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IIT M FOUNDATION DIPLOMA AN EXAM - 01 Sep 2024

MLT End Term30 questions50 marks14 MCQ · 14 SA · 2 MSQFoundation / Diploma / afternoon

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Q1MCQ2 marks

Q2MCQ3 marks

Q3MCQ3 marks

Q4MCQ3 marks

Match the characteristics given below with the appropriate ensemble technique. 1. Decision stumps 2. Deep decision trees 3. Parallel execution 4. Sequential execution

Bagging → (2), (3); Boosting → (1), (4)
Bagging → (1), (4); Boosting → (2), (3)
Bagging → (1), (3); Boosting → (2), (4)
Bagging → (2), (4); Boosting → (1), (3)

Q5MCQ3 marks

Q6MCQ3 marks

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Q8MCQ3 marks

0.75
0.25
0.5
0.15

Q9MSQ3 marksselect all that apply

Q10MSQ3 marksselect all that apply

The dataset is linearly separable with a positive margin.
The perceptron algorithm will terminate after a finite number of iterationswhen trained on this dataset.
The dataset is linearly separable, but the margin may be zero.
The dataset is not linearly separable.

Q11SA3 marks

Your numeric answer:

Q12SA3 marks

Your numeric answer:

Q13SA3 marks

Your numeric answer:

Comprehension passage - the questions below it refer to this

Q14MCQ1 mark

The weight vector output by the perceptron algorithm can be expressed as a linear combination of the data-points where the coefficients of the linear combination are integers.

TRUE
FALSE

Q15MCQ1 mark

TRUE
FALSE

Q16MCQ1 mark

If a soft-margin SVM is trained on this dataset, the optimal weight vector it returns will be the same as the one returned by a hard-margin SVM, irrespective of the value of the hyperparameter C.

TRUE
FALSE

Comprehension passage - the questions below it refer to this

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

Q17SA0.5 marks

Your numeric answer:

Q18SA0.5 marks

Your numeric answer:

Q19SA0.5 marks

Your numeric answer:

Q20SA0.5 marks

Your numeric answer:

Q21SA0.5 marks

Your numeric answer:

Q22SA0.5 marks

Your numeric answer:

Comprehension passage - the questions below it refer to this

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

Q23SA0.5 marks

Enter the number corresponding to the logistic loss.

Your numeric answer:

Q24SA0.5 marks

Enter the number corresponding to the (SVM) hinge loss.

Your numeric answer:

Q25SA0.5 marks

Enter the number corresponding to the perceptron loss.

Your numeric answer:

Q26SA0.5 marks

Enter the number corresponding to the squared loss.

Your numeric answer:

Q27MCQ1 mark

Comprehension passage - the questions below it refer to this

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

Q28SA1 mark

How many learnable parameters does this network have? Ignore the biases in the computation.

Your numeric answer:

Q29MCQ1 mark

What is the most appropriate choice of activation function for the output layer if the binary cross-entropy loss is used?

Sigmoid
Linear
ReLU

Q30MCQ1 mark

ReLU
Sigmoid

Answer key

Q1 (MCQ, 2 marks): A
Q2 (MCQ, 3 marks): C
Q3 (MCQ, 3 marks): A
Q4 (MCQ, 3 marks): A
Q5 (MCQ, 3 marks): B
Q6 (MCQ, 3 marks): A
Q7 (MCQ, 3 marks): A
Q8 (MCQ, 3 marks): A
Q9 (MSQ, 3 marks): A, B
Q10 (MSQ, 3 marks): A, B
Q11 (SA, 3 marks): 10
Q12 (SA, 3 marks): 0.75
Q13 (SA, 3 marks): 0.50 to 0.60
Q14 (MCQ, 1 marks): A
Q15 (MCQ, 1 marks): B
Q16 (MCQ, 1 marks): B
Q17 (SA, 0.5 marks): 0
Q18 (SA, 0.5 marks): 1
Q19 (SA, 0.5 marks): 2
Q20 (SA, 0.5 marks): 0
Q21 (SA, 0.5 marks): 5
Q22 (SA, 0.5 marks): -1
Q23 (SA, 0.5 marks): 3
Q24 (SA, 0.5 marks): 2
Q25 (SA, 0.5 marks): 4
Q26 (SA, 0.5 marks): 1
Q27 (MCQ, 1 marks): A
Q28 (SA, 1 marks): 205
Q29 (MCQ, 1 marks): A
Q30 (MCQ, 1 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 for the Diploma Level: Machine Learning Techniques exam, along with Mermaid knowledge graphs to visualize relationships.

1. Core Topics & Concepts

A. Linear Regression & Gradient Descent

Sum of Squared Errors (SSE):

\text{SSE} = \sum_{i=1}^n (y_i - \hat{y}_i)^2 = \sum_{i=1}^n (y_i - w^T x_i)^2

Gradient of SSE w.r.t. $w$ (for a single data point):

\nabla_w \text{SSE} = -2 (y - w^T x) x

Key Idea: Minimize SSE using gradient descent.

B. Principal Component Analysis (PCA)

Covariance Matrix $C$ :

C = \frac{1}{n} X^T X \quad (\text{for centered data})

Variance along Principal Component $w$ :

\text{Var}(w) = w^T C w

Eigenvalue Decomposition:

C = V \Lambda V^T

where $V$ contains eigenvectors (principal components) and $\Lambda$ contains eigenvalues (variances).

C. Regularization (Ridge/Lasso)

Ridge Regression (L2):

\text{Loss} = \text{SSE} + \lambda \|w\|_2^2

Small $\lambda$ : Overfitting (high variance).
Large $\lambda$ : Underfitting (high bias).
- Lasso (L1):

\text{Loss} = \text{SSE} + \lambda \|w\|_1

Encourages sparsity (feature selection).

D. Support Vector Machines (SVM)

Hard-Margin SVM (linearly separable data):

\min_{w,b} \frac{1}{2} \|w\|^2 \quad \text{s.t.} \quad y_i (w^T x_i + b) \geq 1

Margin: $\frac{2}{\|w\|}$ .
Support Vectors: Points where $y_i (w^T x_i + b) = 1$ .
- Soft-Margin SVM (non-separable data):

\min_{w,b,\xi} \frac{1}{2} \|w\|^2 + C \sum \xi_i \quad \text{s.t.} \quad y_i (w^T x_i + b) \geq 1 - \xi_i, \xi_i \geq 0

Slack Variables $\xi_i$ : Measure misclassification.
Lagrange Multipliers $\alpha_i$ :
- $\alpha_i > 0$ : Support vector.
- $\alpha_i = C$ : Misclassified point.

E. Ensemble Methods

Method	Key Characteristics	Example Models
Bagging	- Parallel execution	Random Forest
	- Uses deep trees
	- Reduces variance
Boosting	- Sequential execution	AdaBoost, Gradient Boosting
	- Uses weak learners (e.g., decision stumps)
	- Reduces bias

F. Naive Bayes

Class Conditional Independence:

p(x_1, x_2, \dots, x_d | y) = \prod_{i=1}^d p(x_i | y)

Posterior Probability:

p(y | x) \propto p(y) \prod_{i=1}^d p(x_i | y)

G. Clustering (k-Means)

Objective: Minimize within-cluster sum of squares (WCSS).
Cluster Boundary: Perpendicular bisector between centroids.
- For 1D data: Midpoint between centroids.
- For 2D data: Line equidistant to centroids.

H. Logistic Regression

Sigmoid Function:

\sigma(z) = \frac{1}{1 + e^{-z}}, \quad z = w^T x + b

Probability Interpretation:

p(y=1 | x) = \sigma(w^T x + b)

Symmetry Property:

p(y=1 | x) = 0.75 \implies p(y=1 | -x) = 0.25

I. Kernel Methods

Valid Kernels must satisfy Mercer’s Condition (positive semi-definite Gram matrix).
Examples of Valid Kernels:
1. Linear: $k(x, y) = x^T y$
2. Polynomial: $k(x, y) = (x^T y + c)^d$
3. RBF/Gaussian: $k(x, y) = \exp(-\gamma \|x - y\|^2)$

J. Decision Trees & Information Gain

Entropy:

H(S) = -\sum_{i} p_i \log_2 p_i

Information Gain:

\text{Gain}(S, A) = H(S) - \sum_{v \in \text{values}(A)} \frac{|S_v|}{|S|} H(S_v)

Decision Stump: Tree with 1 split (2 leaves).

K. Neural Networks

Learnable Parameters (ignoring biases):

\text{Params} = \sum_{l=1}^{L-1} (\text{neurons in layer } l) \times (\text{neurons in layer } l+1)

Activation Functions:
- Output Layer (Binary Classification): Sigmoid (with cross-entropy loss).
- Hidden Layers: ReLU, tanh, etc.
ReLU Property:

\text{ReLU}(x) = \max(0, x)

If any activation is 0, the input to ReLU was ≤ 0.

L. Loss Functions

Loss Function	Formula	Use Case
0-1 Loss	$L = \mathbb{I}(y \neq \hat{y})$	Classification (non-convex)
Hinge Loss (SVM)	$L = \max(0, 1 - y \hat{y})$	SVM
Logistic Loss	$L = \log(1 + e^{-y \hat{y}})$	Logistic Regression
Perceptron Loss	$L = \max(0, -y \hat{y})$	Perceptron
Squared Loss	$L = (y - \hat{y})^2$	Regression

Intersection of Logistic & Hinge Loss:

(\mathbf{w}^T \mathbf{x}) y = \ln(e - 1)

M. Bayesian Learning

Beta-Bernoulli Model:
- Prior: $p \sim \text{Beta}(\alpha, \beta)$
- Posterior: $p | \text{data} \sim \text{Beta}(\alpha + \text{successes}, \beta + \text{failures})$
- Point Estimate (Expected Value):

\hat{p} = \frac{\alpha + \text{successes}}{\alpha + \beta + n}

Graph 2: Unsupervised Learning Relationships

Graph 3: Ensemble Methods

Graph 4: SVM Components

Graph 5: Neural Network Architecture

Graph 6: Loss Functions

Graph 7: Bayesian Learning

3. Key Equations Summary

Topic	Equation
SSE Gradient	$\nabla_w \text{SSE} = -2 (y - w^T x) x$
PCA Variance	$\text{Var}(w) = w^T C w$
Ridge Regression	$\text{Loss} = \text{SSE} + \lambda \\|w\\|_2^2$
SVM Hard-Margin	$\min \frac{1}{2} \\|w\\|^2$ s.t. $y_i (w^T x_i + b) \geq 1$
SVM Soft-Margin	$\min \frac{1}{2} \\|w\\|^2 + C \sum \xi_i$ s.t. $y_i (w^T x_i + b) \geq 1 - \xi_i$
Logistic Regression	$p(y=1\|x) = \sigma(w^T x + b)$
Information Gain	$\text{Gain}(S, A) = H(S) - \sum \frac{\|S_v\|}{\|S\|} H(S_v)$
k-Means Objective	$\min \sum_{i=1}^k \sum_{x \in C_i} \\|x - \mu_i\\|^2$
Neural Network Params	$\sum_{l=1}^{L-1} n_l \times n_{l+1}$ (ignoring biases)
Beta Posterior	$\text{Beta}(\alpha + \text{successes}, \beta + \text{failures})$

4. Exam Tips

Linear Algebra: Focus on eigenvalues, gradients, and matrix operations (PCA, SVM).
Optimization: Understand gradient descent, Lagrange multipliers (SVM), and regularization.
Probability: Naive Bayes, Bayesian updating (Beta-Bernoulli).
Geometry: SVM margins, cluster boundaries (k-Means), decision boundaries.
Loss Functions: Know when to use which loss (hinge for SVM, logistic for classification, squared for regression).
Ensemble Methods: Bagging vs. Boosting (parallel vs. sequential, deep trees vs. stumps).
Neural Networks: Parameter counting, activation functions, output layer choices.