Each update is now much faster to calculate than in batch gradient descent, and over many updates, we will head in the same general direction. The idea is that the gradient calculated this way is a stochastic approximation to the gradient calculated using the entire training data. Stochastic gradient descent (SGD) computes the gradient for each update using a single training data point x_i (chosen at random).Since we need to calculate the gradients for the whole dataset to perform one parameter update, batch gradient descent can be very slow. Batch gradient descent computes the gradient of the cost function w.r.t to parameter W for entire training data.A dataset may have millions of data points, and calculating the gradient over the entire dataset can be computationally expensive. The main reason for these variations is computational efficiency. There are multiple variants of gradient descent, depending on how much of the data is being used to calculate the gradient. If you’re interested in learning Data Science / ML, definitely recommend checking it out.ĪDVERTISEMENT Variants of Gradient Descent The courses include many hands-on assignments and projects. You are blind folded, since we don’t have the luxury of evaluating (or ‘seeing’) the value of the function for every possible set of parameters.įeeling the slope of the terrain around you is analogous to calculating the gradient, and taking a step is analogous to one iteration of update to the parameters.īy the way - as a small aside - this tutorial is part of the free Data Science Course and free Machine Learning Course on Commonlounge. The rough terrain is analogous to the cost function, and minimizing the cost function is analogous to trying to reach lower altitudes. Source: Andrej Karpathy’s Stanford Course Lecture 3 If you keep repeating this process, you might end up at the lake, or even better, somewhere in the huge valley. One of the simplest strategies you can use, is to feel the ground in every direction, and take a step in the direction where the ground is descending the fastest. Imagine you’re blindfolded in rough terrain, and your objective is to reach the lowest altitude. High values of η may overshoot the minimum, and very low values will reach the minimum very slowly.Ī popular choice for the termination criteria is that the cost J( w) stops reducing on a validation dataset.ĪDVERTISEMENT Intuition for Gradient Descent We need to be very careful about this parameter. In step 3, η is the learning rate which determines the size of the steps we take to reach a minimum. Repeat until the cost J( w) stops reducing, or some other pre-defined termination criteria is met.Update the weights by an amount proportional to G, i.e.You might need to revisit the topic of differentiation if you are calculating the gradient by hand. The value of the gradient G depends on the inputs, the current values of the model parameters, and the cost function. This is done using partial differentiation: G = ∂J(W)/∂W. Calculate the gradients G of cost function w.r.t parameters.Hence, to minimize the cost function, we move in the direction opposite to the gradient.
The gradient (or derivative) tells us the incline or slope of the cost function. Gradient descent is used to minimize a cost function J(W) parameterized by a model parameters W. Then we move in the direction which reduces the cost function.īy repeating this step thousands of times, we’ll continually minimize our cost function.ĪDVERTISEMENT Pseudocode for Gradient Descent To improve a given set of weights, we try to get a sense of the value of the cost function for weights similar to the current weights (by calculating the gradient). We start with some set of values for our model parameters (weights and biases), and improve them slowly. Gradient descent illustration for Linear Regression This means our prediction p will be close to the target t. During training, our aim is to find a set of values for W such that (p - t)² is small. Note that the predicted value p depends on the input X as well as the machine learning model and (current) values of the parameters W. Many machine learning problems reduce to finding a set of weights for the model which minimizes the cost function.įor example, if the prediction is p, the target is t, and our error metric is squared error, then the cost function J(W) = (p - t)². Machine learning models typically have parameters (weights and biases) and a cost function to evaluate how good a particular set of parameters are. Gradient Descent is one of the most popular and widely used algorithms for training machine learning models. By Keshav Dhandhania How to understand Gradient Descent, the most popular ML algorithm
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