Calculating Autocorrelation

Autocorrelation

Autocorrelation is a useful statistic for assessing mixing of a Markov chain. Keanu provides a method of calculating autocorrelation on samples.

Example

Java

With a network defined, we can get the autocorrelation vertex A. The result is a tensor containing the autocorrelation at varying lags.

NetworkSamples posteriorSamples = Keanu.Sampling.MetropolisHastings.withDefaultConfig().getPosteriorSamples(
    model,
    model.getLatentVariables(),
    100
);
DoubleTensor autocorrelation = posteriorSamples.getDoubleTensorSamples(A).getAutocorrelation();

When the samples are tensors, we need to specify the tensor index on which to calculate the autocorrelation. For example, if the sample shape is [1,5] we can evaluate the autocorrelation at index [0,1].

NetworkSamples posteriorSamples = Keanu.Sampling.MetropolisHastings.withDefaultConfig().getPosteriorSamples(
    model,
    model.getLatentVariables(),
    100
);
DoubleTensor autocorrelation = posteriorSamples.getDoubleTensorSamples(A).getAutocorrelation(0, 1);

Python

It’s also possible to calculate the autocorrelation of samples in Python.

algo = MetropolisHastingsSampler(proposal_distribution='prior', latents=bayes_net.iter_latent_vertices())
posterior_samples = sample(net=bayes_net, sample_from=bayes_net.iter_latent_vertices(),
                           sampling_algorithm=algo, draws=100)
vertex_samples = posterior_samples.get('a')
ac = stats.autocorrelation(vertex_samples)

When the samples are ndarrays the index on which to calculate the autocorrelation can be specified as a tuple.

algo = MetropolisHastingsSampler(proposal_distribution='prior', latents=bayes_net.iter_latent_vertices())
posterior_samples = sample(net=bayes_net, sample_from=bayes_net.iter_latent_vertices(),
                           sampling_algorithm=algo, draws=100)
vertex_samples = posterior_samples.get(('a', (0, 1)))
ac = stats.autocorrelation(vertex_samples)