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Questions tagged [distance-covariance]

A measure of dependence between two random variables (or two random vectors of any dimension). Also called Brownian covariance.

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Joint Distribution Formulation of a Spatial X, Spatial Y, and Spatial Error Model

Introductory Problem: I have $n$ points in 3-D space, where I know their X and Y coordinates (not Z), and therefore the distances between points in those 2 dimensions. Each of the three dimensions has ...
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Bridging the gap from theory to implementation in "Conditional Distance Correlation" by Wang et al. 2015?

In an attempt to implement a form of conditional distance correlation for random variables represented as vectors of observations, I came upon this paper that nicely extends the notion of distance ...
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Variance calculation in matrix notation for $var(z-Ax)$

I noted from a post here that $$var(z - \mathbf{A}x)=var(z)+var(\mathbf{A}x)-\mathbf{A}cov(z, -x)-cov(z,-x)\mathbf{A}^T (Eq. 1)$$ (I dropped the conditional part in the original formula from the post ...
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Probability for all points on a path in a gaussian random field

I have a gaussian random field $u(x)$, $x \in R^2$ , with a covariance function $C(d)$ and I need to calculate probability $P[ u(x) < u_0, \forall x \in S]$, where $S$ is a straight segment in $R^2$...
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1 vote
1 answer
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multivariate classification r

I am analyzing a dataset with 5 factors(Y1,Y2,Y3,Y4,Y5). ...
1 vote
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Does distance correlation work for count data?

I'm considering using partial distance correlation to test for conditional independence in multivariate count data. However, I haven't been able to find any good sources that discuss whether (partial) ...
3 votes
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84 views

Interpretable General Measure of Dependence

I am looking for an interpretable measure between two random variables $X$ and $Y$ which quantifies the dependence between the two but does not assume linearity. Essentially, I am looking for a ...
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6 votes
1 answer
2k views

Explaining the difference between Pearson correlation and distance correlation

This question and its answer might highlight my naivete regarding Brownian/distance correlation. I'm using the difference between a matrix of distance correlations, as calculated by ...
1 vote
1 answer
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Why is distance covariance defined squared, while covariance is not?

I am dealing in a data science project with correlation analyses using pearson and distance correlation. While trying to understand the differences between them, I learned about the differences by ...
2 votes
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55 views

Methods for determining temporal covariance among many time series?

We are trying to quantify synchrony in water chemistry variation among several thousand sites. For each site we have a time-series of concentration. We'd like to quantify the overall temporal ...
1 vote
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502 views

Different length of data in distance correlations

I would like to use a distance correlation/covariance analysis to detect (non-linear) dependencies in my data in R. However, my data has a lot of NAs so, after filter them (because dcor/dcov ...
1 vote
0 answers
325 views

Why is the precision matrix not positive definite? [duplicate]

I have a data matrix $X$ with shape $p\times n$. It might not matter but I interpret $X$ is $n$ vectors each containing $p$ features. Then I compute $Q = X X^{T} / n$. This implies that $Q$ is ...
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When is distance covariance less appropriate than linear covariance?

I've just been introduced (vaguely) to brownian/distance covariance/correlation. It seems particularly useful in many non-linear situations, when testing for dependence. But it doesn't seem to be used ...
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16 votes
1 answer
4k views

Distance correlation versus mutual information

I've worked with the mutual information for some time. But I found a very recent measure in the "correlation world" that can also be used to measure distribution independence, the so called "distance ...
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