Discussing the article: "Hilbert-Schmidt Independence Criterion (HSIC)" - page 4
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The computational complexity of HSIC is many orders of magnitude (with significance checks) higher than Pearson, so I expected a different result.
If the increments are independent, but their sums are suddenly "dependent", this is a strange result for such a resource-intensive criterion even in theory.
A series obtained as a sum of iid does not become dependent, it loses the property of stationarity and it does not allow using statistical criteria. That is, it is formally possible to calculate them for such series, but they will produce nonsense. Therefore, to get a meaningful result, it is necessary to observe the conditions imposed on such criteria. For example, for correlation, we need constant variance. In the case of a Gaussian SB series, the variance grows linearly with time, i.e. it is not a constant, hence the "dependence" of ACF = 0.99, hence the "dependence" of HSIC, etc.
There's a good old Spearman rank for non-linearity. Still, the article is more serious.
Spearman is weaker. It won't find many nonlinear relationships. Besides, it's only for comparing two scalar quantities.
I wanted to do a comparison with Pearson. There in the code Pearson counts on (X1, Y) and on (X2, Y) - independently.
And then, when calculating hsic_Gamma_test() X1 and X2 are shoved into one matrix.... and some 'mystical pairing' of matrix X (from two columns) with matrix Y from one column is performed
.
Can't hsic_Gamma_test() just be calculated like that - over two one-dimensional rows? Well, or
not hsic_Gamma_test(), but at least something that is the subject of this article.
Of course, I tried to make one column at X... something counted... some result
is there..... But what is it? If we knew what it is, and we don't know what it is.....
The correlation coefficient is counted independently for each quantity because it compares two scalar random variables, but HSIC works with pairs:
If you just calculated correlation, you would conclude that the data are independent, but HSIC was able to detect a non-linear relationship. Isn't that enough?
It's just that it's often claimed that there are non-linear relationships in stock data that are very difficult to detect. Well, HSIC is a tool to quantitatively detect these relationships.
The series obtained as the sum of iid does not become dependent, it loses the property of stationarity and it does not allow to use statistical criteria.
I doubt that this should be accepted with respect to computationally super-heavy criteria.
In the absence of information loss, transformations should not affect the result of the dependence estimation.
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Discussion of the article "Hilbert-Schmidt Independence Criterion (HSIC)"
fxsaber, 2025.05.13 05:46 pm.
Assertion.
If after transformation of series (without loss of information - we can return to the initial state) we get independence, then the initial series are independent.
I doubt this should be accepted with respect to computationally super-heavy criteria.
In the absence of information loss, transformations should not affect the result of the dependency evaluation.
Unfortunately, this is true for most statistical methods, both complex and simpler. What is to say, 95% of MO methods are based on iid assumptions (except ARIMA, dynamic neural networks, hidden Markov models, etc.). It is necessary to remember about it otherwise we will get nonsense.
95% of IO methods are built on iid assumptions
I guess there are attempts to create a dependency criterion via MO - same approach, but just the criterion itself in an ONNX file.
I guess there are attempts to create a dependency criterion via MO - same approach, but just the criterion itself in an ONNX file.
MO models learn to make a prediction and if this prediction is better than the "naive" one, then we conclude that there is a relationship in the data. That is, it is an indirect detection of a relationship, without significance testing. The independence criterion, in its turn, does not make any predictions, but gives statistical confirmation of the detected dependencies. It is a kind of two sides of the same coin. The R package has an implementation of the more general dHSIC criterion. It includes the implementation I gave for pairwise independence and further extends the test to joint independence.