Stanford CS229 - Machine Learning & Supervised Learning Foundations Flashcards

Question 1

What is Machine Learning (ML)?

Accepted Answer

ML is a field of AI that enables systems to learn from data, identify patterns, and make decisions with minimal human intervention. It's broadly categorized into Supervised, Unsupervised, and Reinforcement Learning.

Question 2

Define Supervised Learning.

Accepted Answer

A type of ML where the model learns from a labeled dataset, meaning each training example includes both input features ($x$) and the corresponding correct output label ($y$). The goal is to learn a mapping function from input to output.

Question 3

What is a hypothesis function $h_	heta(x)$ in machine learning?

Accepted Answer

The hypothesis function is the model's learned mapping from input features ($x$) to predicted output. It represents the function that the learning algorithm has chosen to best approximate the target function, parameterized by $	heta$.

Question 4

What is the purpose of a Loss Function (or Cost Function) $J(	heta)$?

Accepted Answer

A loss function quantifies the error between the predicted output of a model and the true output for a given set of parameters $	heta$. The goal of a learning algorithm is to find the parameters $	heta$ that minimize this function, thereby minimizing the prediction error.

Question 5

Explain the Gradient Descent algorithm.

Accepted Answer

Gradient Descent is an iterative optimization algorithm used to find the minimum of a function (typically the cost function). It works by repeatedly adjusting the model's parameters $	heta$ in the direction opposite to the gradient of the cost function with respect to $	heta$.

Question 6

Provide the general update rule for Gradient Descent.

Accepted Answer

For each parameter $	heta_j$, the update rule is:
$	heta_j := 	heta_j - \alpha \frac{\partial}{\partial \	heta_j} J(\	heta)$
where $\alpha$ is the learning rate, controlling the step size, and $\frac{\partial}{\partial \	heta_j} J(\	heta)$ is the partial derivative of the cost function with respect to $\	heta_j$.

Question 7

What is the hypothesis function for Linear Regression?

Accepted Answer

In linear regression, the hypothesis function predicts a continuous output based on a linear combination of input features:
$h_\	heta(x) = \	heta_0 + \	heta_1 x_1 + \dots + \	heta_n x_n = \	heta^T x$
where $\	heta$ are the parameters (weights) and $x$ are the input features (with $x_0=1$).

Question 8

What is the Cost Function for Linear Regression?

Accepted Answer

The cost function for linear regression is typically the Mean Squared Error (MSE), which measures the average squared difference between predicted and actual values:
$J(\	heta) = \frac{1}{2m} \sum_{i=1}^m (h_\	heta(x^{(i)}) - y^{(i)})^2$
where $m$ is the number of training examples.

Question 9

What is the Normal Equation for Linear Regression?

Accepted Answer

The Normal Equation provides a closed-form solution for the optimal parameters $\	heta$ in linear regression, without requiring an iterative algorithm like gradient descent.
$\	heta = (X^T X)^{-1} X^T y$
where $X$ is the design matrix (features) and $y$ is the vector of target values.

Question 10

What is the hypothesis function for Logistic Regression?

Accepted Answer

Logistic Regression uses the sigmoid (or logistic) function to output a probability between 0 and 1, suitable for binary classification:
$h_\	heta(x) = g(\	heta^T x) = \frac{1}{1 + e^{-\	heta^T x}}$
where $g(z) = \frac{1}{1 + e^{-z}}$ is the sigmoid function.

Question 11

Define the Sigmoid Function $g(z)$.

Accepted Answer

The sigmoid function, also known as the logistic function, is defined as $g(z) = \frac{1}{1 + e^{-z}}$. It maps any real-valued number to a value between 0 and 1, making it useful for representing probabilities in classification tasks.

Question 12

What is the Cost Function for Logistic Regression?

Accepted Answer

The cost function for logistic regression (binary classification) is the log-loss or binary cross-entropy loss:
$J(\	heta) = -\frac{1}{m} \sum_{i=1}^m [y^{(i)} \log(h_\	heta(x^{(i)})) + (1 - y^{(i)}) \log(1 - h_\	heta(x^{(i)}))]$
This function is convex and suitable for gradient descent.

Question 13

How is the decision boundary defined in Logistic Regression?

Accepted Answer

The decision boundary in logistic regression is the line or hyperplane where the predicted probability $h_\	heta(x)$ equals 0.5. This occurs when $\	heta^T x = 0$. For inputs on one side of this boundary, $h_\	heta(x) \ge 0.5$ (predict class 1), and on the other side, $h_\	heta(x) < 0.5$ (predict class 0).

Question 14

What is overfitting in machine learning?

Accepted Answer

Overfitting occurs when a model learns the training data too well, including its noise and specific patterns, leading to excellent performance on the training set but poor generalization to unseen data. This often happens with overly complex models.

Question 15

What is underfitting in machine learning?

Accepted Answer

Underfitting occurs when a model is too simple to capture the underlying patterns in the training data, resulting in poor performance on both the training set and unseen data. This often indicates the model has high bias.

Question 16

Explain the Bias-Variance Tradeoff.

Accepted Answer

The Bias-Variance Tradeoff describes the conflict in simultaneously minimizing two sources of error that prevent supervised learning algorithms from generalizing beyond their training data:
*   **Bias:** Error from erroneous assumptions in the learning algorithm (underfitting).
*   **Variance:** Error from sensitivity to small fluctuations in the training set (overfitting).
A good model balances these two, achieving low bias and low variance.

Question 17

What is the general purpose of regularization in machine learning?

Accepted Answer

Regularization is a technique used to prevent overfitting by adding a penalty term to the cost function. This penalty discourages the model from assigning excessively large weights to features, thereby simplifying the model and improving its generalization ability.

Question 18

What is $L_1$ Regularization (Lasso) and its formula?

Accepted Answer

$L_1$ regularization adds the sum of the absolute values of the weights to the cost function.
$J(\	heta) + \lambda \sum_{j=1}^n |\	heta_j|$
It encourages sparsity, meaning it can drive some weights exactly to zero, effectively performing feature selection.

Question 19

What is $L_2$ Regularization (Ridge) and its formula?

Accepted Answer

$L_2$ regularization adds the sum of the squared values of the weights to the cost function.
$J(\	heta) + \lambda \sum_{j=1}^n \	heta_j^2$
It encourages weights to be small but rarely exactly zero, leading to "weight decay" and preventing any single feature from dominating the prediction.

Question 20

What is the primary objective of a Support Vector Machine (SVM)?

Accepted Answer

The primary objective of an SVM is to find the optimal hyperplane that maximally separates the different classes in the feature space. This is achieved by maximizing the margin, which is the distance between the hyperplane and the closest training data points (support vectors) from each class.

Question 21

What is the hypothesis function for a binary SVM classifier?

Accepted Answer

For a binary SVM, the hypothesis function predicts the class label based on the sign of the decision function:
$h(x) = \	ext{sign}(w^T x + b)$
where $w$ is the weight vector, $x$ is the input feature vector, and $b$ is the bias term.

Question 22

Differentiate between Functional Margin and Geometric Margin in SVMs.

Accepted Answer

*   **Functional Margin:** For a training example $(x^{(i)}, y^{(i)})$, it's $y^{(i)}(w^T x^{(i)} + b)$. It measures the correctness and confidence of the classification.
*   **Geometric Margin:** The actual Euclidean distance from a training example to the decision boundary. For a normalized $w$ (i.e., $||w||=1$), the geometric margin is $y^{(i)}(w^T x^{(i)} + b)$. It's scale-invariant. SVMs maximize the geometric margin.

Question 23

State the optimization problem for a Hard Margin SVM.

Accepted Answer

A Hard Margin SVM seeks to find $w, b$ such that:
$\min_{w,b} \frac{1}{2} ||w||^2$
subject to $y^{(i)}(w^T x^{(i)} + b) \ge 1$ for all $i=1, \dots, m$.
This assumes the data is linearly separable.

Question 24

How does a Soft Margin SVM handle non-linearly separable data?

Accepted Answer

Soft Margin SVMs introduce **slack variables** ($\xi_i \ge 0$) to allow some training examples to violate the margin or even cross the decision boundary. The optimization problem includes a penalty term for these violations, controlled by the **regularization parameter C**:
$\min_{w,b,\xi} \frac{1}{2} ||w||^2 + C \sum_{i=1}^m \xi_i$
subject to $y^{(i)}(w^T x^{(i)} + b) \ge 1 - \xi_i$ and $\xi_i \ge 0$.
A larger C means a higher penalty for errors.

Question 25

What is the role of Kernels in SVMs?

Accepted Answer

Kernels allow SVMs to implicitly map input features into a higher-dimensional space, where the data might become linearly separable, without explicitly computing the coordinates in that space. This is known as the "kernel trick." Common kernels include polynomial, Gaussian (RBF), and sigmoid.

Stanford CS229 - Machine Learning & Supervised Learning Foundations

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