IIT M DEGREE AN EXAM QDB3 31 Aug 2025 - 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. Supervised Learning

1. Linear Regression & Cross-Validation

• Key Concepts:

  • LinearRegression from sklearn.linear_model.

  • K-Fold Cross-Validation (KFold from sklearn.model_selection).

    • Splits data into n_splits folds.
    • Trains model n_splits times (each fold used once for validation).
  • cross_val_score evaluates model performance across folds.

• Equation:

  • Linear Regression:

• Mean Squared Error (MSE):

• Example:

  from sklearn.linear_model import LinearRegression
  from sklearn.model_selection import cross_val_score, KFold
  lin_reg = LinearRegression()
  kf = KFold(n_splits=10)
  scores = cross_val_score(lin_reg, X, y, cv=kf)  # Trains 10 models

2. Perceptron & Warm Start

• Key Concepts:

  • Perceptron from sklearn.linear_model.

  • Warm Start: Retains model weights between fit() calls.

    • Useful for incremental learning.

• Parameter:

  Perceptron(max_iter=100, random_state=1729, warm_start=True)

3. Logistic Regression & Regularization

• Key Concepts:

  • Elastic-Net Regularization: Combines L1 (Lasso) and L2 (Ridge) penalties.

    • Controlled by l1_ratio (0 = Ridge, 1 = Lasso).

  • Solvers:

    • saga: Supports Elastic-Net.
    • liblinear: Supports L1/L2 but not Elastic-Net.

• Equation:

  • Elastic-Net Penalty:

4. SGDRegressor & Loss Functions

• Key Concepts:

  • Stochastic Gradient Descent (SGD):

    • Optimizes loss functions incrementally.

  • Loss Functions:

    • loss='huber': Less sensitive to outliers than squared loss.
    • learning_rate='adaptive': Adjusts learning rate if loss doesn’t improve.

• Parameters:

  SGDRegressor(loss='huber', learning_rate='adaptive', eta0=0.1)

5. Evaluation Metrics

• Key Concepts:

  • Confusion Matrix: TP, TN, FP, FN.

    • Precision: $\frac{TP}{TP + FP}$
    • Recall: $\frac{TP}{TP + FN}$
    • F1-Score: $2 \cdot \frac{\text{Precision} \cdot \text{Recall}}{\text{Precision} + \text{Recall}}$
  • R² Score:

• Imbalanced Data: Use Precision, Recall, F1 (not Accuracy).

B. Unsupervised Learning

1. K-Means Clustering

• Key Concepts:

  • Elbow Method: Plots inertia (within-cluster sum of squares) vs. number of clusters.

    • "Elbow" = optimal cluster count.
  • Inertia:

• Parameters:

  KMeans(n_clusters=5, init='random', n_init=20, random_state=0)

  • n_init: Number of initializations (avoids poor local minima).

2. Dimensionality Reduction (TF-IDF)

• Key Concepts:

  • TF-IDF (Term Frequency-Inverse Document Frequency):

    • Weights words by importance in a document vs. corpus.

  • Parameters:

    TfidfVectorizer(lowercase=True, smooth_idf=False, norm=None, ngram_range=(1, 2))

    • ngram_range=(1, 2): Includes unigrams and bigrams.

C. Time Series Analysis

1. Stationarity & ADF Test

• Key Concepts:

  • Augmented Dickey-Fuller (ADF) Test:

    • Null Hypothesis ($H_0$): Time series is non-stationary.
    • p-value < 0.05: Reject $H_0$ (series is stationary).

  • Decomposition:

    • Multiplicative Model:

2. Collaborative Filtering

• Key Concepts:

  • User-User Similarity: Cosine similarity between user ratings.

• Prediction: Weighted average of similar users' ratings.

D. Data Preprocessing

1. Pipelines & Caching

• Key Concepts:

  • Pipeline: Sequential data transformations.

    from sklearn.pipeline import Pipeline
    pipeline = Pipeline([
        ('imputer', SimpleImputer(strategy='most_frequent')),
        ('scaler', MinMaxScaler())
    ])

  • Caching (memory parameter):

    • Stores intermediate results to avoid recomputation.
    • Useful for GridSearchCV and cross-validation.

2. Handling Missing Data

• Key Methods:

  • dropna(): Remove rows/columns with missing values.

    df.dropna(subset=["English", "Physics"], how="all")  # Drops if both are NA

  • fillna(): Impute missing values.
  • mean(axis=1, skipna=True): Compute row-wise mean ignoring NaN.

E. Model Selection & Hyperparameter Tuning

1. GridSearchCV

• Key Concepts:

  • Exhaustive search over hyperparameter grid.

  • Parameters:

    param_grid = {
        'n_estimators': [50, 100, 200],
        'loss': ['ls', 'lad', 'huber', 'quantile'],
        'max_depth': [3, 5, 7]
    }
    grid_search = GridSearchCV(estimator, param_grid, cv=4, scoring='r2')

  • Total Models: Product of hyperparameter options (e.g., $3 \times 4 \times 3 = 36$).

2. Scoring Metrics

• Regression:

  • r2, neg_mean_absolute_error.

• Classification:

  • precision, recall, f1, roc_auc.

F. Neural Networks (MLP)

1. MLPClassifier

• Key Concepts:

  • Hidden Layers: Specified as a tuple (e.g., (128, 64) = 2 layers).
  • Activation Functions: relu, tanh, softmax.
  • Solvers: adam, sgd, lbfgs.

• Parameters:

  MLPClassifier(
      hidden_layer_sizes=(128, 64),
      activation='relu',
      solver='adam',
      alpha=1e-4,
      learning_rate_init=0.001,
      max_iter=300,
      random_state=42
  )

Graph 2: Unsupervised Learning

Graph 3: Time Series Analysis

Graph 4: Model Tuning & Pipelines

Graph 5: Collaborative Filtering

3. Key Equations Summary