Added changes to the MCMC sampling code. Added an MCMC example.

examples/mcmc/warmup_mcmc.py

@@ -0,0 +1,75 @@
+from manim import *
+
+import scipy.stats
+from manim_ml.diffusion.mcmc import MCMCAxes
+import matplotlib.pyplot as plt
+import numpy as np
+
+plt.style.use('dark_background')
+
+# Make the specific scene
+config.pixel_height = 720
+config.pixel_width = 720
+config.frame_height = 7.0
+config.frame_width = 7.0
+
+class MCMCWarmupScene(Scene):
+
+    def construct(self):
+        # Define the Gaussian Mixture likelihood
+        def gaussian_mm_logpdf(x):
+            """Gaussian Mixture Model Log PDF"""
+            # Choose two arbitrary Gaussians
+            # Big Gaussian
+            big_gaussian_pdf = scipy.stats.multivariate_normal(
+                mean=[-0.5, -0.5],
+                cov=[1.0, 1.0]
+            ).pdf(x)
+            # Little Gaussian
+            little_gaussian_pdf = scipy.stats.multivariate_normal(
+                mean=[2.3, 1.9],
+                cov=[0.3, 0.3]
+            ).pdf(x)
+            # Sum their likelihoods and take the log
+            logpdf = np.log(big_gaussian_pdf + little_gaussian_pdf)
+
+            return logpdf
+
+        # Generate a bunch of true samples
+        true_samples = []
+        # Generate samples for little gaussian
+        little_gaussian_samples = np.random.multivariate_normal(
+            mean=[2.3, 1.9],
+            cov=[[0.3, 0.0], [0.0, 0.3]],
+            size=(10000)
+        )
+        big_gaussian_samples = np.random.multivariate_normal(
+            mean=[-0.5, -0.5],
+            cov=[[1.0, 0.0], [0.0, 1.0]],
+            size=(10000)
+        )
+        true_samples = np.concatenate((little_gaussian_samples, big_gaussian_samples))
+        # Make the MCMC axes
+        axes = MCMCAxes(
+            x_range=[-5, 5],
+            y_range=[-5, 5],
+            x_length=7.0,
+            y_length=7.0
+        )
+        axes.move_to(ORIGIN)
+        self.play(
+            Create(axes)
+        )
+        # Make the chain sampling animation 
+        chain_sampling_animation = axes.visualize_metropolis_hastings_chain_sampling(
+            log_prob_fn=gaussian_mm_logpdf, 
+            true_samples=true_samples,
+            sampling_kwargs={
+                "iterations": 2000,
+                "warm_up": 50,
+                "initial_location": np.array([-3.5, 3.5]),
+                "sampling_seed": 4
+            },
+        )
+        self.play(chain_sampling_animation)
+        self.wait(3)

manim_ml/diffusion/mcmc.py

@@ -2,16 +2,20 @@
     Tool for animating Markov Chain Monte Carlo simulations in 2D. 
 """
 from manim import *
+import matplotlib
+import matplotlib.pyplot as plt
+from manim_ml.utils.mobjects.plotting import convert_matplotlib_figure_to_image_mobject
 import numpy as np
 import scipy
 import scipy.stats
 from tqdm import tqdm
+import seaborn as sns
 
 from manim_ml.utils.mobjects.probability import GaussianDistribution
 
 ######################## MCMC Algorithms #########################
 
-def gaussian_proposal(x, sigma=1.0):
+def gaussian_proposal(x, sigma=0.3):
     """
     Gaussian proposal distribution.
 
@@ -94,6 +98,7 @@ def metropolis_hastings_sampler(
     iterations=25,
     warm_up=0,
     ndim=2,
+    sampling_seed=1
 ):
     """Samples using a Metropolis-Hastings sampler.
 
@@ -119,7 +124,7 @@ def metropolis_hastings_sampler(
     candidate_samples: np.ndarray
         numpy array of the candidate samples for each time step
     """
-    assert warm_up == 0, "Warmup not implemented yet"
+    np.random.seed(sampling_seed)
     # initialize chain, acceptance rate and lnprob
     chain = np.zeros((iterations, ndim))
     proposals = np.zeros((iterations, ndim))
@@ -156,6 +161,43 @@ def metropolis_hastings_sampler(
 
 #################### MCMC Visualization Tools ######################
 
+def make_dist_image_mobject_from_samples(samples, ylim, xlim):
+    # Make the plot
+    matplotlib.use('Agg')
+    plt.figure(figsize=(10,10), dpi=100)
+    print(np.shape(samples[:, 0]))
+    displot = sns.displot(
+        x=samples[:, 0], 
+        y=samples[:, 1], 
+        cmap="Reds", 
+        kind="kde",
+        norm=matplotlib.colors.LogNorm()
+    )
+    plt.ylim(ylim[0], ylim[1])
+    plt.xlim(xlim[0], xlim[1])
+    plt.axis('off')
+    fig = displot.fig
+    image_mobject = convert_matplotlib_figure_to_image_mobject(fig)
+
+    return image_mobject
+
+class Uncreate(Create):
+    def __init__(
+        self,
+        mobject,
+        reverse_rate_function: bool = True,
+        introducer: bool = True,
+        remover: bool = True,
+        **kwargs,
+    ) -> None:
+        super().__init__(
+            mobject,
+            reverse_rate_function=reverse_rate_function,
+            introducer=introducer,
+            remover=remover,
+            **kwargs,
+        )
+
 class MCMCAxes(Group):
     """Container object for visualizing MCMC on a 2D axis"""
 
@@ -166,7 +208,7 @@ class MCMCAxes(Group):
         accept_line_color=GREEN,
         reject_line_color=RED,
         line_color=BLUE,
-        line_stroke_width=3,
+        line_stroke_width=2,
         x_range=[-3, 3],
         y_range=[-3, 3],
         x_length=5,
@@ -180,6 +222,10 @@ class MCMCAxes(Group):
         self.line_color = line_color
         self.line_stroke_width = line_stroke_width
         # Make the axes
+        self.x_length = x_length
+        self.y_length = y_length
+        self.x_range = x_range
+        self.y_range = y_range
         self.axes = Axes(
             x_range=x_range,
             y_range=y_range,
@@ -290,6 +336,7 @@ class MCMCAxes(Group):
         log_prob_fn=MultidimensionalGaussianPosterior(),
         prop_fn=gaussian_proposal,
         show_dots=False,
+        true_samples=None,
         sampling_kwargs={},
     ):
         """
@@ -318,12 +365,14 @@ class MCMCAxes(Group):
         """
         # Compute the chain samples using a Metropolis Hastings Sampler
         mcmc_samples, warm_up_samples, candidate_samples = metropolis_hastings_sampler(
-            log_prob_fn=log_prob_fn, prop_fn=prop_fn, **sampling_kwargs
+            log_prob_fn=log_prob_fn, 
+            prop_fn=prop_fn,
+            **sampling_kwargs
         )
         # print(f"MCMC samples: {mcmc_samples}")
         # print(f"Candidate samples: {candidate_samples}")
         # Make the animation for visualizing the chain
-        animations = []
+        transition_animations = []
         # Place the initial point
         current_point = mcmc_samples[0]
         current_point = Dot(
@@ -332,10 +381,11 @@ class MCMCAxes(Group):
             radius=self.dot_radius,
         )
         create_initial_point = Create(current_point)
-        animations.append(create_initial_point)
+        transition_animations.append(create_initial_point)
         # Show the initial point's proposal distribution
         # NOTE: visualize the warm up and the iterations
         lines = []
+        warmup_points = [] 
         num_iterations = len(mcmc_samples) + len(warm_up_samples)
         for iteration in tqdm(range(1, num_iterations)):
             next_sample = mcmc_samples[iteration]
@@ -362,14 +412,50 @@ class MCMCAxes(Group):
             transition_animation, line = self.make_transition_animation(
                 current_point, next_point, candidate_point
             )
+            # Save assets
             lines.append(line)
-            animations.append(transition_animation)
+            if iteration < len(warm_up_samples):
+                warmup_points.append(candidate_point)
+
+            # Add the transition animation
+            transition_animations.append(transition_animation)
             # Setup for next iteration
             current_point = next_point
-        # Make the final animation group
-        animation_group = AnimationGroup(
-            *animations, 
+        # Overall MCMC animation
+        # 1. Fade in the distribution
+        image_mobject = make_dist_image_mobject_from_samples(
+            true_samples,
+            xlim=(self.x_range[0], self.x_range[1]),
+            ylim=(self.y_range[0], self.y_range[1])
+        )
+        image_mobject.scale_to_fit_height(
+            self.y_length     
+        )
+        image_mobject.move_to(self.axes)
+        fade_in_distribution = FadeIn(
+            image_mobject,
+            run_time=0.5
+        )
+        # 2. Start sampling the chain
+        chain_sampling_animation = AnimationGroup(
+            *transition_animations, 
+            lag_ratio=1.0,
+            run_time=5.0
+        )
+        # 3. Convert the chain to points, excluding the warmup
+        lines = VGroup(*lines)
+        warm_up_points = VGroup(*warmup_points)
+        fade_out_lines_and_warmup = AnimationGroup(
+            Uncreate(lines), 
+            Uncreate(warm_up_points),
+            lag_ratio=0.0
+        )
+        # Make the final animation
+        animation_group = Succession(
+            fade_in_distribution,
+            chain_sampling_animation,
+            fade_out_lines_and_warmup,
             lag_ratio=1.0
         )
 
-        return animation_group, VGroup(*lines)
+        return animation_group

manim_ml/utils/mobjects/plotting.py

@@ -14,7 +14,7 @@ def convert_matplotlib_figure_to_image_mobject(fig, dpi=200):
         matplotlib figure
     """
     fig.tight_layout(pad=0)
-    plt.axis('off')
+    # plt.axis('off')
     fig.canvas.draw()
     # Save data into a buffer
     image_buffer = io.BytesIO()

tests/test_mcmc.py

@@ -15,8 +15,8 @@ plt.style.use('dark_background')
 # Make the specific scene
 config.pixel_height = 1200
 config.pixel_width = 1200
-config.frame_height = 10.0
-config.frame_width = 10.0
+config.frame_height = 7.0
+config.frame_width = 7.0
 
 def test_metropolis_hastings_sampler(iterations=100):
     samples, _, candidates = metropolis_hastings_sampler(iterations=iterations)