IIT M IMPROVEMENT AN EXAM QIC3 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

1. Cross-Validation (K-Fold)

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

   • Equation:

     • Inertia (for clustering): $\sum_{i=1}^{n} \min_{\mu \in C} ||x_i - \mu||^2$
     • $R^2$-score: $1 - \frac{\sum (y_i - \hat{y}_i)^2}{\sum (y_i - \bar{y})^2}$

   • Key Points:

     • KFold(n_splits=10) → 10 models trained.
     • cross_val_score returns scores for each fold.

1. Model Persistence (warm_start)

   • warm_start=True retains weights between .fit() calls (e.g., in Perceptron).
   • Useful for incremental learning.

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: $2 \times \frac{Precision \times Recall}{Precision + Recall}$

1. Evaluation for Imbalanced Data

   • Avoid Accuracy: Use Precision, Recall, F1, or ROC-AUC.
   • Example: Rare disease (0.5% prevalence) → Accuracy is misleading.

B. Preprocessing & Feature Engineering

1. Image Processing

   • Resize: (1280, 1920, 3) → (200, 200) (grayscale).
   • Flatten: (200, 200) → (40000,).

   • Equation:

     • Grayscale conversion: $0.299R + 0.587G + 0.114B$.

1. Text Vectorization (TF-IDF)

   • TF-IDF: $\text{TF-IDF}(t, d) = \text{TF}(t, d) \times \text{IDF}(t)$

     • $\text{TF}(t, d)$: Term frequency in document $d$.
     • $\text{IDF}(t)$: $\log \frac{N}{\text{DF}(t)}$ (N = total docs, DF = doc frequency).
   • Sparsity: Most entries in X_array are 0 (e.g., 10 zeros in the example).

1. Handling Missing Data

   • SimpleImputer(strategy='most_frequent'): Replaces NaN with mode.
   • dropna(subset=["col1", "col2"], how="all"): Drops rows where all specified columns are NaN.

1. Feature Scaling

   • MinMaxScaler: $X_{\text{scaled}} = \frac{X - X_{\min}}{X_{\max} - X_{\min}}$
   • StandardScaler: $X_{\text{scaled}} = \frac{X - \mu}{\sigma}$

C. Algorithms & Hyperparameters

1. Linear Models

   • SGDRegressor:

     • loss='huber' (robust to outliers).
     • learning_rate='adaptive': Reduces LR if loss doesn’t improve.
     • Huber Loss:

1. Neural Networks (MLP)

   • MLPClassifier:

     • hidden_layer_sizes=(128, 64): 2 hidden layers (128 and 64 neurons).
     • activation='relu': $\text{ReLU}(x) = \max(0, x)$.
     • solver='adam': Adaptive Moment Estimation (optimization).
     • Elastic Net in LogisticRegression: Requires solver='saga'.

1. Clustering (K-Means)

   • Elbow Method: Plot inertia vs. $k$; choose $k$ at the "elbow."
   • Inertia: Sum of squared distances to nearest cluster center.
   • Silhouette Score: $\frac{b - a}{\max(a, b)}$ (a = intra-cluster distance, b = inter-cluster distance).

1. Time Series

   • ADF Test:

     • Null hypothesis: Time series is non-stationary.
     • Low p-value (e.g., < 0.05): Reject null → series is stationary.

   • Decomposition:

     • Additive: $y_t = \text{Trend} + \text{Seasonality} + \text{Residual}$.
     • Multiplicative: $y_t = \text{Trend} \times \text{Seasonality} \times \text{Residual}$.

1. Collaborative Filtering

   • Cosine Similarity:

• Prediction: Weighted average of similar users' ratings.

D. Pipelines & Grid Search

1. Pipeline

   • Example:

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

   • Caching: memory='path' stores intermediate results to speed up repeated runs.

1. GridSearchCV

   • Total Models: Product of hyperparameter values.

     • Example: n_estimators=[50,100,200], loss=['squared_error','huber'], max_depth=[3,5,7] → $3 \times 2 \times 3 = 18$ models.

   • Scoring Metrics:

     • Regression: neg_mean_absolute_error, r2.
     • Classification: precision, recall, f1, roc_auc.

E. Pandas Operations

1. Filtering

   • df[(df['Class'] == 'XI') & (df['Physics'] > 85)]
   • df.query('Class == "XI" & Physics > 85')

1. Aggregations

   • df[['English', 'Physics']].mean(axis=1, skipna=True)
   • df.assign(Average=lambda x: x[['English', 'Physics']].mean(axis=1))

Graph 2: Preprocessing Workflow

Graph 3: Algorithm Selection

Graph 4: Hyperparameter Tuning

Graph 5: Time Series Analysis

3. Key Equations Summary

4. Exam Tips

1. Cross-Validation: Always count models as n_splits (e.g., 10-fold → 10 models).
2. Imbalanced Data: Avoid accuracy; prioritize precision, recall, F1.
3. Pipelines: Order matters (e.g., impute → scale).
4. GridSearchCV: Total models = product of hyperparameter options.
5. TF-IDF: Expect sparse matrices (many zeros).
6. Time Series: ADF p-value < 0.05 → stationary.
7. Cosine Similarity: Ignore missing values (treat as 0 in dot product).
8. Elbow Method: Look for the "bend" in inertia plot.