Using Neural Networks in Trading. - page 6

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Mathemat писал(а) >>

OK, Sergei, let's take it slowly and sadly. First let's deal with the general theorems. Here's the link. See theorems 24, 25, 26.

Note: Th 24 deals with the density function of the distribution.

But Th 25 does exactly what you need, and it is about the distribution function.

Look also, for fun, at consequence 8 of Th 26. The third formula of the consequence is exactly what I was talking about when I wanted to get a Gaussian from a uniform one.

And for your exponentially distributed one just needs to neatly get its distribution function (integral) and apply Th 25.

Thanks. I'll have a look.

I looked it up - just what I need! I will study it.

FION wrote >>

What do you mean by "architecture scaled arbitrarily". As far as I understand, architecture is the structure of the network. And scaling is the use of some data rationing function. 100 inputs is a bit much. Or is your 100 something else?

I meant what I deduced as TC input parameters - number of inputs (using 100 now), can be changed from 1 to 200. Number of layers (from 1 to 3). Number of neurons in each layer (from 1 to 1024). The output layer always contains one neuron.
 
sol >> :

My network simply retrains every 24 hours. I don't know if that's a plus or a minus. But, so far, it's funky.

>> great.)

 

Machine Learning Repository
Here is a link to standard tasks. They are usually used to test different algorithms, preprocessing methods, etc.
You can also train on them, learn how to use networks, see with your own eyes "What is prognosis or classification by means of NS", or rather what kind of errors can be expected from neural networks, etc.
The description of the tasks is in the same place, above...
Here is a small example from a sample of one task(OptDigits):
Input values:
000000000101100111111111111110000000
00000000011111111111111111110000
00000000011111111111111111110000

00000000011111111111111111111111111111110000
00000000011111111111111100000000
00000000011111111111110000000000000000


0000000111111111111110000000000
000000011111111111111000000
000000011111111111111000000
00000001111111111111111000000
0000000111111111111111110000
0000000111111111111111110000
00000001111111111111110000
0000000111111111111110000
000000011111111100
0000000000000000000011111111110000
0000000000000000000000000111111111110000
0000000000000000000000000001111111100000
0000000000000000000001111111100000
00000000000000000111111111100000
000000000000000000000111111111110000

00000000001111111111111000000
0000000000111111111000000
000000000011111111111000000
000000000001111111111110000000000
0000000000011111111110000000000
0000000000111111100000000000000
000000001111100000000000000

Output: 5

 
Mathemat писал(а) >>

Here's the link. See theorems 24, 25, 26.

I didn't get it.

Let's see. On the left is the probability density for EURUSD minute bar open prices, on the right is the distribution function:

Now for the link:

Suppose I want to obtain a constant of 1 from the distribution shown in the first fig. Then it is not difficult to obtain the following identity:

where f(x) is the probability density from which I want to go to equal, and g(x) is some function by which I need to multiply the input data to get a "shelf". So, what next? Solve this differential equation... I don't know how.

Let's keep looking.

We won't say anything about the segment, it's not important. What does it say? Literally, that if I have a distribution function F(x) (fig. right), then it does not cost anything to get the desired "shelf" - for this is enough to influence the input data by this opener... But this is nonsense! In my opinion, you can't get such a uniform distribution from the initial one. Anyway, who's good at real maths here. >> Ow!

 
Neutron писал(а) >>

We won't say anything about the section for now - it's not the point. What is being argued here? Literally, that if I have a distribution function F(x) (fig. right), then it does not cost anything to get the desired "shelf" - for this is enough to influence the input data by this opener... But this is nonsense! In my opinion, you can't get such a uniform distribution from the initial one. Anyway, who's good at real maths. Ow!

That's right, Sergei, that's right. Take this nonsense and check it (or better yet, try to understand why it is exactly so). Generate a normally distributed quantity and influence it with a Gaussian function (integral). Just remember to make sure that the two functions (the integral distribution law and the second function) are absolutely identical.

P.S. Don't bother with distribution densities and derivatives. What do you need them for? That would be the same thing, only from the side.

P.P.S. Sergei, well, I myself have obtained a normally distributed value from a uniform value, by acting on the first one with the inverse of the integral Gaussian function. And now let's take and invert the calculations...

 

What the hell are you guys doing here... my poor brain...

SZS: by the way, I've long wanted to ask - why should we consider the price function to be continuous? what if it's discrete?

 

Well, Sergei, Mathemat is now saying what I wrote to you. Let's see for ourselves.

Here is the distribution function (empirically)

Then let's build a theoretical one (I don't remember, is it called correctly?) using formula (1/OREN(6,2828))*EXP(-ABS(DIVISION(A1;2)/2))

The light green just needs to approximate the blue perfectly. Then you can get a perfect "shelf" with the integral...

Here's a view of the integral (sigmoid!!!)

The way I see it, you should approximate the empirical distribution function by coefficients (I don't know what kind) with the theoretical one. Then these coefficients should be substituted into sigmoid and the distribution will be equal after passing the data through the sigmoid.

Alexey, am I thinking correctly at all? Maybe you can suggest something on this subject?

 
Okay, I missed that thread. Now I'll look around and see if it's still there. I have downloaded Tikhonov's maths, he has how to get the required PD of a given value (with examples), but it does not seem to be for all. Must be calculated inverse function ... I do not remember to what only
 
StatBars писал(а) >>

Well, Sergei, Mathemat is now saying what I wrote to you. Now let's try to make sure of it.

Let's make sure.

Here is the distribution function (empirically)

No, it's not a distribution function, it's a probability density function (see Alexei's link).

The light green one should approximate the blue one perfectly. Then you can get an ideal "shelf" with an integral...

Here's a view of the integral (sigmoid!!!)

It's not a sigmoid, to be precise - it's an integral of a Gaussian with a variable upper limit - erf(x) is a tabulated function.

I see the problem as follows: I should approximate an empirical distribution function by coefficients (I don't know) with a theoretical one. Then these coefficients should be substituted into sigmoid, and after the data are passed through sigmoid, it will be a uniform distribution.

There are no problems with approximation; they begin when it is not clear what to do with the obtained distribution function erf(x). This is what I was talking about above.

 

Yes, indeed, I was wrong with the definitions(distribution/density of distribution)...

What to do with erf() - I don't know.

Here's a regular sigmoid and its derivative. Why sigmoid? - Simply because sigmoid is not erf(x). :)

Now take data, build empirical, select coefficients A and B, so that densities would coincide. The graph is also the integral.

Now, we substitute the found coefficients into the integral and calculate.

That is what we get:

Now we need to "fit" everything theoretically, because I did it more by intuition than by theoretical knowledge.

Question for all the experts - How do I find coefficients A and B? Maybe A and B are not necessary, there are some other forms of recording distribution laws, etc.?

Or maybe it's all bullshit and can't be done that way?

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