistic, tanh.
  • solver: adam, lbfgs, sgd.
  • early_stopping: Stops training if validation score doesn’t improve.
• Scaling: Critical for convergence (use StandardScaler).

5. Ensemble Methods

Key Concepts:

• Voting Classifier:

  • weights: Assigns importance to each model (e.g., [1, 2, 3]).

• Bagging (Random Forest):

  • Reduces variance by averaging multiple models.

• Boosting (AdaBoost):

  • Sequentially corrects errors of weak learners.

6. Dimensionality Reduction

Key Concepts:

• PCA:

  • Transforms data into orthogonal components ordered by variance.
  • n_components: Number of PCs to retain.

• Feature Union:

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

7. Model Interpretation

Key Concepts:

• Feature Importance:

  • Random Forest: feature_importances_.
  • Linear Models: Coefficient magnitudes.
• Partial Dependence Plots: Shows relationship between a feature and predictions.

8. Handling Missing Data

Key Concepts:

• Pandas:

  • df.isnull().sum(): Counts null values per column.
  • df.dropna(): Drops rows/columns with nulls.
  • df.fillna(): Imputes missing values.

9. Pandas Operations

Key Concepts:

• Filtering:

  df[(df['sex'] == 'female') & (df['alive'] == 'yes')]

• Applying Functions:

  df['isAdult'] = df['age'].apply(lambda x: x >= 18)

Graph 2: Model Evaluation Metrics

Graph 3: Hyperparameter Tuning

Graph 4: Ensemble Methods

Graph 5: Clustering Algorithms

Graph 6: Neural Networks

Graph 7: SVM Key Parameters