If I use the trained RNN(or LSTM) to generate series data(name the network with generated-RNN), then I use the series data to train the RNN(i.e. the same structure with the generated-RNN) from scratch, is it possible to get the same trained network(the same trained weights) with the generated-RNN?
You take series with X as input and Y as output to train a model, then with that model you generate series O.
Now you want to recreate the Ws from O=sigmoid(XWL1+b)...*WLN+bn with O as input and X as output.
Is it possible?
Unless X=O, then most likely not. I can't give a formal mathematical proof but multiplying forward through a network isn't equal to multiplying backwards, mainly due to the activation function. If you removed the activation function or took the inverse of the activation function you would more likely approach the Ws you desired, though another set of weights might also get you the the same output for a given input.
Also, this question would be better received in stats.stackexchange than stackoverflow.
Related
I'm trying to create a sample neural network that can be used for credit scoring. Since this is a complicated structure for me, i'm trying to learn them small first.
I created a network using back propagation - input layer (2 nodes), 1 hidden layer (2 nodes +1 bias), output layer (1 node), which makes use of sigmoid as activation function for all layers. I'm trying to test it first using a^2+b2^2=c^2 which means my input would be a and b, and the target output would be c.
My problem is that my input and target output values are real numbers which can range from (-/infty, +/infty). So when I'm passing these values to my network, my error function would be something like (target- network output). Would that be correct or accurate? In the sense that I'm getting the difference between the network output (which is ranged from 0 to 1) and the target output (which is a large number).
I've read that the solution would be to normalise first, but I'm not really sure how to do this. Should i normalise both the input and target output values before feeding them to the network? What normalisation function is best to use cause I read different methods in normalising. After getting the optimized weights and use them to test some data, Im getting an output value between 0 and 1 because of the sigmoid function. Should i revert the computed values to the un-normalized/original form/value? Or should i only normalise the target output and not the input values? This really got me stuck for weeks as I'm not getting the desired outcome and not sure how to incorporate the normalisation idea in my training algorithm and testing..
Thank you very much!!
So to answer your questions :
Sigmoid function is squashing its input to interval (0, 1). It's usually useful in classification task because you can interpret its output as a probability of a certain class. Your network performes regression task (you need to approximate real valued function) - so it's better to set a linear function as an activation from your last hidden layer (in your case also first :) ).
I would advise you not to use sigmoid function as an activation function in your hidden layers. It's much better to use tanh or relu nolinearities. The detailed explaination (as well as some useful tips if you want to keep sigmoid as your activation) might be found here.
It's also important to understand that architecture of your network is not suitable for a task which you are trying to solve. You can learn a little bit of what different networks might learn here.
In case of normalization : the main reason why you should normalize your data is to not giving any spourius prior knowledge to your network. Consider two variables : age and income. First one varies from e.g. 5 to 90. Second one varies from e.g. 1000 to 100000. The mean absolute value is much bigger for income than for age so due to linear tranformations in your model - ANN is treating income as more important at the beginning of your training (because of random initialization). Now consider that you are trying to solve a task where you need to classify if a person given has grey hair :) Is income truly more important variable for this task?
There are a lot of rules of thumb on how you should normalize your input data. One is to squash all inputs to [0, 1] interval. Another is to make every variable to have mean = 0 and sd = 1. I usually use second method when the distribiution of a given variable is similiar to Normal Distribiution and first - in other cases.
When it comes to normalize the output it's usually also useful to normalize it when you are solving regression task (especially in multiple regression case) but it's not so crucial as in input case.
You should remember to keep parameters needed to restore the original size of your inputs and outputs. You should also remember to compute them only on a training set and apply it on both training, test and validation sets.
In my undergrad thesis I am creating a neural network to control automated shifting algorithm for a vehicle.
I have created the nn from scratch starting from .m script which works correctly. I tested it to recognize some shapes.
A brief background information;
NN rewires neurons which are mathematical blocks located in a layer. There are multiple layers. output of a layer is input of preceding layer. Actual output is subtracted from known output and error is obtained by this manner. By using back propagation algorithm which are some algebraic equation the coefficient of neurons are updated.
What I want to do is;
in code there are 6 input matrices, don't have to be matrix just anything and corresponding outputs. lets call them as x(i) matrices and y(i) vectors. In for loop I go through each matrix and vector to teach the network. Finally by using last known updated coeffs networks give some responses according to unknown input.
I couldn't find the way that, how to simulate that for loop in simulink to go through each different input and output pairs. When the network is done with one pair it should change the input and compare with corresponding output then update the coefficient matrices.
I model the layers as given and just fed with one input but I need multiple.
When it comes to automatic transmission control issue it should do all this real time. It should continuously read the output and updates the coeffs and gives the decision.
Check out the "For each Subsystem". Exists since 2011b
To create the input signals you use the "Concatenate" Block which would have six inputs in your case, and a three dimensional output x.dim = [1x20x6] then you could iterate over the third dimension...
A very useful pattern to create smaller models that run faster and to keep your code DRY (Dont repeat yourself)
I recently started studying ANN, and there is something that I've been trying to figure out that I can't seem to find an answer to (probably because it's too trivial or because I'm searching for the wrong keywords..).
When do you use multiple outputs instead of single outputs? I guess in simplest case of 1/0-classification its the easiest to use the "sign" as the output activiation function. But in which case do you use several outputs? Is it if you have for instance a multiple classification problem, so you want to classify something as, say for instance, A, B or C and you choose 1 output neuron for each class? How do you determine which class it belongs to?
In a classification context, there are a couple of situations where using multiple output units can be helpful: multiclass classification, and explicit confidence estimation.
Multiclass
For the multiclass case, as you wrote in your question, you typically have one output unit in your network for each class of data you're interested in. So if you're trying to classify data as one of A, B, or C, you can train your network on labeled data, but convert all of your "A" labels to [1 0 0], all your "B" labels to [0 1 0], and your "C" labels to [0 0 1]. (This is called a "one-hot" encoding.) You also probably want to use a logistic activation on your output units to restrict their activation values to the interval (0, 1).
Then, when you're training your network, it's often useful to optimize a "cross-entropy" loss (as opposed to a somewhat more intuitive Euclidean distance loss), since you're basically trying to teach your network to output the probability of each class for a given input. Often one uses a "softmax" (also sometimes called a Boltzmann) distribution to define this probability.
For more info, please check out http://www.willamette.edu/~gorr/classes/cs449/classify.html (slightly more theoretical) and http://deeplearning.net/tutorial/logreg.html (more aimed at the code side of things).
Confidence estimation
Another cool use of multiple outputs is to use one output as a standard classifier (e.g., just one output unit that generates a 0 or 1), and a second output to indicate the confidence that this network has in its classification of the input signal (e.g., another output unit that generates a value in the interval (0, 1)).
This could be useful if you trained up a separate network on each of your A, B, and C classes of data, but then also presented data to the system later that came from class D (or whatever) -- in this case, you'd want each of the networks to indicate that they were uncertain of the output because they've never seen something from class D before.
Have a look at softmax layer for instance. Maximum output of this layer is your class. And it has got nice theoretical justification.
To be concise : you take previous layer's output and interpret it as a vector in m dimensional space. After that you fit K gaussians to it, which are sharing covariance matrices. If you model it and write out equations it amounts to softmax layer. For more details see "Machine Learning. A Probabilistic Perspective" by Kevin Murphy.
It is just an example of using last layer for multiclass classification. You can as well use multiple outputs for something else. For instance you can train ANN to "compress" your data, that is calculate a function from N dimensional to M dimensional space that minimizes loss of information (this model is called autoencoder)
I used ntstool to create NAR (nonlinear Autoregressive) net object, by training on a 1x1247 input vector. (daily stock price for 6 years)
I have finished all the steps and saved the resulting net object to workspace.
Now I am clueless on how to use this object to predict the y(t) for example t = 2000, (I trained the model for t = 1:1247)
In some other threads, people recommended to use sim(net, t) function - however this will give me the same result for any value of t. (same with net(t) function)
I am not familiar with the specific neural net commands, but I think you are approaching this problem in the wrong way. Typically you want to model the evolution in time. You do this by specifying a certain window, say 3 months.
What you are training now is a single input vector, which has no information about evolution in time. The reason you always get the same prediction is because you only used a single point for training (even though it is 1247 dimensional, it is still 1 point).
You probably want to make input vectors of this nature (for simplicity, assume you are working with months):
[month1 month2; month2 month 3; month3 month4]
This example contains 2 training points with the evolution of 3 months. Note that they overlap.
Use the Network
After the network is trained and validated, the network object can be used to calculate the network response to any input. For example, if you want to find the network response to the fifth input vector in the building data set, you can use the following
a = net(houseInputs(:,5))
a =
34.3922
If you try this command, your output might be different, depending on the state of your random number generator when the network was initialized. Below, the network object is called to calculate the outputs for a concurrent set of all the input vectors in the housing data set. This is the batch mode form of simulation, in which all the input vectors are placed in one matrix. This is much more efficient than presenting the vectors one at a time.
a = net(houseInputs);
Each time a neural network is trained, can result in a different solution due to different initial weight and bias values and different divisions of data into training, validation, and test sets. As a result, different neural networks trained on the same problem can give different outputs for the same input. To ensure that a neural network of good accuracy has been found, retrain several times.
There are several other techniques for improving upon initial solutions if higher accuracy is desired. For more information, see Improve Neural Network Generalization and Avoid Overfitting.
strong text
My task is to classify time-series data with use of MATLAB and any neural-network framework.
Describing task more specifically:
Is is a problem from computer-vision field. Is is a scene boundary detection task.
Source data are 4 arrays of neighbouring frame histogram correlations from the videoflow.
Based on this data, we have to classify this timeseries with 2 classes:
"scene break"
"no scene break"
So network input is 4 double values for each source data entry, and output is one binary value. I am going to show example of src data below:
0.997894,0.999413,0.982098,0.992164
0.998964,0.999986,0.999127,0.982068
0.993807,0.998823,0.994008,0.994299
0.225917,0.000000,0.407494,0.400424
0.881150,0.999427,0.949031,0.994918
Problem is that pattern-recogition tools from Matlab Neural Toolbox (like patternnet) threat source data like independant entrues. But I have strong belief that results will be precise only if net take decision based on the history of previous correlations.
But I also did not manage to get valid response from reccurent nets which serve time series analysis (like delaynet and narxnet).
narxnet and delaynet return lousy result and it looks like these types of networks not supposed to solve classification tasks. I am not insert any code here while it is allmost totally autogenerated with use of Matlab Neural Toolbox GUI.
I would apprecite any help. Especially, some advice which tool fits better for accomplishing my task.
I am not sure how difficult to classify this problem.
Given your sample, 4 input and 1 output feed-forward neural network is sufficient.
If you insist on using historical inputs, you simply pre-process your input d, such that
Your new input D(t) (a vector at time t) is composed of d(t) is a 1x4 vector at time t; d(t-1) is 1x4 vector at time t-1;... and d(t-k) is a 1x4 vector at time t-k.
If t-k <0, just treat it as '0'.
So you have a 1x(4(k+1)) vector as input, and 1 output.
Similar as Dan mentioned, you need to find a good k.
Speaking of the weights, I think additional pre-processing like windowing method on the input is not necessary, since neural network would be trained to assign weights to each input dimension.
It sounds a bit messy, since the neural network would consider each input dimension independently. That means you lose the information as four neighboring correlations.
One possible solution is the pre-processing extracts the neighborhood features, e.g. using mean and std as two features representative for the originals.