17 plotting functionality

Plotting functionality

Here we will have a look at the different options for finetuning pairplots and marginal_plots.

Lets first draw some samples from the posterior used in a previous tutorial.

import torch 
from sbi.analysis import pairplot
from toy_posterior_for_07_cc import ExamplePosterior

posterior = ExamplePosterior()
posterior_samples = posterior.sample((100,))

WARNING (pytensor.tensor.blas): Using NumPy C-API based implementation for BLAS functions.

We will start with the default plot and gradually make it prettier

_ = pairplot(
    posterior_samples,
)

Customisation

The pairplots are split into three regions, the diagonal (diag) and the upper and lower off-diagonal regions(upper and lower). We can pass separate arguments (e.g. hist, kde, scatter) for each region, as well as corresponding style keywords in a dictionary (by using e.g. upper_kwargs). For overall figure stylisation one can use fig_kwargs.

To get a closer look at the potential options, have a look at the _get_default_fig_kwargs, _get_default_diag_kwargs and _get_default_offdiag_kwargs functions in analysis/plot.py.

As illustrated below, we can directly use any matplotlib keywords (such as cmap for images) by passing them in the mpl_kwargs entry of upper_kwargs or diag_kwargs.

Let’s now make a scatter plot for the upper diagonal, a histogram for the diagonal, and pass keyword dictionaries for both.

_ = pairplot(
    posterior_samples,
    limits=[[-3, 3] * 3],
    figsize=(5, 5),
    diag="hist",
    upper="scatter",
    diag_kwargs={
        "mpl_kwargs": {
            "bins": 10,
            "color": 'tab:blue',
            "edgecolor": 'white',
            "linewidth": 1,
            "alpha": 0.6,
            "histtype": "bar",
            "fill": True,
        }
    },
    upper_kwargs={"mpl_kwargs": {"color": 'tab:blue', "s": 20, "alpha": 0.8}},
    labels=[r"$\theta_1$", r"$\theta_2$", r"$\theta_3$"],
)

Compare two sets of samples

By passing a list of samples, we can plot two sets of samples on top of each other.

# draw two different subsets of samples to plot
posterior_samples1 = posterior.sample((20,))
posterior_samples2 = posterior.sample((20,))

_ = pairplot(
    [posterior_samples1, posterior_samples2],
    limits=[[-3, 3] * 3],
    figsize=(5, 5),
    diag=["hist", "hist"],
    upper=["scatter", "scatter"],
    diag_kwargs={
        "mpl_kwargs": {
            "bins": 10,
            "edgecolor": 'white',
            "linewidth": 1,
            "alpha": 0.6,
            "histtype": "bar",
            "fill": True,
        }
    },
    upper_kwargs={"mpl_kwargs": {"s": 50, "alpha": 0.8}},
    labels=[r"$\theta_1$", r"$\theta_2$", r"$\theta_3$"],
)

Multi-layered plots

We can use the same functionality to make a multi-layered plot using the same set of samples, e.g. a kernel-density estimate on top of a scatter plot.

_ = pairplot(
    [posterior_samples, posterior_samples],
    limits=[[-3, 3] * 3],
    figsize=(5, 5),
    diag=["hist", None],
    upper=["scatter", "contour"],
    diag_kwargs={
        "mpl_kwargs": {
            "bins": 10,
            "color": 'tab:blue',
            "edgecolor": 'white',
            "linewidth": 1,
            "alpha": 0.6,
            "histtype": "bar",
            "fill": True,
        },
    },
    upper_kwargs=[
        {
            "mpl_kwargs": {"color": 'tab:blue', "s": 20, "alpha": 0.8},
        },
        {"mpl_kwargs": {"cmap": 'Blues_r', "alpha": 0.8, "colors": None}},
    ],
    labels=[r"$\theta_1$", r"$\theta_2$", r"$\theta_3$"],
    fig_kwargs={"despine": {"offset": 0}},
)

Lower diagonal

We can add something in the lower off-diagonal as well.

_ = pairplot(
    [posterior_samples, posterior_samples],
    limits=[[-3, 3] * 3],
    figsize=(5, 5),
    diag=["hist", None],
    upper=["scatter", "contour"],
    lower=["kde", None],
    diag_kwargs={
        "mpl_kwargs": {
            "bins": 10,
            "color": 'tab:blue',
            "edgecolor": 'white',
            "linewidth": 1,
            "alpha": 0.6,
            "histtype": "bar",
            "fill": True,
        }
    },
    upper_kwargs=[
        {"mpl_kwargs": {"color": 'tab:blue', "s": 20, "alpha": 0.8}},
        {"mpl_kwargs": {"cmap": 'Blues_r', "alpha": 0.8, "colors": None}},
    ],
    lower_kwargs={"mpl_kwargs": {"cmap": "Blues_r"}},
    labels=[r"$\theta_1$", r"$\theta_2$", r"$\theta_3$"],
)

Adding observed data

We can also add points, e.g., our observed data \(\theta_o\) to the plot.

# fake observed data:
theta_o = torch.ones(1, 3)

_ = pairplot(
    [posterior_samples, posterior_samples],
    limits=[[-3, 3] * 3],
    figsize=(5, 5),
    diag=["hist", None],
    upper=["scatter", "contour"],
    diag_kwargs={
        "mpl_kwargs": {
            "bins": 10,
            "color": 'tab:blue',
            "edgecolor": 'white',
            "linewidth": 1,
            "alpha": 0.6,
            "histtype": "bar",
            "fill": True,
        }
    },
    upper_kwargs=[
        {"mpl_kwargs": {"color": 'tab:blue', "s": 20, "alpha": 0.8}},
        {"mpl_kwargs": {"cmap": 'Blues_r', "alpha": 0.8, "colors": None}},
    ],
    labels=[r"$\theta_1$", r"$\theta_2$", r"$\theta_3$"],
    points=theta_o,
    fig_kwargs={
        "points_labels": [r"$\theta_o$"],
        "legend": True,
        "points_colors": ["purple"],
        "points_offdiag": {"marker": "+", "markersize": 20},
        "despine": {"offset": 0},
    },
)

Subsetting the plot

For high-dimensional posteriors, we might only want to visualise a subset of the marginals. This can be done by passing a list of entries to plot to the subset argument of the pairplot function.

_ = pairplot(
    [posterior_samples, posterior_samples],
    limits=[[-3, 3] * 3],
    figsize=(5, 5),
    subset=[0, 2],
    diag=["hist", None],
    upper=["scatter", "contour"],
    diag_kwargs={
        "mpl_kwargs": {
            "bins": 10,
            "color": 'tab:blue',
            "edgecolor": 'white',
            "linewidth": 1,
            "alpha": 0.6,
            "histtype": "bar",
            "fill": True,
        }
    },
    upper_kwargs=[
        {"mpl_kwargs": {"color": 'tab:blue', "s": 20, "alpha": 0.8}},
        {"mpl_kwargs": {"cmap": 'Blues_r', "alpha": 0.8, "colors": None}},
    ],
    labels=[r"$\theta_1$", r"$\theta_2$", r"$\theta_3$"],
    points=theta_o,
    fig_kwargs={
        "points_labels": [r"$\theta_o$"],
        "legend": True,
        "points_colors": ["purple"],
        "points_offdiag": {"marker": "+", "markersize": 20},
        "despine": {"offset": 0},
    },
)

Plot just the marginals

1D Marginals can also be visualised using the marginal_plot function

from sbi.analysis import marginal_plot

# plot posterior samples
_ = marginal_plot(
    [posterior_samples, posterior_samples],
    limits=[[-3, 3] * 3],
    subset=[0, 1],
    diag=["hist", None],
    diag_kwargs={
        "mpl_kwargs": {
            "bins": 10,
            "color": 'tab:blue',
            "edgecolor": 'white',
            "linewidth": 1,
            "alpha": 0.6,
            "histtype": "bar",
            "fill": True,
        },
    },
    labels=[r"$\theta_1$", r"$\theta_2$", r"$\theta_3$"],
    points=[torch.ones(1, 3)],
    figsize=(4, 2),
    fig_kwargs={
        "points_labels": [r"$\theta_o$"],
        "legend": True,
        "points_colors": ["purple"],
        "points_offdiag": {"marker": "+", "markersize": 20},
        "despine": {"offset": 0},
    },
)