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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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multivariate classification r

I am analyzing a dataset with 5 factors(Y1,Y2,Y3,Y4,Y5). ...
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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) ...
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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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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 ...
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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 ...
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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 ...
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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 ...
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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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What conditions are needed for a differentiable random field?

I've been playing around with some random field models and noticed that the apparent differentiability seems to be related to the covariance function's behavior at 0. My initial guess was that if $\...
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What does fractional value represent for distance correlation?

I understand that if distance correlation is 1, then it's statistically dependent but independent if 0. But if distance correlation turns out to be about, say, 0.65 or 0.5 what does that mean in ...
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Can I use distance covariance for similarity measure in manifold learning?

In manifold learning such as Laplacian Eigenmap, a common method of obtaining the similarity matrix (that measures "affinity" or "connectivity") is to use Gaussian kernel in terms of the data points' ...
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What is the distance correlation for Anscombe’s quartet?

Is the newer descriptive statistic (distance correlation) able to resolve these troubling four datasets (Anscombe’s quartet)?
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Explanation and proof of distance and correlation expression found in ebook

I am reading 'Data Analysis for the Life Sciences' and came across a small section touching upon what I believe relates to distance correlation. I am new to this concept and would like some help ...
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Energy Distance and $L^2$ Convergence

$\newcommand{\E}{\mathbb{E}}$ Question: If we have a sequence of $\mathbb{R}$-valued random variables $X_n$ which converge in the metric space of random variables defined by the energy distance to ...
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Finding discrepancies in distances between random variable samples

There are $N$ independent and unknown points $p_i$, $q_i \in \mathbb{R}^3$, $i \in [1, N]$. I want to find if the pairwise squared Euclidean distance of each $i$ pair is the same for all of them, or ...
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If distance correlation $DCOR(X,Y) = 0.5$ then are X and Y dependent or independent?

If distance correlation $DCOR(X,Y) = 0.5$ then are $X$ and $Y$ statistically dependent or independent? What about when $DCOR(X,Y) > 0$, are they statistically dependent for sure even when it's less ...
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Real data example of Mahalanobis distance - proper data values given

Here is my real data example (these are real data check below pictures to see. I am comparing real documents (words represented as TF-IDF values). I equalize list sizes with missing words added as 0 ...
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Understanding distance correlation computations

As far as I understood, distance correlation is a robust and universal way to check if there is a relation between two numeric variables. For example, if we have a set of pairs of numbers: ...
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Distance between independent observations of a categorical variable

I have a random variable $T$ that takes values in $\{ \text{blue}, \text{green}, \text{red} \}$, and a number of observations of $T$: ...
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Is there an intuitive characterization of distance correlation?

I've been staring at the wikipedia page for distance correlation where it seems to be characterized by how it can be calculated. While I could do the calculations I struggle to get what distance ...
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What precisely is the interpretation of distance correlation?

The key feature of distance correlation is that if it is $0$ then two variables are independent. If the pearson correlation is zero, however, this does not imply independence. How would one interpret ...
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Is the absolute value of distance covariance a metric?

I'm reasonably certain the absolute value of the distance covariance satisfies $d(x, y) \ge 0$ (non-negativity, or separation axiom) $d(x, y) = 0$ if and only if $x = y$ (identity of ...
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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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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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