Linear Regression and Gradient Descent Quiz

11 Questions

What is the main goal of linear regression according to the given text?

To predict a continuous value

Which gradient descent variant uses a single example per iteration?

Stochastic

What is a common issue that arises when the learning rate is too large as mentioned in the text?

Oscillation and potentially diverging

What aspect of gradient descent does the learning rate control?

The size of the step taken at each iteration

Which statement about the analytical solution to linear regression is accurate based on the text?

It can be computationally expensive for large datasets

In gradient descent, how does momentum affect the process as described in the text?

By adding a fraction of the previous step to the current step

What is a potential drawback of using mini-batch in Stochastic Gradient Descent?

It may increase the noise in the gradient estimate

Why is adjusting the learning rate necessary in gradient descent?

To balance the speed of convergence and the risk of overshooting

In Stochastic Gradient Descent, what does the term 'mini-batch' refer to?

Using a subset of the dataset for each iteration

Which optimization algorithm automatically adjusts learning rates for different parameters?

Adagrad

What characteristic is NOT associated with mini-batch in Stochastic Gradient Descent?

Finding the global minimum

Study Notes

Linear Regression

The main goal of linear regression is to find the best-fitting linear line that minimizes the sum of the squared errors.

Gradient Descent

Stochastic Gradient Descent (SGD) with online learning uses a single example per iteration.
If the learning rate is too large, it can cause oscillations and fail to converge.
The learning rate controls how quickly the model learns from new data.
Momentum in gradient descent helps the process by adding a fraction of the previous weight update to the current update, helping to escape local minima.

Analytical Solution

The analytical solution to linear regression involves minimizing the cost function using normal equations, which have a closed-form solution.

Stochastic Gradient Descent

Mini-batch in Stochastic Gradient Descent refers to a subset of the training data used to compute the gradient of the loss function.
A potential drawback of using mini-batch is that it can still be computationally expensive.
Adjusting the learning rate is necessary to ensure convergence and avoid oscillations.

Optimization Algorithms

The Adam optimization algorithm automatically adjusts learning rates for different parameters.

Mini-Batch Characteristic

Mini-batch is not associated with full-batch gradient descent, which uses the entire training dataset to compute the gradient.