Bayesian probability: I cannot understand why the correlation matrix is ​​not diagonal means that the samples taken from the class are correlated

When I am studying about things of the Bayes classifier I cannot see the following passage in the textbook.

When $ X $ It has an average value that depends on whether it belongs to $ C_1 $ Y $ C_2 $, but the covariance matrix of $ X $ It is the same for both classes. The covariance matrix $ X $ it is not diagonal, which means that samples taken from $ C_1 $ Y $ C_2 $ are correlated

Can anyone help why both classes are correlated when the covariance matrix is ​​not diagonal?

Distributed systems: what is the correlation between the actor model and reactive programming?

Could anyone explain the difference / correlation between the Actor model Y Reactive programming?

They seem to be located at different levels of abstraction: can the interaction between the components of any distributed system be designed using the Actor approach, would they send messages and, within the actors, write code in reactive style?

This question is related to How do Functional Reactive Programming and the actor model relate to each other?

However, the answers were not clear enough, and my question refers to reactive programming in general, not FRP in particular.

python 3.x: what does it mean when there is more precision and less correlation between the "predictor variables and the objective variable"?

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Macos: correlation between actions and records of the Mac OS X GUI

I am not sure if it is possible, but I was trying to discover / see / analyze if there is any correlation between the actions performed by a normal user on the GUI side with some records within the system (records, var or console).

I would like to know if I can see all the command lines that are executed when the user interacts with the graphical interface.

Let me give you an example.

On Mac OS X, if you want to add a new user to the system, use the System preferences > Users and groups > + add user > etc.

And more or less the same can be achieved with the use of a command line:

sudo dscl . -create /Users/username
sudo dscl . -create /Users/username UserShell /bin/bash
sudo dscl . -create /Users/username RealName "John Smith"
sudo dscl . -create /Users/username UniqueID 1001
etc. etc.

My question is, is there any way to find the previous code somewhere? Above is just an example.

Another example.

The user creates a new folder in his / her using the normal GUI. Right click on your desktop and create a new folder.

Can I see something in the system like:

mkdir /Users/username/Desktop/directory_name

I hope I was clear.

Thank you very much beforehand for your help.

st.statistics – How to use a scalar to measure the correlation of dimensions of multivariate variables?

I am trying to use the correlation of dimensions as a criterion to determine if a given batch of samples is sampled from the previous isotropic distribution of Gauss. Now I have m lots of data that are supposed to have independent dimensions, and other m lots of data that are supposed to have dependent dimensions. I want to use the correlation to distinguish these two sets of lots. A direct idea is to use a scalar to measure the correlation of dimensions. In this way, I can establish a scalar threshold t such that the second m batches of data can be distinguished from the first m batches.

I have tried the following two methods.

  1. Collect the non-diagonal elements of the correlation matrix (noted as set E) and calculate the variance of E (noted as sigma). Then sigma is used as the correlation metric.

  2. adjust a Gaussian distribution of the samples as N (E_1, Sigma_1) and calculate the total correlation = KL (N (E_1, Sigma_1) || N (0, I)). Then use the total correlation as the correlation metric.

In my problem, I find that the second method is much better than the first method, except that in a special case the second method fails completely. In such a special case, the first method works best when the lot size increases. But the second method is much worse.
Can somebody help me?

How do SEO platforms find the correlation between organic search terms and specific URLs?

I want to test and implement something similar to what other SEO platforms do. Products like SEMRush, SE Ranking, SERP Stat. They can display the organic keywords that were used to search for a particular web page.

Sample screenshot of the SE ranking
This is an example of what I am talking about. The service, SE Ranking, can display the organic keywords corresponding to the URLs. I was wondering how you can get this information. I want to see if I can create something similar, which can be done for almost any third-party URL.

The Graylog correlation governs the original messages

I am using Graylog V3.1.2 with a business plug-in.

I created a correlation rule that triggers the alert every time two events occur.

When I look at the sequence "All events" and find the correlation event in the origin_context property, I get only the last event that triggered this rule.

I have the same problem with the aggregation rules that I don't get the origin_context for them.

Is there any way to see all the original events that triggered the correlation rule or aggregation rules?

Thank you.

Probability or statistics: is there a problem with the correlation function?

I think you want the correlation between $ X $ Y $ sqrt {1-X ^ 2} $ where $ X sim Uniform (0.1) $.

μX = Mean(UniformDistribution())
(* 1/2 *)

varX = Variance(UniformDistribution())
(* 1/12 *)

distY = TransformedDistribution(Sqrt(1 - x^2), x (Distributed) UniformDistribution());
μY = Mean(distY)
(* π/4 *)

varY = Variance(distY)
(* 1/48 (32-3 π^2) *)

covXY = Integrate(x Sqrt(1 - x^2), {x, 0, 1}) - μX μY
(* 1/48 (32-3 π^2) *)

ρ = covXY/Sqrt(varX varY) // FullSimplify
(* (8-3 π)/Sqrt(32-3 π^2) *)
ρ // N

For verification, consider random samples of a uniform distribution:

SeedRandom(12345);
n = 100000;
z = RandomVariate(UniformDistribution(), n);
Correlation(z, Sqrt(1 - z^2))
(* -0.9214182413747128` *)

Trading – Binance and altcoin / bitcoin correlation

I am new to the cryptocurrency trade.

I'm getting confused in the PIVX / BTC trade. I bought PIVX on a support and currently up 2%. However, I lost 8% of my wallet (probably due to the fall of Bitcoin, although I don't have Bitcoin at the moment).

Binance always shows the value of my Bitcoin wallet, and that's why I'm losing money! It's as if I didn't have PIVX at all, just Bitcoin.

How can you trade if Bitcoin is down? It seems impossible to make a profit.

Thank you!

Matrices – Factoring Correlation Matrix

I have the following set of random variables:

$ X_i = Y * beta_i + Z_i * (1- beta_i) $ for $ i = 1, …, n $

$ Y, Z_i $ they are independent normal variables with distribution from $ Normal (0.1) $.

Now notice that:

$ E (X_i, X_j) = beta_i * beta_j $ for $ i neq j $

Y

$ E (X_i, X_j) = 1 $ for $ i = j $

My question has a correlation matrix $ M $ Is it possible to calculate the $ beta_i $& # 39; s. And if possible how to do it?

Even if the set of $ { beta_i } $ It is not unique, is it possible to find a solution $ { beta_i } $ that produces the correlation matrix $ M $.