24 Questions
The primary goal of ______ is to minimize the cost function.
Gradient Descent
The ______ is the vector of partial derivatives of the cost function with respect to each parameter.
gradient
In linear regression, the ______ are the coefficients of the line.
parameters
The size of each step in gradient descent is determined by the ______.
learning rate
Linear regression is an example of a ______ regression model.
simple
Gradient descent seeks to find the ______ values for the parameters.
best-fit
The cost function measures the difference between the model's predictions and the actual ______.
values
The goal of Linear Regression is to find the ______ that minimizes the cost function.
parameters
The correct approach to updating parameters in gradient descent is ______ update.
simultaneous
The ______ descent algorithm is an optimization algorithm used to minimize the cost function in machine learning and deep learning.
Gradient
The cost function used in Linear Regression is the ______ error function or least square mean.
squared
The ______ plot is used to visualize the cost function in terms of the parameters.
contour
The hypothesis in Linear Regression depends on the ______ x and the ______ parameters.
value, estimated
The cost function J(0,1) is equal to ______ for fixed x.
0
The learning algorithm used to update the parameters is ______ descent.
Gradient
The feature used in Linear Regression is the ______ of the house in feet2.
size
To simplify, assume ______ = 0
θ0
If slope is +ve, θj = θj – ______ value
positive
If ______ is too small, gradient descent is slow
α
Gradient descent converges when it fails to reduce the ______ function
cost
Finding the best learning rate is an example of ______ tuning
hyperparameter
One strategy to find the best learning rate is to plot ______ of iterations versus ______ function
number; cost
Making sure gradient descent is working correctly by checking the number of ______
iterations
The number of iterations required for gradient descent to converge varies ______
considerably
Study Notes
Gradient Descent
- Gradient descent is an optimization algorithm used to minimize the cost function in machine learning and deep learning.
- It works by moving downward toward the pits or valleys in the graph to find the minimum value.
Objective (Cost) Function
- The cost function is the function that you want to minimize.
- In machine learning, the cost function is typically the loss function, which measures the difference between the model's predictions and the actual values.
Parameters
- Parameters are the variables in the model that are adjusted to minimize the cost function.
- In a linear regression model, the parameters are the coefficients of the line.
Gradient
- The gradient is the vector of partial derivatives of the cost function with respect to each parameter.
- Gradient descent uses the gradient to adjust the parameters in the direction of the steepest descent.
Learning Rate
- The learning rate (α) is a hyperparameter that controls how much the parameters are adjusted with respect to the gradient during each update.
- The learning rate determines the size of each step in the gradient descent algorithm.
Gradient Descent Algorithm
- The gradient descent algorithm starts with an initial value of the parameters and iteratively updates them to reduce the cost function.
- The algorithm uses the gradient and the learning rate to adjust the parameters in the direction of the steepest descent.
Linear Regression
- Linear regression is a model that predicts a continuous output variable based on one or more input features.
- The goal of linear regression is to find the best-fit values for the parameters that minimize the cost function.
Cost Function for Linear Regression
- The cost function for linear regression is often the squared error function or least square mean.
- The goal is to minimize the difference between the predicted values and the actual values.
Gradient Descent for Linear Regression
- Gradient descent is used to update the parameters of the linear regression model to minimize the cost function.
- The algorithm uses the gradient and the learning rate to adjust the parameters in the direction of the steepest descent.
Convergence of Gradient Descent
- Gradient descent can converge to a local minimum, even with the learning rate α fixed.
- The algorithm automatically takes smaller steps as it approaches a local minimum.
- The convergence of gradient descent is guaranteed if the cost function is convex.
Choosing the Learning Rate
- There is no formula to find the right learning rate, and it requires hyperparameter tuning.
- One strategy is to run gradient descent with different values of learning rate and plot the number of iterations versus the cost function to choose the best value.
Number of Iterations
- The number of iterations required for gradient descent to converge varies considerably.
- It is difficult to estimate the number of iterations in advance.
- Gradient descent converges when it fails to reduce the cost function, and stays at the same level.
Learn about gradient descent, an essential part of machine learning training models. Understand the objective function, parameters, and gradient in minimizing the cost function.
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