I have earlier worked in shallow(one or two layered) neural networks, so i have understanding of them, that how they work, and it is quite easy to visualize the derivations for forward and backward pass during the training of them, Currently I am studying about Deep neural networks(More precisely CNN), I have read lots of articles about their training, but still I am unable to understand the big picture of the training of the CNN, because in some cases people using pre- trained layers where convolution weights are extracted using auto-encoders, in some cases random weights were used for convolution, and then using back propagation they train the weights, Can any one help me to give full picture of the training process from input to fully connected layer(Forward Pass) and from fully connected layer to input layer (Backward pass).
Thank You
I'd like to recommend you a very good explanation of how to train a multilayer neural network using backpropagation. This tutorial is the 5th post of a very detailed explanation of how backpropagation works, and it also has Python examples of different types of neural nets to fully understand what's going on.
As a summary of Peter Roelants tutorial, I'll try to explain a little bit what is backpropagation.
As you have already said, there are two ways to initialize a deep NN: with random weights or pre-trained weights. In the case of random weights and for a supervised learning scenario, backpropagation works as following:
Initialize your network parameters randomly.
Feed forward a batch of labeled examples.
Compute the error (given by your loss function) within the desired output and the actual one.
Compute the partial derivative of the output error w.r.t each parameter.
These derivatives are the gradients of the error w.r.t to the network's parameters. In other words, they are telling you how to change the value of the weights in order to get the desired output, instead of the produced one.
Update the weights according to those gradients and the desired learning rate.
Perform another forward pass with different training examples, repeat the following steps until the error stops decreasing.
Starting with random weights is not a problem for the backpropagation algorithm, given enough training data and iterations it will tune the weights until they work for the given task.
I really encourage you to follow the full tutorial I linked, because you'll get a very detalied view of how and why backpropagation works for multi layered neural networks.
Related
I am currently looking through Michael Nielsen's ebook Neural Networks and Deep Learning and have run the code found at the end of chapter 1 which trains a neural network to recognize hand-written digits (with a slight modification to make the backpropagation algorithm over a mini-batch matrix-based).
However, having run this code and achieving a classification accuracy of just under 94%, I decided to remove the use of biases from the network. After re-training the modified network, I found no difference in classification accuracy!
NB: The output layer of this network contains ten neurons; if the ith of these neurons has the highest activation then the input is classified as being the digit i.
This got me wondering why it is necessary to use biases in a neural network, rather than just weights, and what differentiates between a task where biases will improve the performance of a network and a task where they will not?
My code can be found here: https://github.com/pipthagoras/neural-network-1
Biases are used to account for the fact that your underlying data might not be centered. It is clearer to see in the case of a linear regression.
If you do a regression without an intercept (or bias), you are forcing the underlying model to pass through the origin, which will result in a poor model if the underlying data is not centered (for example if the true generating process is Y=3000). If, on the other hand, your data is centered or close to centered, then eliminating bias is good, since you won't introduce a term that is, in fact, independent to your predictive variable (it's like selecting a simpler model, which will tend to generalize better PROVIDED that it actually reflects the underlying data).
I understand all the computational steps of training a neural network with gradient descent using forwardprop and backprop, but I'm trying to wrap my head around why they work so much better than logistic regression.
For now all I can think of is:
A) the neural network can learn it's own parameters
B) there are many more weights than simple logistic regression thus allowing for more complex hypotheses
Can someone explain why a neural network works so well in general? I am a relative beginner.
Neural Networks can have a large number of free parameters (the weights and biases between interconnected units) and this gives them the flexibility to fit highly complex data (when trained correctly) that other models are too simple to fit. This model complexity brings with it the problems of training such a complex network and ensuring the resultant model generalises to the examples it’s trained on (typically neural networks require large volumes of training data, that other models don't).
Classically logistic regression has been limited to binary classification using a linear classifier (although multi-class classification can easily be achieved with one-vs-all, one-vs-one approaches etc. and there are kernalised variants of logistic regression that allow for non-linear classification tasks). In general therefore, logistic regression is typically applied to more simple, linearly-separable classification tasks, where small amounts of training data are available.
Models such as logistic regression and linear regression can be thought of as simple multi-layer perceptrons (check out this site for one explanation of how).
To conclude, it’s the model complexity that allows neural nets to solve more complex classification tasks, and to have a broader application (particularly when applied to raw data such as image pixel intensities etc.), but their complexity means that large volumes of training data are required and training them can be a difficult task.
Recently Dr. Naftali Tishby's idea of Information Bottleneck to explain the effectiveness of deep neural networks is making the rounds in the academic circles.
His video explaining the idea (link below) can be rather dense so I'll try to give the distilled/general form of the core idea to help build intuition
https://www.youtube.com/watch?v=XL07WEc2TRI
To ground your thinking, vizualize the MNIST task of classifying the digit in the image. For this, I am only talking about simple fully-connected neural networks (not Convolutional NN as is typically used for MNIST)
The input to a NN contains information about the output hidden inside of it. Some function is needed to transform the input to the output form. Pretty obvious.
The key difference in thinking needed to build better intuition is to think of the input as a signal with "information" in it (I won't go into information theory here). Some of this information is relevant for the task at hand (predicting the output). Think of the output as also a signal with a certain amount of "information". The neural network tries to "successively refine" and compress the input signal's information to match the desired output signal. Think of each layer as cutting away at the unneccessary parts of the input information, and
keeping and/or transforming the output information along the way through the network.
The fully-connected neural network will transform the input information into a form in the final hidden layer, such that it is linearly separable by the output layer.
This is a very high-level and fundamental interpretation of the NN, and I hope it will help you see it clearer. If there are parts you'd like me to clarify, let me know.
There are other essential pieces in Dr.Tishby's work, such as how minibatch noise helps training, and how the weights of a neural network layer can be seen as doing a random walk within the constraints of the problem.
These parts are a little more detailed, and I'd recommend first toying with neural networks and taking a course on Information Theory to help build your understanding.
Consider you have a large dataset and you want to build a binary classification model for that, Now you have two options that you have pointed out
Logistic Regression
Neural Networks ( Consider FFN for now )
Each node in a neural network will be associated with an activation function for example let's choose Sigmoid since Logistic regression also uses sigmoid internally to make decision.
Let's see how the decision of logistic regression looks when applied on the data
See some of the green spots present in the red boundary?
Now let's see the decision boundary of neural network (Forgive me for using a different color)
Why this happens? Why does the decision boundary of neural network is so flexible which gives more accurate results than Logistic regression?
or the question you asked is "Why neural networks works so well ?" is because of it's hidden units or hidden layers and their representation power.
Let me put it this way.
You have a logistic regression model and a Neural network which has say 100 neurons each of Sigmoid activation. Now each neuron will be equivalent to one logistic regression.
Now assume a hundred logistic units trained together to solve one problem versus one logistic regression model. Because of these hidden layers the decision boundary expands and yields better results.
While you are experimenting you can add more number of neurons and see how the decision boundary is changing. A logistic regression is same as a neural network with single neuron.
The above given is just an example. Neural networks can be trained to get very complex decision boundaries
Neural networks allow the person training them to algorithmically discover features, as you pointed out. However, they also allow for very general nonlinearity. If you wish, you can use polynomial terms in logistic regression to achieve some degree of nonlinearity, however, you must decide which terms you will use. That is you must decide a priori which model will work. Neural networks can discover the nonlinear model that is needed.
'Work so well' depends on the concrete scenario. Both of them do essentially the same thing: predicting.
The main difference here is neural network can have hidden nodes for concepts, if it's propperly set up (not easy), using these inputs to make the final decission.
Whereas linear regression is based on more obvious facts, and not side effects. A neural network should de able to make more accurate predictions than linear regression.
Neural networks excel at a variety of tasks, but to get an understanding of exactly why, it may be easier to take a particular task like classification and dive deeper.
In simple terms, machine learning techniques learn a function to predict which class a particular input belongs to, depending on past examples. What sets neural nets apart is their ability to construct these functions that can explain even complex patterns in the data. The heart of a neural network is an activation function like Relu, which allows it to draw some basic classification boundaries like:
Example classification boundaries of Relus
By composing hundreds of such Relus together, neural networks can create arbitrarily complex classification boundaries, for example:
Composing classification boundaries
The following article tries to explain the intuition behind how neural networks work: https://medium.com/machine-intelligence-report/how-do-neural-networks-work-57d1ab5337ce
Before you step into neural network see if you have assessed all aspects of normal regression.
Use this as a guide
and even before you discard normal regression - for curved type of dependencies - you should strongly consider kernels with SVM
Neural networks are defined with an objective and loss function. The only process that happens within a neural net is to optimize for the objective function by reducing the loss function or error. The back propagation helps in finding the optimized objective function and reach our output with an output condition.
In scenario 1, I had a multi-layer sparse autoencoder that tries to reproduce my input, so all my layers are trained together with random-initiated weights. Without a supervised layer, on my data this didn't learn any relevant information (the code works fine, verified as I've already used it in many other deep neural network problems)
In scenario 2, I simply train multiple auto-encoders in a greedy layer-wise training similar to that of deep learning (but without a supervised step in the end), each layer on the output of the hidden layer of the previous autoencoder. They'll now learn some patterns (as I see from the visualized weights) separately, but not awesome, as I'd expect it from single layer AEs.
So I've decided to try if now the pretrained layers connected into 1 multi-layer AE could perform better than the random-initialized version. As you see this is same as the idea of the fine-tuning step in deep neural networks.
But during my fine-tuning, instead of improvement, the neurons of all the layers seem to quickly converge towards an all-the-same pattern and end up learning nothing.
Question: What's the best configuration to train a fully unsupervised multi-layer reconstructive neural network? Layer-wise first and then some sort of fine tuning? Why is my configuration not working?
After some tests I've came up with a method that seems to give very good results, and as you'd expect from a 'fine-tuning' it improves the performance of all the layers:
Just like normally, during the greedy layer-wise learning phase, each new autoencoder tries to reconstruct the activations of the previous autoencoder's hidden layer. However, the last autoencoder (that will be the last layer of our multi-layer autoencoder during fine-tuning) is different, this one will use the activations of the previous layer and tries to reconstruct the 'global' input (ie the original input that was fed to the first layer).
This way when I connect all the layers and train them together, the multi-layer autoencoder will really reconstruct the original image in the final output. I found a huge improvement in the features learned, even without a supervised step.
I don't know if this is supposed to somehow correspond with standard implementations but I haven't found this trick anywhere before.
So after you have a machine learning algorithm trained, with your layers, nodes, and weights, how exactly does it go about getting a prediction for an input vector? I am using MultiLayer Perceptron (neural networks).
From what I currently understand, you start with your input vector to be predicted. Then you send it to your hidden layer(s) where it adds your bias term to each data point, then adds the sum of the product of each data point and the weight for each node (found in training), then runs that through the same activation function used in training. Repeat for each hidden layer, then does the same for your output layer. Then each node in the output layer is your prediction(s).
Is this correct?
I got confused when using opencv to do this, because in the guide it says when you use the function predict:
If you are using the default cvANN_MLP::SIGMOID_SYM activation
function with the default parameter values fparam1=0 and fparam2=0
then the function used is y = 1.7159*tanh(2/3 * x), so the output
will range from [-1.7159, 1.7159], instead of [0,1].
However, when training it is also stated in the documentation that SIGMOID_SYM uses the activation function:
f(x)= beta*(1-e^{-alpha x})/(1+e^{-alpha x} )
Where alpha and beta are user defined variables.
So, I'm not quite sure what this means. Where does the tanh function come into play? Can anyone clear this up please? Thanks for the time!
The documentation where this is found is here:
reference to the tanh is under function descriptions predict.
reference to activation function is by the S looking graph in the top part of the page.
Since this is a general question, and not code specific, I did not post any code with it.
I would suggest that you read about appropriate algorithm that your are using or plan to use. To be honest there is no one definite algorithm to solve a problem but you can explore what features you got and what you need.
Regarding how an algorithm performs prediction is totally depended on the choice of algorithm. Support Vector Machine (SVM) performs prediction by fitting hyperplanes on the feature space and using some metric such as distance for learning and than the learnt model is used for prediction. KNN on the other than uses simple nearest neighbor measurement for prediction.
Please do more work on what exactly you need and read through the research papers to get proper understanding. There is not magic involved in prediction but rather mathematical formulations.
I'm having trouble with some of the concepts in machine learning through neural networks. One of them is backpropagation. In the weight updating equation,
delta_w = a*(t - y)*g'(h)*x
t is the "target output", which would be your class label, or something, in the case of supervised learning. But what would the "target output" be for unsupervised learning?
Can someone kindly provide an example of how you'd use BP in unsupervised learning, specifically for clustering of classification?
Thanks in advance.
The most common thing to do is train an autoencoder, where the desired outputs are equal to the inputs. This makes the network try to learn a representation that best "compresses" the input distribution.
Here's a patent describing a different approach, where the output labels are assigned randomly and then sometimes flipped based on convergence rates. It seems weird to me, but okay.
I'm not familiar with other methods that use backpropogation for clustering or other unsupervised tasks. Clustering approaches with ANNs seem to use other algorithms (example 1, example 2).
I'm not sure which unsupervised machine learning algorithm uses backpropagation specifically; if there is one I haven't heard of it. Can you point to an example?
Backpropagation is used to compute the derivatives of the error function for training an artificial neural network with respect to the weights in the network. It's named as such because the "errors" are "propagating" through the network "backwards". You need it in this case because the final error with respect to the target depends on a function of functions (of functions ... depending on how many layers in your ANN.) The derivatives allow you to then adjust the values to improve the error function, tempered by the learning rate (this is gradient descent).
In unsupervised algorithms, you don't need to do this. For example, in k-Means, where you are trying to minimize the mean squared error (MSE), you can minimize the error directly at each step given the assignments; no gradients needed. In other clustering models, such as a mixture of Gaussians, the expectation-maximization (EM) algorithm is much more powerful and accurate than any gradient-descent based method.
What you might be asking is about unsupervised feature learning and deep learning.
Feature learning is the only unsupervised method I can think of with respect of NN or its recent variant.(a variant called mixture of RBM's is there analogous to mixture of gaussians but you can build a lot of models based on the two). But basically Two models I am familiar with are RBM's(restricted boltzman machines) and Autoencoders.
Autoencoders(optionally sparse activations can be encoded in optimization function) are just feedforward neural networks which tune its weights in such a way that the output is a reconstructed input. Multiple hidden layers can be used but the weight initialization uses a greedy layer wise training for better starting point. So to answer the question the target function will be input itself.
RBM's are stochastic networks usually interpreted as graphical model which has restrictions on connections. In this setting there is no output layer and the connection between input and latent layer is bidirectional like an undirected graphical model. What it tries to learn is a distribution on inputs(observed and unobserved variables). Here also your answer would be input is the target.
Mixture of RBM's(analogous to mixture of gaussians) can be used for soft clustering or KRBM(analogous to K-means) can be used for hard clustering. Which in effect feels like learning multiple non-linear subspaces.
http://deeplearning.net/tutorial/rbm.html
http://ufldl.stanford.edu/wiki/index.php/UFLDL_Tutorial
An alternative approach is to use something like generative backpropagation. In this scenario, you train a neural network updating the weights AND the input values. The given values are used as the output values since you can compute an error value directly. This approach has been used in dimensionality reduction, matrix completion (missing value imputation) among other applications. For more information, see non-linear principal component analysis (NLPCA) and unsupervised backpropagation (UBP) which uses the idea of generative backpropagation. UBP extends NLPCA by introducing a pre-training stage. An implementation of UBP and NLPCA and unsupervised backpropagation can be found in the waffles machine learning toolkit. The documentation for UBP and NLPCA can be found using the nlpca command.
To use back-propagation for unsupervised learning it is merely necessary to set t, the target output, at each stage of the algorithm to the class for which the average distance to each element of the class before updating is least. In short we always try to train the ANN to place its input into the class whose members are most similar in terms of our input. Because this process is sensitive to input scale it is necessary to first normalize the input data in each dimension by subtracting the average and dividing by the standard deviation for each component in order to calculate the distance in a scale-invariant manner.
The advantage to using a back-prop neural network rather than a simple distance from a center definition of the clusters is that neural networks can allow for more complex and irregular boundaries between clusters.