IIT M FOUNDATION DIPLOMA FN EXAM - 01 Sep 2024

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 Diploma Level: Machine Learning Practice (Computer-Based Exam), along with Mermaid knowledge graphs to visualize relationships.

1. Core Topics & Concepts

A. Python Libraries & Data Handling

Key Libraries:

• pandas (DataFrames, shape, isna(), value_counts(), iloc, query, dropna, fillna)
• numpy (Handling np.nan, numerical operations)
• sklearn (Machine learning models, preprocessing, evaluation)

Key Pandas Operations:

B. Data Preprocessing

Key Concepts:

1. Handling Missing Data:

   • df.dropna(): Remove rows/columns with missing values.
   • SimpleImputer or KNNImputer: Fill missing values (e.g., KNNImputer(n_neighbors=3)).

2. Feature Scaling:

   • StandardScaler: Standardizes features (mean=0, std=1).
   • MinMaxScaler: Scales features to a range (e.g., [0, 1]).
   • Impacted Algorithms: Linear Regression, SVM, KNN, Neural Networks.

3. Feature Extraction:

   • DictVectorizer: Converts dictionaries to feature matrices (for structured data).
   • HashingVectorizer: Converts text to fixed-size vectors (not used here).

Equations:

• Standard Scaling:

where $\mu$ = mean, $\sigma$ = standard deviation.

• Min-Max Scaling:

C. Machine Learning Models

1. Linear Models

Key Equations:

• Ridge/Lasso Loss:

• For Ridge (L2): $\alpha \sum_{i=1}^n w_i^2$
• For Lasso (L1): $\alpha \sum_{i=1}^n |w_i|$

• Logistic Regression Probability:

2. Tree-Based Models

Key Concepts:

• max_depth: Limits tree depth to prevent overfitting.
• min_samples_split: Minimum samples required to split a node.

• criterion:

  • Classification: gini (Gini impurity) or entropy.
  • Regression: mse (Mean Squared Error).
• Bootstrapping: Random sampling with replacement (used in Random Forest).

3. Clustering

Key Equations:

• K-Means Inertia:

where $\mu_j$ = centroid of cluster $j$.

4. Model Evaluation

Key Terms:

• TP/FP/TN/FN: True Positive, False Positive, True Negative, False Negative.
• SS_res: Sum of squared residuals.
• SS_tot: Total sum of squares.

D. Hyperparameter Tuning

Key Concepts:

• Grid Search: Exhaustive search over specified parameter values. Example:

  parameter_grid = {
      'n_estimators': [10, 20, 30],
      'max_features': [2, 3, 4],
      'bootstrap': [True, False]
  }

  • Total combinations: $3 \times 3 \times 2 = 18$ (but in Q7, it’s $3 \times 5 \times 2 \times 3 = 90$, but answer is 21 → likely a subset).

• Cross-Validation:

  • Leave-One-Out (LOO): $n$ folds (where $n$ = number of samples).
  • k-Fold: Split data into $k$ folds.

Equation for LOO:

• Number of models trained = $n$ (where $n$ = number of samples).

E. Ensemble Methods

Key Differences:

• Bagging: Parallel training (e.g., Random Forest).
• Boosting: Sequential training (e.g., AdaBoost, Gradient Boosting).

F. Dimensionality Reduction & Feature Engineering

Key Concepts:

• Feature Importance: Tree-based models provide feature importance scores.
• PCA: Linear dimensionality reduction (not covered in questions).
• DictVectorizer: Converts categorical features to numerical (one-hot encoding).

G. Special Topics

1. Data Snooping:

   • Peeking at test data → biased estimates, increased false positives.

2. Ordinal vs. Nominal Variables:

   • Ordinal: Ordered categories (e.g., satisfaction ratings).
   • Nominal: Unordered categories (e.g., blood type).

3. Dummy Classifier:

   • Baseline model (e.g., strategy='most_frequent' always predicts the majority class).

4. Perceptron:

   • Linear classifier (binary).
   • tol: Tolerance for stopping criteria.
   • shuffle: Whether to shuffle data before each epoch.

Graph 2: Machine Learning Models

Graph 3: Model Evaluation

Graph 4: Ensemble Methods

Graph 5: Clustering

Graph 6: Hyperparameter Tuning

3. Key Equations Summary

4. Exam Tips

1. Pandas/Numpy: Focus on shape, isna(), value_counts(), query, iloc, and handling NaN.

2. Sklearn Models:

   • Know default parameters (e.g., SGDRegressor uses max_iter for epochs).
   • Understand alpha in Ridge/Lasso vs. C in Logistic Regression (inverse relationship).

3. Evaluation Metrics:

   • Confusion matrix → Precision/Recall/F1.
   • Regression → R², MSE.

4. Clustering:

   • K-Means: Inertia = within-cluster sum of squares.
   • Agglomerative: Hierarchical, uses linkage methods.

5. Ensemble Methods:

   • Random Forest: bootstrap=True by default.
   • Bagging vs. Boosting: Parallel vs. sequential.

6. Hyperparameter Tuning:

   • Grid search combinations = product of parameter options.
   • LOO CV trains $n$ models for $n$ samples.

Final Note: Focus on code snippets, parameter interpretations, and mathematical formulas for regression/classification metrics. The Mermaid graphs help visualize relationships between concepts. Good luck!