Solved – a probability heat map

data visualizationheatmap

What is a probability heat map? In general, what is a heat map? Many papers on neural networks use probability heat maps for visualisation. My understanding is that heat maps are plots of (typically continuous) values where there is a one-one correspondence between the range of values displayed and a spectrum of colours. Probability heat map is similar with different colours indicating regions of different probability. Is this intuition correct?

For example, see the paper Stacked Hourglass Networks for Human Pose Estimation which uses probability heatmaps for different human keypoints (although it doesn't explicitly use the term probability heatmap).

Best Answer

From wikipedia (https://en.wikipedia.org/wiki/Heat_map), you get that

"A heat map (or heatmap) is a graphical representation of data where the individual values contained in a matrix are represented as colors."

There is nothing more really... As an example, consider the following multivariate normal data.

library(mvtnorm)

Sigma <- matrix(0, nrow = 8, ncol = 8)
Sigma[1:3,4:5] <- .25
Sigma[1:3,6:8] <- .1
Sigma[4:5,6:8] <- .2

Sigma <- Sigma + t(Sigma)

Sigma[1:3,1:3] <- .5
Sigma[4:5,4:5] <- .75
Sigma[6:8,6:8] <- .35

diag(Sigma) <- 1

X <- rmvnorm(30, rep(0,8), Sigma)

par(mar = c(0,0,0,0))
image(t(cor(X)[8:1,]))

enter image description here

The image produced actually uses R's color palette known as heat.colors by default. The "heat" term comes from the colors used I guess.

A probability heat map (seems to be, from this question for example: https://stackoverflow.com/questions/14363252/probabilty-heatmap-in-ggplot?noredirect=1&lq=1) is the same kind of technique applied to probability distributions instead of correlation matrices.

In particular, if you have $(X_1,X_2)$ and want to predict $Y \in \{0,1\}$, then you could color your 2D space (at point (x_1,x_2)) using $P(Y = 1 | X_1 = x_1, X_2 = x_2)$, with the color range $[0,1]$.

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