When does gradient descent converge failure?
Gradient Descent Algo will not always converge to global minimum. It will Converge to Global minimum only if the function have one minimum and that will be a global minimum too. (Like the image shown below). More precisely we can say that function must be convex.
Can we use gradient norm as a measure of generalization error for model selection in practice?
Our empirical studies clearly find that the use of approximated gradient norm, as one of the hyper-parameter search objectives, can select the models with lower generalization error, but the efficiency is still low (marginal accuracy improvement but with high computation overhead).
When it is possible to run a gradient descent algorithm What is not guaranteed by the algorithm?
Conjugate gradient is not guaranteed to reach a global optimum or a local optimum! There are points where the gradient is very small, that are not optima (inflection points, saddle points). Gradient Descent could converge to a point x=0 for the function f(x)=x3.
For what values of the learning rate will gradient descent converge to the minimum?
Here, you have to know that it has already been established for GD, GD with momentum and SGD, that for any optimization problem, gradient descent converges to a local minimizer if the learning rate is less than 1/L, where L is the Lipschitz smoothness of the loss function with respect to the parameters.
Does gradient descent always decrease loss?
The gradient always points in the direction of steepest increase in the loss function. The gradient descent algorithm takes a step in the direction of the negative gradient in order to reduce loss as quickly as possible.
Why does gradient descent not converge?
In case of stochastic gradient Descent and mini-batch gradient descent, the algorithm does not converge but keeps on fluctuating around the global minimum. Therefore in order to make it converge, we have to slowly change the learning rate.
How would you test if a learning algorithm generalizes well?
Fortunately, there’s a very convenient way to measure an algorithm’s generalization performance: we measure its performance on a held-out test set, consisting of examples it hasn’t seen before. If an algorithm works well on the training set but fails to generalize, we say it is overfitting.
What is model overfitting?
Overfitting is a concept in data science, which occurs when a statistical model fits exactly against its training data. When this happens, the algorithm unfortunately cannot perform accurately against unseen data, defeating its purpose.
What does gradient descent converge to?
Intuitively, this means that gradient descent is guaranteed to converge and that it converges with rate O(1/k). value strictly decreases with each iteration of gradient descent until it reaches the optimal value f(x) = f(x∗).
How would you explain loss function and gradient descent?
The loss function describes how well the model will perform given the current set of parameters (weights and biases), and gradient descent is used to find the best set of parameters. We use gradient descent to update the parameters of our model.
Is gradient descent guaranteed to converge?
What does gradient descent algorithm do?
Gradient descent is an optimization algorithm which is commonly-used to train machine learning models and neural networks. Training data helps these models learn over time, and the cost function within gradient descent specifically acts as a barometer, gauging its accuracy with each iteration of parameter updates.
What is a vanishing gradient in machine learning?
The translation of the effect of a change in cost function (C) to the weight in an initial layer, or the norm of the gradient, becomes so small due to increased model complexity with more hidden units, that it becomes zero after a certain point. This is what we call Vanishing Gradients .
Can we afford a large learning rate for gradient descent?
Having a step size too large may cause it to overshoot a minima and bounce between the ridges of the minima. A widely used technique in gradient descent is to have a variable learning rate, rather than a fixed one. Initially, we can afford a large learning rate.
What is gradgradient clipping in machine learning?
Gradient Clipping is a method where the error derivative is changed or clipped to a threshold during backward propagation through the network, and using the clipped gradients to update the weights.
What is the difference between exploding gradients problem and weight problem?
The weights can no longer contribute to the reduction in cost function (C), and go unchanged affecting the network in the Forward Pass, eventually stalling the model. On the other hand, the Exploding gradients problem refers to a large increase in the norm of the gradient during training .