# Multivariate Gaussian Distributions in Clojure

February 18th 2016Tagged: clojure

Yesterday I described my experiences implementing multivariate Gaussian distributions in Julia. I've since repeated the exercise in Clojure, for any time you might need to do such a thing on the JVM. I'm using core.matrix for array operations.

μ, again is just `(mean x)`

.

To calculate the covariance matrix:

```
(defn covariance
"Calculate covariance matrix"
[x]
(let [mu (mean x)]
(div
(inner-product (sub x mu) (transpose (sub x mu)))
(row-count x))))
```

This is just Σ = (X - μ)'(X - μ) / n (where n is the number of examples).

And now that we have μ and Σ, we can use this function for probability:

```
(defn probability
"Calculate probability given mean, covariance matrix, and X"
[mu sigma x]
(let [x-minus-mu (sub x mu)
n (row-count mu)]
(* (exp (* -0.5 (esum
(emul (transpose x-minus-mu)
(inverse sigma)
x-minus-mu))))
(Math/pow (* 2 Math/PI) (* n -0.5))
(Math/pow (det sigma) -0.5))))
```

I've wrapped the code for this up in a library, available on Github.