Neural networks, how to master them, where to start? - page 7
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Well don't be so harsh. After all, the network is sometimes retrained (and I do it on every count of the BP being analysed) and the average method finds a minimum. As for dimensionality reduction, it doesn't work for BPs like price ones, unfortunately.
What timeframe are you using? As for downsizing, it depends on what you are going to do it for. If it's trivial pre-processing, then it won't have a proper effect without some a priori considerations, i.e. when you already have enough data and you are only improving the result. If you're using downsizing for something else, it could be anything. ;)
What timeframe do you use?
I don't use any TF.
The reason is that candlesticks are used in all timeframes, therefore BP built by opening prices (or opening) is closer to integrated random BP than BP built from the initial one by other methods (like switching to instrument time etc.).
Thanks gpwr, arnautov!
Шаг 1: Выбираем входные данные. Например,
x1 = WPR Per1
x2 = WPR Per2
x3 = WPR Per3
Closer to the subject? No problem! You should start by writing a neuron, and then combine them into a network. And sophisticated programs - that's afterwards. All other advice is rubbish.
And writing a neuron, can you break it down into stages?
Well? Who wrote in the thread that he would like to use an example, shall we start?
The first steps have been pointed out to us, the advisor is on page five...
I know that not so long ago two theorems were proved.
I will be grateful for references
According to the first one, three-layer nonlinear NS (that consists of three layers of neurons, with nonlinearity at the output of each layer) is a universal approximator
Well it seems to have been proven a long time ago. That you can approximate any function, with however small a given accuracy, with a 3-layer perseptron.
and further increasing the number of layers does not add power to the network.
According to the second theorem, the computational power of the network does not depend on the specific type of non-linearity at the outputs of its neurons. It is important that it (non-linearity) should be in principle, and it does not matter what exactly it is - sigmoid or arctangent.
What I was saying is the result of practical experiments. As for non-linearity... you have to familiarise yourself with these theorems first.
In addition, it is proved an unambiguous relation between the optimal training sample length on historical data, the dimensionality of the NS input and the total number of its synapses, in the sense of minimizing the prediction error on data not involved in the training of the network. This allows one not to engage in Leninism by manually selecting this optimum. With existing MS capacities, this saves a lot of time and effort.
Did you mean numbers of adjustable parameters? Thresholds are included too. By the way, it would also be helpful to have a documentary proof. And it wouldn't hurt those who are beginning to deal with neural networks to get acquainted with this material.
And writing a neuron, can you break it down into steps?
It is better to write in an object-oriented language.
Neuron is too shallow a concept when writing NS.
A layer is a union of identical neurons, so it makes no sense to consider a neuron separately.
I have used only 2 types of abstractions in my library -- layer and weights.
Weights are a block of synapses connecting 2 layers.
A layer has an input buffer, an output buffer and an error buffer, and an activation function. The synapses are a two-dimensional array, and link the output buffer of the layer to the input buffer as follows.
A network is a set of layers and links between them. Any layer that has non-zero signals in the error buffer can be considered an output layer.
Well, that's been proven a long time ago. That a 3-layer Perspectron can sapproximate any function, with any small given accuracy.
Error, not precision.
If that's clear, then what's the point of all this complexity:
TheXpert wrote >>
On many problems the 4 layer perseptron shows much better results and convergence.
And in some places a 5-layer is used. As for complex networks (with multiple output layers and complex links) based on a perseptron, I'll leave that part out for now.
Did you mean the number of adjustable parameters? Thresholds are included too. By the way, it would also be helpful to document them. And those who are beginning to engage in neural networks would do well to get acquainted with this material.
Yes, I meant the number of weights in NS and their relation to the number of inputs and optimal length of the training sample. The derivation of the relationship is given in the article attached to Attach on pages 64-65. 64-65. Briefly, if the number of weights of NS is w , the number of inputs d and the length of training sample P, at the optimum, the following condition must be satisfied: P = (w^2)/d
References to theorems I will give later - I need to find them.
By margin of error, not accuracy.
Yes.
If this is clear, then why the complexity:
It's simple, when adding a layer or changing the architecture is done with a few clicks of the mouse or a few lines of code, then those complexities turn into interesting extras.
>> Thank you. And the proof of the theorem? Or at least the exact wording?
The suitability theorem for any non-linear neuron function was proved by former Soviet and, since the late 1980s, American mathematician Vladik Kreynovich [1] and published in one of the leading Western neural network journals.
1. Kreinovich V.Y. Arbitrary nonlinearity is sufficient to represent all functions by neural networks: A theorem / Neural Networks, 1991, Vol.4, № 3. - pp.381-383.
P.S. About sufficiency of 3 layers - later.
The proof of sufficiency of 3 layers I saw in Gorban A.N.'s article "..." - I cannot find it.
The constancy of the fact of sufficiency is in the article attached below on page 39.