Machine learning in trading: theory, models, practice and algo-trading - page 205
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You will probably be offered to use these functions yourself if necessary https://www.mql5.com/ru/docs/opencl.
I have an old video card, OpenCL doesn't seem to support it. If they shove support right into the library, what will happen?
So I was talking about what would be the ability to choose to support both the vision, as well as other cores of the processor, or not to use OpenCL at all. It's just a real opportunity to see how to use OpenCL effectively.
When we get to heavy calculations, maybe we will use OpenCL. But something tells me that using multicore CPU will give acceptable results and more guaranteed.
For now there is no question about acceleration. We are working on the basic functionality of the libraries.
According to the formula in the R help file, this is calculated using the formula
The problem is that in this case x^(a-1) = 0^(1-1) = 0^0 that is undefined, i.e. there is no point in calling a function with such a parameter and there is no point in comparing results with other software. For 0^0 in different software can be different, depending on the religion of the developers.f(x)= 1/(s^a Gamma(a)) x^(a-1) e^-(x/s)
(shape= a and scale= s,forx ≥ 0,a > 0 ands > 0)
scale is 1/rate by default
Dr.Trader:
The supposed error is that
dgamma(x=0, shape=1, rate=1,log=FALSE)== 1
According to the formula in the R help file, this is calculated using the formula
The problem is that in this case x^(a-1) = 0^(1-1) = 0^0, which is undefined, i.e. there is no point in calling a function with this parameter and there is no point in comparing results with other software. For 0^0 in different software can be different, depending on the religion of the developers.f(x)= 1/(s^a Gamma(a)) x^(a-1) e^-(x/s)
(shape= a and scale= s,forx ≥ 0,a > 0 ands > 0)
scale is 1/rate by default
Great. It turns out that we can't call it a definition, since there are uncertainties.
You can build a graph and make sure that at the point x=0 the expression at these parameters tends to 1. This is a normal number, there is no divergence at other points.
We can sum the whole density, the result is some number (the normalization factor), by which we divide and get the unit probability, which is smeared out over the area of definition. The curve is normalized, the area under the curve = 1. In this case we can talk about probability density.
However, with parameters 0.5 and 1 at the point x=0 the situation is different. The limit value at this point is equal to infinity. When approaching 0 it tends to infinity. It is possible not to integrate after this point, the result will not change. How to normalize to infinity? With this normalization, any curve becomes a line.
But if we consider the expression to work only when x>0, then the expression can be viewed as the definition of the function, since there are no uncertainties at x=0. All values are finite and nothing breaks.
This hypothesis explains the results that Mathematica and Matlab produce: at point x=0, density=0.
This was the question.
When we get to heavy calculations, maybe we will use OpenCL. But something tells me that using multicore CPU will give acceptable results and more guaranteed.
For now there is no question about acceleration. We are busy tweaking the basic functionality of the libraries.
Got it. I will wait for developments.
Great. It turns out that we can't call it a definition, since there are uncertainties.
You can plot the graph and make sure that at the point x=0 the expression tends to 1 with these parameters. This is a normal number, there is no divergence at other points.
We can sum all the densities, resulting in some number (the normalization factor), by which we divide and get the unit probability, which is smeared over the area of the definition. The curve is normalized, the area under the curve = 1. In this case we can talk about probability density.
However, the situation with parameters 0.5 and 1 at x=0 is different. The limit value at this point is equal to infinity. When approaching 0 it tends to infinity. It is possible not to integrate after this point, the result will not change. How to normalize to infinity? With this normalization, any curve becomes a line.
But if we consider the expression to work only when x>0, then the expression can be viewed as the definition of the function, since there are no uncertainties at x=0. All values are finite and nothing breaks down.
This hypothesis explains the results that Mathematica and Matlab produce: at point x=0, density=0.
That was the question.
Are you saying that this kind of transformation to the Dirac delta function is OK? What is the point of everything else?
Tell me what happens to infinity in the pgamma process at point x=0, when the "correct" (as you say) answer in dgamma(0,0.5,1)=+inf has been given.
Show graphically the function and integration ranges when calculating pgamma.
Interesting fact.
The definitions of gamma distribution density values in the Russian translation of
Johnson N.L., Kotz S., Balakrishnan N. Univariate Continuous Distributions. part 1 and the earlier English version are different:
but the English version has a suspected typo due to different signs.
Are you saying that this kind of transformation into a Dirac delta function is OK? What's the point of everything else then?
Tell me what happens to infinity in the pgamma process at x=0 when the "correct" as you say answer in dgamma(0,0.5,1)=+inf was given.