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IIT M FOUNDATION DIPLOMA FN EXAM QDF2 28 Apr 2024 - 28 Apr 2024

MLP End Term40 questions100 marks20 MCQ · 11 SA · 9 MSQFoundation / Diploma / forenoon / QDF2

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Q1MCQ0 marks

Instruction: Note: For numerical answer type questions enter your answer correct upto 2 decimal places without rounding off, unless stated otherwise.

Instruction has been mentioned above.
This Instruction is just for a reference & not for an evaluation.

Q2MCQ2 marks

Select multilabel multiclass classification problems:

There is a collection of photographs. Each photograph can have multipleanimals, e.g., cats, dogs and birds. Your model should indicate all the animals which are present.
From appropriate weather data, your model must predict, averagetemperature and average humidity for next seven days.
Predicting expected price of a second hand car with appropriate features.
None of these.

Q3MCQ2 marks

Q4MCQ2 marks

Which of the following can be used (with appropriate supporting code) to compute training error after each iteration?

Q5MCQ2 marks

1106
82
1024
5
None of these

Q6MCQ2 marks

What is the purpose of k-fold cross-validation ?

To split data into training and testing sets.
To tune hyperparameters.
To evaluate model performance on multiple subsets.
To preprocess data.

Q7MCQ2 marks

Statement 1 is True and Statement 2 is False
Statement 2 is True and Statement 1 is False
Both the statements are True
Both the statements are False

Q8MCQ2 marks

Which assumption does Naive Bayes make about the features?

They are independent of each other.
They are always a numerical representation of the text data.
They are linearly related.
They are categorical.
None of these.

Q9MCQ3 marks

Q10MCQ3 marks

You’re working on a dataset containing customer purchase data, and you want to segment the customers into distinct groups based on their purchasing behavior. Each data point represents a customer and includes features like “Total Amount Spent” and “Number of Items Purchased.” Which algorithm is suitable for this scenario?

Linear Regression
Decision Tree
K-means Clustering
Support Vector Machine
None of these

Q11MCQ3 marks

Increasing the number of neurons in hidden layers will always lead to bettermodel performance.
Decreasing the number of neurons in hidden layers reduces the model’scapacity to capture complex patterns.
The number of neurons in hidden layers does not significantly affect themodel’s performance.
Finding the optimal number of neurons is a trial-and-error process and mayrequire experimentation.

Q12MCQ3 marks

How does agglomerative clustering handle outliers?

It ignores outliers during the clustering process.
It assigns outliers to the nearest cluster.
It creates separate clusters for outliers.
It removes outliers from the dataset before clustering.

Q13MCQ3 marks

What is agglomerative clustering?

A hierarchical clustering technique that starts with each data point as itscluster and merges the closest clusters iteratively.
A method for partitioning data into a predefined number of clusters.
A clustering algorithm that uses centroids to iteratively assign data points toclusters.
A dimensionality reduction technique that projects data onto a lower-dimensional space.

Q14MCQ3 marks

What initialization method is best in KMeans to select initial cluster centroids?

Random initialization
K-means++ initialization
Hierarchical agglomerative initialization
Weighted initialization

Q15MCQ3 marks

The distance between cluster centroids
The number of clusters formed
Sum of squared distances of samples to their closest cluster center.
The silhouette coefficient

Q16MCQ4 marks

Q17MCQ4 marks

Q18MCQ4 marks

Q19MCQ4 marks

Q20MSQ2 marksselect all that apply

What is the solution for overfitting?

To have less constraints/regularization
To have more constraints/regularization
Delete a significant portion of data
Increase the dataset size.
None of these.

Q21MSQ2 marksselect all that apply

Select all the correct options:

The more the SGD iterations, the lesser the fluctuations in training error.
More iterations require more computation time.
The tol (error tolerance) parameter restricts the number of iterationsperformed.
Training error might not consistently decrease while performing SGDiterations.
None of these

Q22MSQ2 marksselect all that apply

Q23MSQ2 marksselect all that apply

Which of the following statements are true?

Q24MSQ2 marksselect all that apply

Which of the following options are correct regarding regularization?

It is a technique used to minimize the adjusted loss function and avoidunderfitting.
It helps in increasing the bias of the training model.
It determines the rows to be selected as a training dataset.
Elastic net regularization is a combination of L1 and L2 regularization both.

Q25MSQ3 marksselect all that apply

Which of the following techniques are used in decision trees to make decisions or to measure the quality of a split while training the model?

Entropy
RoC Curve
Cross Entropy
Gini Impurity

Q26MSQ3 marksselect all that apply

Which of the following approaches is(are) helpful to find a good value for k in k−means clustering algorithm?

Plotting an Elbow curve.
Using classifiers before making clusters.
Plotting Silhouette coefficient for various values of k.
Using k-fold cross validation

Q27MSQ4 marksselect all that apply

10 number of samples at node N. If it is split, it can split such that 2 samples inthe left child and 8 samples in the right child.
6 number of samples at node N. If it is split, it can split such that 3 samples inthe left child and 3 samples in the right child.
12 number of samples at node N. If it is split, it can split such that 5 samples inthe left child and 7 samples in the right child.
4 number of samples at node N. If it is split, it can split such that 3 samples inthe left child and 1 samples in the right child.

Q28SA2 marks

Your numeric answer:

Q29SA2 marks

Your numeric answer:

Q30SA2 marks

Your numeric answer:

Q31SA2 marks

Your numeric answer:

Q32SA2 marks

Your numeric answer:

Q33SA3 marks

Your numeric answer:

Q34SA3 marks

Your numeric answer:

Q35SA3 marks

Your numeric answer:

Comprehension passage - the questions below it refer to this

Based on the above data, answer the given subquestions. question figure

Q36MSQ2 marksselect all that apply

Q37SA2 marks

Your numeric answer:

Q38SA2 marks

Your numeric answer:

Q39SA2 marks

Your numeric answer:

Q40MCQ2 marks

The number of rows will decrease in the dataset.
The number of columns will decrease in the dataset.
The number of columns and number of rows, both, will decrease in thedataset.
There will be no change.
Insufficient information.

Answer key

Q1 (MCQ, 0 marks): A
Q2 (MCQ, 2 marks): A
Q3 (MCQ, 2 marks): A
Q4 (MCQ, 2 marks): A
Q5 (MCQ, 2 marks): C
Q6 (MCQ, 2 marks): C
Q7 (MCQ, 2 marks): A
Q8 (MCQ, 2 marks): A
Q9 (MCQ, 3 marks): A
Q10 (MCQ, 3 marks): C
Q11 (MCQ, 3 marks): D
Q12 (MCQ, 3 marks): B
Q13 (MCQ, 3 marks): A
Q14 (MCQ, 3 marks): B
Q15 (MCQ, 3 marks): C
Q16 (MCQ, 4 marks): A
Q17 (MCQ, 4 marks): D
Q18 (MCQ, 4 marks): C
Q19 (MCQ, 4 marks): C
Q20 (MSQ, 2 marks): B, D
Q21 (MSQ, 2 marks): A, B, C, D
Q22 (MSQ, 2 marks): B, C
Q23 (MSQ, 2 marks): A, C
Q24 (MSQ, 2 marks): B, D
Q25 (MSQ, 3 marks): A, D
Q26 (MSQ, 3 marks): A, C
Q27 (MSQ, 4 marks): A, D
Q28 (SA, 2 marks): 0.5
Q29 (SA, 2 marks): 0.8
Q30 (SA, 2 marks): 0.37 to 0.38
Q31 (SA, 2 marks): 0.32 to 0.35
Q32 (SA, 2 marks): 1
Q33 (SA, 3 marks): 36
Q34 (SA, 3 marks): 1.00
Q35 (SA, 3 marks): 1
Q36 (MSQ, 2 marks): A, C
Q37 (SA, 2 marks): 120
Q38 (SA, 2 marks): 3
Q39 (SA, 2 marks): -1
Q40 (MCQ, 2 marks): A

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 Practices (Computer-Based Exam). The summary is organized by themes (e.g., Supervised Learning, Unsupervised Learning, Model Evaluation, etc.), followed by a knowledge graph in Mermaid syntax to visualize relationships.

1. Core Topics & Concepts

A. Supervised Learning

1. Classification

Algorithms:
- Logistic Regression: Binary/multi-class classification using sigmoid/log-softmax.
- Decision Trees:
  - Splitting criteria: Gini Impurity, Entropy (Information Gain).
  - Hyperparameters: max_depth, min_samples_split, min_samples_leaf, class_weight.
  - Pruning to avoid overfitting.
- Support Vector Machines (SVM):
  - Kernels: linear, rbf, poly.
  - Margin maximization (support vectors).
- k-Nearest Neighbors (k-NN):
  - Distance metrics: Euclidean, Manhattan.
  - Curse of dimensionality: Feature scaling (e.g., StandardScaler) is critical.
  - n_neighbors: Low → complex boundaries; High → smooth boundaries.
- Naive Bayes:
  - Assumption: Features are conditionally independent given the class.
  - Variants: Gaussian (continuous features), Multinomial (discrete counts).
- Perceptron:
  - Linear classifier; updates weights via gradient descent.
  - Limited to linearly separable data (accuracy ≤ 80% in Q30).
- AdaBoost:
  - Ensemble of weak learners (e.g., decision stumps).
  - Hyperparameters: n_estimators, learning_rate.
- Random Forest:
  - Ensemble of decision trees; reduces variance via bagging.
  - Hyperparameters: max_features (default: sqrt(n_features)), bootstrap.
  - Feature importance via feature_importances_.

Evaluation Metrics:
- Confusion Matrix: TP, TN, FP, FN.
- Precision = TP / (TP + FP) (Q31: 0.375).
- Recall, F1-Score, Accuracy.
- Class Imbalance: Use class_weight='balanced' or resampling.

2. Regression

Algorithms:
- Linear Regression: Minimizes MSE (Mean Squared Error).
- SGDRegressor:
  - Stochastic Gradient Descent; supports shuffle=True (Q4).
  - Hyperparameters: learning_rate (constant, invscaling, optimal), max_iter, warm_start (Q5).
  - Training Error: May fluctuate; not guaranteed to decrease monotonically (Q22).
- Polynomial Regression: Use PolynomialFeatures (Q34: 36 features after degree=3).

Regularization (Avoid Overfitting):
- L1 (Lasso): Sparse weights (feature selection).
- L2 (Ridge): Smooth weights.
- Elastic Net: Combines L1 + L2 (Q25).
- Hyperparameter: alpha (strength), l1_ratio (mix).

3. Neural Networks

MLPClassifier (Multi-Layer Perceptron):
- Hyperparameters: hidden_layer_sizes, activation (relu, tanh).
- Trial-and-error for optimal architecture (Q12).
- Overfitting: Use dropout, early stopping, or reduce layers/neurons.

B. Unsupervised Learning

1. Clustering

k-Means:
- Initialization: k-means++ (better than random; Q15).
- Inertia: Sum of squared distances to centroids (Q16).
- Optimal k: Elbow method (Q27), Silhouette Score.
- Limitations: Sensitive to outliers, assumes spherical clusters.
Agglomerative Clustering:
- Hierarchical; merges closest clusters (Q14).
- Handles outliers: Assigns to nearest cluster (Q13).
DBSCAN: Density-based; robust to noise.

2. Dimensionality Reduction

PCA (Principal Component Analysis):
- Transforms features to orthogonal components (Q35: explained variance ratio = 1.0).
- n_components: Number of principal components.
- Standardization required (use StandardScaler).
FeatureUnion: Combines multiple transformations (e.g., PCA + PolynomialFeatures; Q34).

C. Model Evaluation & Selection

1. Cross-Validation

k-Fold CV: Evaluates model on multiple subsets (Q7).
Leave-One-Out (LOO): n_models = n_samples (Q6: 1024 scores for 1024 samples).
Stratified k-Fold: Preserves class distribution.

2. Hyperparameter Tuning

GridSearchCV: Exhaustive search over parameter grid (Q18: D is most comprehensive).
RandomizedSearchCV: Faster; samples random combinations.

3. Overfitting & Underfitting

Solutions for Overfitting (Q21):
- Regularization (L1/L2), pruning (decision trees), dropout (NNs).
- More data, feature selection, simpler models.
Bias-Variance Tradeoff:
- High bias → underfitting; high variance → overfitting.

D. Data Preprocessing

1. Feature Scaling

StandardScaler: Mean=0, std=1 (Q10: first row = [0.1768, 1, 0, 0, 0]).
MinMaxScaler: Scales to [0, 1].
MaxAbsScaler: Scales by max absolute value (Q29: max = 0.5).

2. Encoding

One-Hot Encoding: For categorical features (Q10).
Label Encoding: For target variables (Q32: p(y="No") ≈ 0.33).

3. Handling Missing Data

dropna(): Removes rows/columns with NaN (Q41: reduces rows).
Imputation: SimpleImputer (mean/median/mode).

4. Feature Engineering

PolynomialFeatures: Generates interaction terms (Q34: 35 features for degree=3).
ColumnTransformer: Applies different transformers to columns (Q10).

E. Ensemble Methods

1. Bagging

Random Forest: Trains trees on bootstrapped samples (Q20: max_features < n_features).
BaggingClassifier: Can use any base estimator (e.g., k-NN; Q19: max_samples=0.5).

2. Boosting

AdaBoost: Sequentially corrects errors of weak learners (Q18).
Gradient Boosting: Optimizes loss function (e.g., XGBoost).

F. Practical ML with scikit-learn

1. Key Methods

fit(): Trains the model (Q8: Statement 1 is True).
transform(): Applies preprocessing (e.g., scaling, encoding).
predict(): Generates predictions (Q33: k-NN predicts 1 for [8,9]).
score(): Returns accuracy (or R² for regression).

2. Pipelines

Pipeline: Chains transformers and estimators (Q34).
FeatureUnion: Combines multiple feature transformations.

3. Common Errors

Data Leakage: Preprocessing before train-test split.
Shape Mismatch: Ensure X and y dimensions align.
Non-Numeric Data: Use encoders (Q39: df.Hindi.apply(type).nunique() = 3).

2. Key Equations

A. Supervised Learning

Linear Regression (MSE Loss):

\mathcal{L}(w) = \frac{1}{n} \sum_{i=1}^n (y_i - w^T x_i)^2

Logistic Regression (Log Loss):

\mathcal{L}(w) = -\frac{1}{n} \sum_{i=1}^n [y_i \log(p_i) + (1-y_i) \log(1-p_i)]

where $p_i = \sigma(w^T x_i)$ .

Decision Tree Splitting (Gini/Entropy):

\text{Gini}(S) = 1 - \sum_{i=1}^c p_i^2, \quad \text{Entropy}(S) = -\sum_{i=1}^c p_i \log(p_i)

SVM Margin:

\text{Maximize } \frac{2}{||w||} \quad \text{subject to } y_i(w^T x_i + b) \geq 1

k-NN Prediction:

\hat{y} = \text{mode}\{y_i \mid x_i \in \text{k nearest neighbors}\}

Perceptron Update Rule:

w_{t+1} = w_t + \eta \cdot (y_i - \hat{y_i}) x_i

B. Unsupervised Learning

k-Means Objective (Inertia):

J = \sum_{i=1}^n \sum_{k=1}^K r_{ik} ||x_i - \mu_k||^2

where $r_{ik} = 1$ if $x_i$ is assigned to cluster $k$ .

PCA Variance Maximization:

\text{Maximize } \text{Var}(X w) \quad \text{subject to } ||w|| = 1

C. Model Evaluation

Precision/Recall:

\text{Precision} = \frac{TP}{TP + FP}, \quad \text{Recall} = \frac{TP}{TP + FN}

Silhouette Score (for clustering):

s(i) = \frac{b(i) - a(i)}{\max\{a(i), b(i)\}}

where $a(i)$ = intra-cluster distance, $b(i)$ = inter-cluster distance.

D. Regularization

L1 (Lasso) Penalty:

\mathcal{L}_{\text{reg}} = \mathcal{L} + \alpha \sum_{j=1}^p |w_j|

L2 (Ridge) Penalty:

\mathcal{L}_{\text{reg}} = \mathcal{L} + \alpha \sum_{j=1}^p w_j^2

Elastic Net:

\mathcal{L}_{\text{reg}} = \mathcal{L} + \alpha \left( \rho \sum_{j=1}^p |w_j| + \frac{1-\rho}{2} \sum_{j=1}^p w_j^2 \right)

Graph 2: Unsupervised Learning Relationships

Graph 3: Model Evaluation & Preprocessing

Graph 4: Ensemble Methods

Graph 5: Neural Networks

4. Exam Tips

Focus Areas:
- Algorithms: Know when to use each (e.g., k-means for clustering, decision trees for interpretability).
- Hyperparameters: Understand their impact (e.g., n_neighbors in k-NN, max_depth in trees).
- Preprocessing: Scaling/encoding is critical for distance-based models (k-NN, SVM, PCA).
- Evaluation: Metrics for classification (precision/recall) vs. regression (MSE/R²).
- Ensembles: Bagging (Random Forest) vs. Boosting (AdaBoost).

Common Pitfalls:
- Data Leakage: Always split data before preprocessing.
- Overfitting: Regularization, pruning, or more data.
- Class Imbalance: Use class_weight or resampling.
- Categorical Features: One-hot encode (not label encode) for non-tree models.

Code Snippets:
- Memorize key scikit-learn syntax (e.g., SGDRegressor(shuffle=True), PCA(n_components=2)).
- Understand Pipeline and ColumnTransformer for workflows.

Math Equations:
- Prioritize loss functions (MSE, log loss), regularization, and evaluation metrics.
- For clustering, focus on inertia and silhouette score.

Practical Questions:
- Q10 (Preprocessing): Output after MinMaxScaler + StandardScaler + OneHotEncoder.
- Q30 (Perceptron): Maximum accuracy for non-linearly separable data (80%).
- Q34 (FeatureUnion): Count features after polynomial + PCA transformations (36).
- Q37 (Pandas): Equivalent iloc for df.loc[13:15, 'Maths':'English'].