tensorflow_probability 分布应该如何用于多维空间？

Question

I would like to create a multi-dimensional gaussian probability density function (let's say a 2D gaussian like in the figure below) with tensorflow.

For 1D, it works like a charm:

d = tfp.distributions.Normal(loc=5.0, scale=3.0)
x = d.prob(tf.range(0,10, dtype=tf.float32))

But for higher dimension, I get InvalidArgumentError: Incompatible shapes error using Normal or MultivariateNormalDiag distributions... What do I miss? How should the prob method be used to output the probability density function on a multi dimensional tensor?

Answer 1

If I understood correctly, you can do something like:

mu = [0,0]
cov = [[1,0],
       [0,1]]
mv_normal = np.random.multivariate_normal(mu, cov, size=1000)
mv_normal_mean = np.mean(mv_normal , axis=0)
mv_normal_cov = np.cov(mv_normal , rowvar=0)
mv_normal_diag = np.diag(mv_normal_cov)
mv_normal_stddev = np.sqrt(mv_normal_diag)

mv_normal is just like:

mv_normal
array([[-1.73476374,  0.17578855],
       [ 0.11866498, -0.66417069],
       [ 1.52000069, -1.3004096 ],
       ...,
       [-1.37625595, -0.46864374],
       [ 0.81659449,  0.70524036],
       [ 1.12183633,  0.14196896]])

mv_normal_mean and mv_normal_cov etc are just arrays here. They will be used to create:

 mvn = tfd.MultivariateNormalDiag(
 loc=mv_normal_mean,
 scale_diag=mv_normal_stddev)

Values can be seen as:

mvn_mean
array([-0.03976356,  0.07387231])

mv_normal_cov
array([[ 1.04138867, -0.00877481],
       [-0.00877481,  0.97736496]])

And you can use contour plot for plotting.

x1, x2 = np.meshgrid(mv_normal[:,0], mv_normal[:,1])
data = np.stack((x1.flatten(), x2.flatten()), axis=1)
prob = mvn.prob(data).numpy()
plt.figure(figsize = (12,9))
ax = plt.axes(projection='3d')
ax.plot_surface(x1, x2, prob.reshape(x1.shape), cmap = 'Blues')
plt.show()

That will produce as follows: