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   • Gradient Descent vs Stochastic Gradient Descent algorithms

     Top Answer

     Answered Mar 01, 2016 · 4 votes

     The new scenario you describe (performing Backpropagation on each randomly picked sample), is one common "flavor" of Stochastic Gradient Descent, as described here: https://www.quora.com/Whats-the-difference-between-gradient-descent-and-stochastic-gradient-descent

     The 3 most common flavors according to this document are (Your flavor is C):

     A)

     randomly shuffle samples in the training setfor one or more epochs, or until approx. cost minimum is reached: for training sample i: compute gradients and perform weight updates

     B)

     for one or more epochs, or until approx. cost minimum is reached: randomly shuffle samples in the training set for training sample i: compute gradients and perform weight updates

     C)

     for iterations t, or until approx. cost minimum is reached: draw random sample from the training set compute gradients and perform weight updates

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   • Gradient Descent: Do we iterate on ALL of the training set with each step in GD? or Do we change GD for each training set?

     Top Answer

     Answered Jun 24, 2013 · 7 votes

     The second way you are describing it is the correct way to perform Gradient Descent. The true gradient is dependent on the whole data set, so one iteration of gradient descent requires using all of the data set. (This is true for any learning algorithm where you can take the gradient)

     The "first way" is close to something that is called Stochastic Gradient Descent. The idea here is that using the whole data set for one update might be overkill, especially if some of the data points are redundant. In this case, we pick a random point from the data set - essentially setting m=1. We then update based on successive selections of single points in the data set. This way we can do m updates at about the same cost as one update of Gradient Descent. But each update is a bit noisy, which can make convergence to the final solution difficult.

     The compromise between these approaches is called "MiniBatch". Taking the gradient of the whole data set is one full round of "batch" processing, as we need the whole data set on hand. Instead we will do a mini batch, selecting only a small subset of the whole data set. In this case we set k, 1 < k < m, where k is the number of points in the mini batch. We select k random data points to create the gradient from at every iteration, and then perform the update. Repeat until convergence. Obviously, increasing / decreasing k is a tradeoff between speed and accuracy.

     Note: For both stochastic & mini batch gradient descent, it is important to shuffle / select randomly the next data point. If you use the same iteration order for each data point, you can get really weird / bad results - often diverging away from the solution.

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   • Gradient Ascent vs Gradient Descent

     Top Answer

     Answered Feb 20, 2022 · 1 votes

     The difference is a sign, gradient ascent means to change parameters according to the gradient of the function (so increase its value) and gradient descent against the gradient (thus decrease).

     You almost never want to increase the loss (apart from say some form of gamified system, e.g. a GAN). But if you frame your problem as maximisation of probability of correct answer then you want to utilise gradient ascent. It is always a dual thing, for every problem expressed as gradient ascent of something you can think about it as gradient descent of minus this function, and vice versa.

     theta_t + grad(f)[theta_t] = theta_t - grad(-f)[theta_t]gradient ascent on f gradient descent on -f-

     In other words there is absolutely no difference in usage of these two methods, they are equivalent. The reason why people use one or the other is just what helps explain the method in most natural terms. It is more natural to say "I am going to decrease the cost" or "I am going to maximise the probability" than it is to say "I am going to decrease minus cost" or "I am going to minimise 1 minus probability".

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     3/5

   • Gradient Descent With RMSProp from Scratch

     Gradient descent is an optimization algorithm used to find the set of parameters (coefficients) of a function that minimizes a cost function. This method iteratively adjusts the coefficients of the function until the cost reaches the local, or global, minimum. Gradient descent works by calculating the partial derivatives of the cost function with respect to each of the coefficients. The algorithm then makes small adjustments to the coefficients in order to reduce the cost until it reaches a minimum. The direction of the adjustments is determined by the negative of the gradient of the cost function. Optimizers are methods or algorithms that reduce a loss (an error) by adjusting various parameters and weights, minimizing the loss function, and thereby improving model accuracy and speed. One such optimization technique is RMSprop.

     RMSProp (Root Mean Squared Propagation) is an adaptive learning rate optimization algorithm. It is an extension of the popular Adaptive Gradient Algorithm and is designed to dramatically reduce the amount of computational effort used in training neural networks. This algorithm works by exponentially decaying the learning rate every time the squared gradient is less than a certain...

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     4/5

   • Also try

     stochastic gradient descent	gradient descent linear regression
     gradient descent machine learning	batch gradient descent
     gradient descent algorithm	gradient descent method
     gradient descent formula	gradient descent python

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2. en.wikipedia.org › wiki › Gradient_descentGradient descent - Wikipedia

   en.wikipedia.org › wiki › Gradient_descent

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   Gradient Descent in 2D. Gradient descent is a method for unconstrained mathematical optimization. It is a first-order iterative algorithm for finding a local minimum of a differentiable multivariate function.

3. www.geeksforgeeks.org › gradient-descent-algorithm-and-its-variantsGradient Descent Algorithm in Machine Learning - GeeksforGeeks

   www.geeksforgeeks.org › gradient-descent-algorithm-and-its-variants

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   Jan 24, 2024 · Gradient Descent Algorithm (GDA) is an iterative optimization algorithm used to find the minimum of a function. It works by repeatedly moving in the direction of the negative gradient of the function, which is the direction that leads to the steepest descent.

4. towardsdatascience.com › gradient-descent-explained-9b953fc0d2cGradient Descent Explained. A comprehensive guide to Gradient… |...

   towardsdatascience.com › gradient-descent-explained-9b953fc0d2c

   May 22, 2020 · Gradient Descent is an optimizing algorithm used in Machine/ Deep Learning algorithms. Gradient Descent with Momentum and Nesterov Accelerated Gradient Descent are advanced versions of Gradient Descent.

5. www.khanacademy.org › a › what-is-gradient-descentGradient descent (article) | Khan Academy

   www.khanacademy.org › a › what-is-gradient-descent

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   Gradient descent is an algorithm that numerically estimates where a function outputs its lowest values. That means it finds local minima, but not by setting ∇ f = 0 ‍ like we've seen before. Instead of finding minima by manipulating symbols, gradient descent approximates the solution with numbers.

6. machinelearningmastery.com › gradient-descent-for-machine-learningGradient Descent For Machine Learning

   machinelearningmastery.com › gradient-descent-for-machine-learning

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   Aug 12, 2019 · Gradient descent is a simple optimization procedure that you can use with many machine learning algorithms. Batch gradient descent refers to calculating the derivative from all training data before calculating an update.

7. www.geeksforgeeks.org › gradient-descent-in-linear-regressionGradient Descent in Linear Regression - GeeksforGeeks

   www.geeksforgeeks.org › gradient-descent-in-linear-regression

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   Jul 30, 2024 · Gradient Descent is an iterative optimization algorithm that tries to find the optimum value (Minimum/Maximum) of an objective function. It is one of the most used optimization techniques in machine learning projects for updating the parameters of a model in order to minimize a cost function.

8. towardsdatascience.com › gradient-descent-algorithm-a-deep-dive-cf04e8115f21Gradient Descent Algorithm — a deep dive | by Robert Kwiatkowski...

   towardsdatascience.com › gradient-descent-algorithm-a-deep-dive-cf04e8115f21

   May 22, 2021 · Gradient descent (GD) is an iterative first-order optimisation algorithm, used to find a local minimum/maximum of a given function. This method is commonly used in machine learning (ML) and deep learning (DL) to minimise a cost/loss function (e.g. in a linear regression).

9. www.ibm.com › topics › gradient-descentWhat is Gradient Descent? | IBM

   www.ibm.com › topics › gradient-descent

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   Gradient descent is an optimization algorithm which is commonly-used to train machine learning models and neural networks. It trains machine learning models by minimizing errors between predicted and actual results. Training data helps these models learn over time, and the cost function within gradient descent specifically acts as a barometer ...

10. www.datacamp.com › tutorial › tutorial-gradient-descentGradient Descent Tutorial | DataCamp

    www.datacamp.com › tutorial › tutorial-gradient-descent

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    Gradient descent is one of the most important algorithms in all of machine learning and deep learning. It is an extremely powerful optimization algorithm that can train linear regression, logistic regression, and neural network models.

11. machinelearningmastery.com › gradient-descent-optimization-from-scratchHow to Implement Gradient Descent Optimization from Scratch

    machinelearningmastery.com › gradient-descent-optimization-from-scratch

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    Oct 12, 2021 · Gradient descent is an optimization algorithm that follows the negative gradient of an objective function in order to locate the minimum of the function. It is a simple and effective technique that can be implemented with just a few lines of code.