Why do we need epochs? - machine-learning

In courses there is nothing about epochs, but in practice they are everywhere used.
Why do we need them if the optimizer finds the best weight in one pass. Why does the model improve?

Generally whenever you want to optimize you use gradient descent. Gradient descent has a parameter called learning rate. In one iteration alone you can not guarantee that the gradient descent algorithm would converge to a local minima with the specified learning rate. That is the reason why you iterate again for the gradient descent to converge better.
Its also a good practice to change learning rates per epoch by observing the learning curves for better convergence.

Why do we need [to train several epochs] if the optimizer finds the best weight in one pass?
That's wrong in most cases. Gradient descent methods (see a list of them) does usually not find the optimal parameters (weights) in one pass. In fact, I have never seen any case where the optimal parameters were even reached (except for constructed cases).
One epoch consists of many weight update steps. One epoch means that the optimizer has used every training example once. Why do we need several epochs? Because gradient descent are iterative algorithms. It improves, but it just gets there in tiny steps. It only uses tiny steps, because it can only use local information. It does not have an idea of the function besides the current point at which it is.
You might want to read the gradient descent part of my optimization basics blog post.

Related

What is the exact difference between strocastic gradient Decent, mini batch gradient decent and gradient decent?

I am new to AI. I just learnt GD and about batches for gradient decent. I am confused about whats the exact difference between them. Any solution for this would be appreciated.
Thanks in advance
All of those methods are first order optimization methods, only require the knowledge of gradients, to minimize fintie sum functions. This means that we minimize a function F that is written as the sum of N functions f_{i}, and we can compute the gradient of each of those functions in any given point.
The GD methods consists in using the gradient of F, wich is equal to the sum of gradients of all f_{i} to do one update, i.e.
x <- x - alpha* grad(F)
The stochastic GD, cinsists in selecting randomly one function f_{i}, and doing an update using its gradients, i.e.
x <- x - alpha*grad(f_{i})
So each update is faster, but we need more updates to find the optimimum.
Mini-batch GD is in between of those two strategies and selects m functions f_{i} randomly to do one update.
For more information look at this link
Check this.
In both gradient descent (GD) and stochastic gradient descent (SGD), you iteratively update a set of parameters to minimize an error function.
While in GD, you have to run through all the samples in your training set to do a single update for a parameter in a particular iteration, in SGD, on the other hand, you use only one or subset of training sample from your training set to do the update for a parameter in a particular iteration. If you use a subset, it is called Minibatch Stochastic gradient Descent.
Thus, if the number of training samples is large, in fact very large, then using gradient descent may take too long because in every iteration when you are updating the values of the parameters, you are running through the complete training set. On the other hand, using SGD will be faster because you use only one training sample and it starts improving itself right away from the first sample.
SGD often converges much faster compared to GD but the error function is not as well minimized as in the case of GD. Often in most cases, the close approximation that you get in SGD for the parameter values is enough because they reach the optimal values and keep oscillating there.
Hope this will help you.

How I can know which type of gradient descent to use?

I understand the three types of gradient descent, but my problem is I can not know which type I must use on my model. I have read a lot, but I did not get it.
No code, it is just question.
Types of Gradient Descent:
Batch Gradient Descent: It processes all the training examples for each iteration of gradient descent. But, this method is computationally expensive when the number of training examples is large and usually not preferred.
Stochastic Gradient Descent: It processes one training example in each iteration. Here, the parameters are being updated after each iteration. This method is faster than batch gradient descent method. But, it increases system overhead when number of training examples is large by increasing the number of iterations.
Mini Batch gradient descent: Mini batch algorithm is the most favorable and widely used algorithm that makes precise and faster results using a batch of m training examples. In mini batch algorithm rather than using the complete data set, in every iteration we use a set of m training examples called batch to compute the gradient of the cost function. Common mini-batch sizes range between 50 and 256, but can vary for different applications.
There are various other optimization algorithms apart from gradient descent variants, like adam, rmsprop, etc.
Which optimizer should we use?
The question was to choose the best optimizer for our Neural Network Model in order to converge fast and to learn properly and tune the internal parameters so as to minimize the Loss function.
Adam works well in practice and outperforms other Adaptive techniques.
If your input data is sparse then methods such as SGD, NAG and momentum are inferior and perform poorly. For sparse data sets one should use one of the adaptive learning-rate methods. An additional benefit is that we won't need to adjust the learning rate but likely achieve the best results with the default value.
If one wants fast convergence and train a deep neural network Model or a highly complex Neural Network, then Adam or any other Adaptive learning rate techniques should be used because they outperforms every other optimization algorithms.
I hope this would help you to decide which one to use for your model.

What is the difference between gradient descent and cost function J(theta)?

I am learning machine learning from coursera. But I'm little confused between gradient descent and cost function. When and where I should use those?
J(ϴ) is minimized by trial and error approach i.e. trying lot of values and then checking the output. So in practice this means that this work is done by hand and is time consuming.
Gradient Descent basically just does what J(ϴ) does but in a automated way — change the theta values, or parameters, bit by bit, until we hopefully arrived a minimum. This is an iterative method where the model moves to the direction of steepest descent i.e. the optimal value of theta.
Why use Gradient descent? it is easy to implement and is generic optimization technique so will work even if you change your model. It is also better to use GD if you have a lot of features because in this case, normal J(ϴ) computation becomes very expensive.
Gradient Descent requires a cost function(there are many types of cost functions). One common function that is often used is mean squared error, which measure the difference between the estimator (the dataset) and the estimated value (the prediction).
We need this cost function because we want to minimize it. Minimizing any function means finding the deepest valley in that function. Keep in mind that, the cost function is used to monitor the error in predictions of an ML model. So minimizing this, basically means getting to the lowest error value possible or increasing the accuracy of the model. In short, We increase the accuracy by iterating over a training data set while tweaking the parameters(the weights and biases) of our model.
In short, the whole point of Gradient descent is to minimize the cost function

Sequential or batch parameters estimation

This is the problem that I should describe. Unfortunately the only one technique that I studied to estimate the parameters in the linear regression is the classic gradient descent algorithm. Is that one of "batch" or "sequential" mode ? And what is the difference between them ?
I wasn't expecting to find exactly the question from the ML exam here! Well the point is that as James Phillips says the gradient descent is an iterative method, so called sequential. The gradient descent is just an iterative optimization algorithm for finding the minimum of a function but you could use it to find the 'best-fitting line'. A complete batch way will be e.g. the Linear Least Squares method applying all the equations at once. You can find all the parameters calculating the partial derivatives of the sum of the square of the errors w.r.t. the best line fit and setting them to zero. Of course, as Phillips said it is not a convenient method, it's more a theoretical definition. Hope, it is useful.
From Liang et al. "A Fast and Accurate Online Sequential Learning Algorithm for Feedforward Networks":
Batch learning is usually a time consuming affair as it may involve many iterations through the training data. In most applications, this may take several minutes to several hours and further the learning parameters (i.e., learning rate, number of learning epochs, stopping criteria, and other predefined parameters) must be properly chosen to ensure convergence. Also, whenever a new data is received batch learning uses the past data together with the new data and performs a retraining, thus consuming a lot of time. There are many industrial applications where online sequential learning algorithms are preferred over batch learning algorithms as sequential learning algorithms do not require retraining whenever a new data is received. The back-propagation (BP) algorithm and its variants have been the backbone for training SLFNs with additive hidden nodes. It is to be noted that BP is basically a batch learning algorithm. Stochastic gradient descent BP (SGBP) is one of the main variants of BP for sequential learning applications.
Basically, gradient descent is theorized in a batch way, but in practice you use iterative methods.
I think the question doesn't ask you to show two ways (batch and sequential) to estimate the parameters of the model, but instead to explain—either in a batch or sequential mode—how such an estimation would work.
For instance, if you are trying to estimate parameters for a linear regression model, you could just describe likelihood maximization, which is equivalent to minimize the least square error:
If you want to show a sequential mode, you can describe the gradient descent algorithm.

Neural networks - why so many learning rules?

I'm starting neural networks, currently following mostly D. Kriesel's tutorial. Right off the beginning it introduces at least three (different?) learning rules (Hebbian, delta rule, backpropagation) concerning supervised learning.
I might be missing something, but if the goal is merely to minimize the error, why not just apply gradient descent over Error(entire_set_of_weights)?
Edit: I must admit the answers still confuse me. It would be helpful if one could point out the actual difference between those methods, and the difference between them and straight gradient descent.
To stress it, these learning rules seem to take the layered structure of the network into account. On the other hand, finding the minimum of Error(W) for the entire set of weights completely ignores it. How does that fit in?
One question is how to apportion the "blame" for an error. The classic Delta Rule or LMS rule is essentially gradient descent. When you apply Delta Rule to a multilayer network, you get backprop. Other rules have been created for various reasons, including the desire for faster convergence, non-supervised learning, temporal questions, models that are believed to be closer to biology, etc.
On your specific question of "why not just gradient descent?" Gradient descent may work for some problems, but many problems have local minima, which naive gradient descent will get stuck in. The initial response to that is to add a "momentum" term, so that you might "roll out" of a local minimum; that's pretty much the classic backprop algorithm.
First off, note that "backpropagation" simply means that you apply the delta rule on each layer from output back to input so it's not a separate rule.
As for why not a simple gradient descent, well, the delta rule is basically gradient descent. However, it tends to overfit the training data and doesn't generalize as efficiently as techniques which don't try to decay the error margin to zero. This makes sense because "error" here simply means the difference between our samples and the output - they are not guaranteed to accurately represent all possible inputs.
Backpropagation and naive gradient descent also differ in computational efficiency. Backprop is basically taking the networks structure into account and for each weight only calculates the actually needed parts.
The derivative of the error with respects to the weights is splitted via the chainrule into: ∂E/∂W = ∂E/∂A * ∂A/∂W. A is the activations of particular units. In most cases, the derivatives will be zero because W is sparse due to the networks topology. With backprop, you get the learning rules on how to ignore those parts of the gradient.
So, from a mathematical perspective, backprop is not that exciting.
there may be problems which for example make backprop run into local minima. Furthermore, just as an example, you can't adjust the topology with backprop. There are also cool learning methods using nature-inspired metaheuristics (for instance, evolutionary strategies) that enable adjusting weight AND topology (even recurrent ones) simultaneously. Probably, I will add one or more chapters to cover them, too.
There is also a discussion function right on the download page of the manuscript - if you find other hazzles that you don't like about the manuscript, feel free to add them to the page so I can change things in the next edition.
Greetz,
David (Kriesel ;-) )

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