It is primarily a tuning parameter in an optimization algorithm and determines the step size at each iteration while moving towards a minimum loss function. Learning rate is a hyper-parameter used to control the rate at which an algorithm updates the parameter estimates or learns the parameters' values. Read data from CSV: column_names = df = pd.read_csv('/content/data.txt', header=None, names=column_names)df.head()įigure 19: Plotting of Data. Import all required packages: import pandas as pdimport numpy as npimport matplotlib.pyplot as plt%matplotlib inline Python Implementation of Gradient Descent with Numpy: There are three common types of gradient descent: Recalculate the new gradient with the new value of the parameter.Given the gradient, calculate the changes in the parameters with the learning rate.Next, we repeat until it hits convergence: Xj^(i) is the jth feature of the i^th training example. Primarily, this formula tells us the next position It needs to go, which is the steepest descent direction. įigure 13: The equation of the gradient descent algorithm. The gradient of a straight line shows how steep a straight line is. That is why it has a close relationship with the cost function. Essentially, it helps the model to find the points at which the minimum loss occurs. In this case, the gradient descent algorithm comes into the picture. Expecting minimal error or loss, such is called the cost function or loss function.įinding the parameter values m and c with minimal loss is always challenging. So, in the linear equation → y= mx + c, generally, the parameter values m and c are calculated. It is always expected to perform a model with high accuracy and minimal error or loss. Suppose that there is a case where the regression model will be applied for the binary classification. In summary, If the cost function is a function of K variables, then the gradient is the length-K vector representing the direction in which the cost is growing most quickly. Gradient descent is a method for finding the minimum of a function of multiple variables, and it can be used to minimize the cost function. The cost function can be the sum of squared errors over the training set. Relationship Between Cost Function and Gradient DescentĪ cost function is a situation that is minimized. The cost function log loss or cross-entropy is used in the classification problem. The equation of Mean Squared Error (MSE):įigure 5: The equation of log loss or cross-entropy. These are the vital cost functions used in machine learning: An excellent value of the cost function is zero - we use the gradient descent algorithm to minimize the cost function. If the cost function has a lower value, then the model can have a better predictive capability. It shows the difference between the predicted and the actual values for a given dataset. Fundamentally, it measures the error in prediction perpetrated by an algorithm. It quantifies the error within the predicted values and the expected values and impersonates it in the form of a single real number. It is essential to understand the topics below in detail to understand gradient descent in-depth:Ĭost function measures the performance of a machine learning algorithm for dispensed data. Its primary purpose is to reach the lowest point of the mountain.įigure 2: Gradient descent visualization. Gradient descent performs in the same way as mentioned in the example. To solve this problem, he will take small steps around and move towards the higher incline direction, applying these steps iteratively by moving one step at a time until he finally reaches the base of the mountain. Suppose that John is on the top of a mountain, and his goal is to reach the bottom field, but John is blind and cannot see the bottom line. It is a derivative that shows the incline or the slope of a cost function. It is mostly used to update the parameters of the model - in this case, parameters refer to coefficients in regression and weights in a neural network.Ī gradient is a vector-valued function that describes the slope of the tangent of a function's graph, pointing to the direction of the most significant rate of increase of the function. Its goal is to apply optimization to find the least or minimal error value. Gradient descent is a popular optimization method of tuning the parameters in a machine learning model. The gradient descent algorithm and its variants can be found in almost every machine learning model. Gradient descent is one of the most common machine learning algorithms used in neural networks, data science, optimization, and machine learning tasks. Figure 1: A gradient descent illustration | Source: Creative Commons by Wikimedia
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