IIT M IMPROVEMENT AN EXAM QIC4 31 Aug - 31 Aug 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 for the Diploma-Level Machine Learning Practice (Computer-Based Exam), along with Mermaid knowledge graphs to visualize relationships.

1. Core Topics & Concepts

A. Model Training & Evaluation

Key Concepts:

1. Cross-Validation (K-Fold)

   • Splits data into k folds, trains k times (each fold as validation once).

   • Equation:

     • Inertia (for clustering): $\sum_{i=1}^{n} \min_{\mu_j \in C} (||x_i - \mu_j||^2)$
     • $R^2$-score: $1 - \frac{\sum (y_i - \hat{y}_i)^2}{\sum (y_i - \bar{y})^2}$
   • Example: 10-fold CV trains 10 models (Q2).

1. Model Persistence (warm_start)

   • Retains weights between .fit() calls (e.g., Perceptron(warm_start=True)) (Q3).

1. Confusion Matrix

   • Structure: | True\Pred | 0 | 1 | |-----------|---------|---------| | 0 | TN | FP | | 1 | FN | TP |

   • Metrics:

     • Precision: $\frac{TP}{TP + FP}$
     • Recall: $\frac{TP}{TP + FN}$
     • F1: $2 \times \frac{Precision \times Recall}{Precision + Recall}$
   • Use Case: Imbalanced data (e.g., rare disease detection) (Q15).

1. Evaluation Metrics for Imbalanced Data

   • Avoid: Accuracy (misleading for rare classes).
   • Use: Precision, Recall, F1, ROC-AUC (Q15).

B. Preprocessing & Feature Engineering

1. Image Processing

   • Resize: (1280, 1920, 3) → (200, 200) (grayscale).
   • Flatten: (200, 200) → (40000,) (Q5).
   • Equation: Flattened shape = $\text{height} \times \text{width} \times \text{channels}$.

1. Text Vectorization (TF-IDF)

   • TF-IDF: $\text{TF-IDF}(t, d) = \text{TF}(t, d) \times \text{IDF}(t)$
   • Sparsity: Most entries = 0 (Q18).

1. Handling Missing Data

   • df.dropna(subset=["col1", "col2"], how="all") (drops rows where both are NaN) (Q20).
   • Imputation: SimpleImputer(strategy="most_frequent") (Q12).

1. Feature Scaling

   • MinMaxScaler: $X_{\text{scaled}} = \frac{X - X_{\min}}{X_{\max} - X_{\min}}$ (scales to [0, 1]) (Q12).

C. Algorithms & Hyperparameters

1. Linear Models

   • SGDRegressor:

     • Loss functions: 'huber', 'squared_error' (Q8, Q22).
     • Learning rate: 'adaptive' (reduces LR if loss plateaus) (Q14).

   • Logistic Regression:

     • Elastic-net: $L1 + L2$ regularization (Q9).
     • Solver: 'saga' (supports elastic-net).

1. Neural Networks (MLP)

   • Hyperparameters:

     MLPClassifier(
         hidden_layer_sizes=(128, 64),  # 2 hidden layers
         activation="relu",
         solver="adam",
         alpha=1e-4,  # L2 regularization
         learning_rate_init=0.001,
         max_iter=300
     )

   • Equation: Output = $\sigma(W_2 \cdot \text{ReLU}(W_1 \cdot X + b_1) + b_2)$ (Q6).

1. Clustering (K-Means)

   • Elbow Method: Plot inertia vs. $k$; choose $k$ at the "elbow" (Q16).
   • Inertia: Sum of squared distances to centroids.

1. Time Series

   • ADF Test:

     • Null hypothesis: Time series is non-stationary (Q7).
     • Interpretation: $p < 0.05$ → stationary.

   • Decomposition:

     • Multiplicative: $Y_t = \text{Trend} \times \text{Seasonality} \times \text{Error}$ (Q11).

1. Collaborative Filtering

   • Cosine Similarity: $\text{similarity}(u, v) = \frac{u \cdot v}{||u|| \cdot ||v||}$
   • Prediction: Weighted average of similar users' ratings (Q25–27).

D. Scikit-Learn Utilities

1. Pipelines

   • Caching: memory="path/to/cache" avoids recomputing transformations (Q13).

   • Example:

     Pipeline([
         ("imputer", SimpleImputer(strategy="most_frequent")),
         ("scaler", MinMaxScaler())
     ])

1. Grid Search

   • Total Models: Product of hyperparameter options (Q24).

     • Example: 3 (n_estimators) × 4 (loss) × 3 (max_depth) = 36 models.

   • Scoring Metrics:

     • Regression: 'neg_mean_squared_error', 'r2'.
     • Classification: 'f1', 'roc_auc' (Q23).

Graph 2: Preprocessing Workflow

Graph 3: Algorithm Selection

Graph 4: Time Series Analysis

Graph 5: Collaborative Filtering

3. Key Equations

4. Exam Tips

1. Cross-Validation: Always count models as n_splits (Q2).
2. Imbalanced Data: Avoid accuracy; use precision/recall/F1 (Q15).
3. Hyperparameter Tuning: Total models = product of options (Q24).
4. Text/Image Data: Flattening → (height × width × channels,) (Q5).
5. Time Series: ADF $p < 0.05$ → stationary (Q7).
6. Collaborative Filtering: Cosine similarity for user-user predictions (Q25–27).