From 74bc35d0b5d5fc3da1d47e5cbda69069dd7e36d2 Mon Sep 17 00:00:00 2001
From: junpenglao <junpenglao@gmail.com>
Date: Fri, 3 Jan 2025 04:56:16 +0000
Subject: [PATCH] =?UTF-8?q?Deploying=20to=20gh-pages=20from=20@=20blackjax?=
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 _sources/algorithms/mclmc.md                  | 151 ++++++++++++++--
 algorithms/mclmc.html                         | 169 ++++++++++++++++--
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diff --git a/_sources/algorithms/mclmc.md b/_sources/algorithms/mclmc.md
index 09d7e9b..77889ea 100644
--- a/_sources/algorithms/mclmc.md
+++ b/_sources/algorithms/mclmc.md
@@ -44,7 +44,7 @@ MCLMC in Blackjax comes with a tuning algorithm which attempts to find optimal v
 
 An example is given below, of tuning and running a chain for a 1000 dimensional Gaussian target (of which a 2 dimensional marginal is plotted):
 
-```{code-cell} ipython3
+```{code-cell}
 :tags: [hide-cell]
 
 import matplotlib.pyplot as plt
@@ -66,7 +66,7 @@ from numpyro.infer.util import initialize_model
 rng_key = jax.random.key(int(date.today().strftime("%Y%m%d")))
 ```
 
-```{code-cell} ipython3
+```{code-cell}
 def run_mclmc(logdensity_fn, num_steps, initial_position, key, transform, desired_energy_variance= 5e-4):
     init_key, tune_key, run_key = jax.random.split(key, 3)
 
@@ -115,7 +115,7 @@ def run_mclmc(logdensity_fn, num_steps, initial_position, key, transform, desire
     return samples, blackjax_state_after_tuning, blackjax_mclmc_sampler_params, run_key
 ```
 
-```{code-cell} ipython3
+```{code-cell}
 # run the algorithm on a high dimensional gaussian, and show two of the dimensions
 
 logdensity_fn = lambda x: -0.5 * jnp.sum(jnp.square(x))
@@ -134,13 +134,13 @@ samples, initial_state, params, chain_key = run_mclmc(
 samples.mean()
 ```
 
-```{code-cell} ipython3
+```{code-cell}
 plt.scatter(x=samples[:, 0], y=samples[:, 1], alpha=0.1)
 plt.axis("equal")
 plt.title("Scatter Plot of Samples")
 ```
 
-```{code-cell} ipython3
+```{code-cell}
 def visualize_results_gauss(samples, label, color):
   x1 = samples[:, 0]
   plt.hist(x1, bins= 30, density= True, histtype= 'step', lw= 4, color= color, label= label)
@@ -165,12 +165,12 @@ ground_truth_gauss()
 
 A natural sanity check is to see if reducing $\epsilon$ changes the inferred distribution to an extent you care about. For example, we can inspect the 1D marginal with a stepsize $\epsilon$ as above, and compare it to a stepsize $\epsilon/2$ (and double the number of steps). We show this comparison below:
 
-```{code-cell} ipython3
+```{code-cell}
 new_params = params._replace(step_size= params.step_size / 2)
 new_num_steps = num_steps * 2
 ```
 
-```{code-cell} ipython3
+```{code-cell}
 sampling_alg = blackjax.mclmc(
     logdensity_fn,
     L=new_params.L,
@@ -211,7 +211,7 @@ Our task is to find the posterior of the parameters $\{R_n\}_{n =1}^N$, $\sigma$
 
 First, we get the data, define a model using NumPyro, and draw samples:
 
-```{code-cell} ipython3
+```{code-cell}
 import matplotlib.dates as mdates
 from numpyro.examples.datasets import SP500, load_dataset
 from numpyro.distributions import StudentT
@@ -243,7 +243,7 @@ def setup():
 setup()
 ```
 
-```{code-cell} ipython3
+```{code-cell}
 def from_numpyro(model, rng_key, model_args):
   init_params, potential_fn_gen, *_ = initialize_model(
       rng_key,
@@ -272,13 +272,13 @@ rng_key = jax.random.key(42)
 logp_sv, x_init = from_numpyro(stochastic_volatility, rng_key, model_args)
 ```
 
-```{code-cell} ipython3
+```{code-cell}
 num_steps = 20000
 
 samples, initial_state, params, chain_key = run_mclmc(logdensity_fn= logp_sv, num_steps= num_steps, initial_position= x_init, key= sample_key, transform=lambda state, info: state.position)
 ```
 
-```{code-cell} ipython3
+```{code-cell}
 def visualize_results_sv(samples, color, label):
 
   R = np.exp(np.array(samples['s'])) # take an exponent to get R
@@ -297,7 +297,7 @@ plt.legend()
 plt.show()
 ```
 
-```{code-cell} ipython3
+```{code-cell}
 new_params = params._replace(step_size = params.step_size/2)
 new_num_steps = num_steps * 2
 
@@ -318,10 +318,9 @@ _, new_samples = blackjax.util.run_inference_algorithm(
     transform=lambda state, info : state.position,
     progress_bar=True,
 )
-
 ```
 
-```{code-cell} ipython3
+```{code-cell}
 setup()
 visualize_results_sv(new_samples,'red', 'MCLMC', )
 visualize_results_sv(samples,'teal', 'MCLMC (stepsize/2)', )
@@ -332,7 +331,7 @@ plt.show()
 
 Here, we have again inspected the effect of halving $\epsilon$. This looks OK, but suppose we are interested in the hierarchial parameters in particular, which tend to be harder to infer. We now inspect the marginal of a hierarchical parameter:
 
-```{code-cell} ipython3
+```{code-cell}
 def visualize_results_sv_marginal(samples, color, label):
     # plt.subplot(1, 2, 1)
     # plt.hist(samples['nu'], bins = 20, histtype= 'step', lw= 4, density= True, color= color, label= label)
@@ -354,9 +353,131 @@ If we care about this parameter in particular, we should reduce step size furthe
 
 +++
 
+## Adjusted MCLMC
+
+Blackjax also provides an adjusted version of the algorithm. This also has two hyperparameters, `step_size` and `L`. `L` is related to the `L` parameter of the unadjusted version, but not identical. The tuning algorithm is also similar, but uses a dual averaging scheme to tune the step size. We find in practice that a target MH acceptance rate of 0.9 is a good choice.
+
+```{code-cell}
+from blackjax.mcmc.adjusted_mclmc import rescale
+from blackjax.util import run_inference_algorithm
+
+def run_adjusted_mclmc(
+    logdensity_fn,
+    num_steps,
+    initial_position,
+    key,
+    transform=lambda state, _ : state.position,
+    diagonal_preconditioning=False,
+    random_trajectory_length=True,
+    L_proposal_factor=jnp.inf
+):
+
+    init_key, tune_key, run_key = jax.random.split(key, 3)
+
+    initial_state = blackjax.mcmc.adjusted_mclmc.init(
+        position=initial_position,
+        logdensity_fn=logdensity_fn,
+        random_generator_arg=init_key,
+    )
+
+    if random_trajectory_length:
+        integration_steps_fn = lambda avg_num_integration_steps: lambda k: jnp.ceil(
+            jax.random.uniform(k) * rescale(avg_num_integration_steps))
+    else:
+        integration_steps_fn = lambda avg_num_integration_steps: lambda _: jnp.ceil(avg_num_integration_steps)
+
+    kernel = lambda rng_key, state, avg_num_integration_steps, step_size, sqrt_diag_cov: blackjax.mcmc.adjusted_mclmc.build_kernel(
+        integration_steps_fn=integration_steps_fn(avg_num_integration_steps),
+        sqrt_diag_cov=sqrt_diag_cov,
+    )(
+        rng_key=rng_key,
+        state=state,
+        step_size=step_size,
+        logdensity_fn=logdensity_fn,
+        L_proposal_factor=L_proposal_factor,
+    )
+
+    target_acc_rate = 0.9 # our recommendation
+
+    (
+        blackjax_state_after_tuning,
+        blackjax_mclmc_sampler_params,
+    ) = blackjax.adjusted_mclmc_find_L_and_step_size(
+        mclmc_kernel=kernel,
+        num_steps=num_steps,
+        state=initial_state,
+        rng_key=tune_key,
+        target=target_acc_rate,
+        frac_tune1=0.1,
+        frac_tune2=0.1,
+        frac_tune3=0.0, # our recommendation
+        diagonal_preconditioning=diagonal_preconditioning,
+    )
+
+    step_size = blackjax_mclmc_sampler_params.step_size
+    L = blackjax_mclmc_sampler_params.L
+
+    alg = blackjax.adjusted_mclmc(
+        logdensity_fn=logdensity_fn,
+        step_size=step_size,
+        integration_steps_fn=lambda key: jnp.ceil(
+            jax.random.uniform(key) * rescale(L / step_size)
+        ),
+        sqrt_diag_cov=blackjax_mclmc_sampler_params.sqrt_diag_cov,
+        L_proposal_factor=L_proposal_factor,
+    )
+
+    _, out = run_inference_algorithm(
+        rng_key=run_key,
+        initial_state=blackjax_state_after_tuning,
+        inference_algorithm=alg,
+        num_steps=num_steps,
+        transform=transform,
+        progress_bar=False,
+    )
+
+    return out
+```
+
+```{code-cell}
+# run the algorithm on a high dimensional gaussian, and show two of the dimensions
+
+sample_key, rng_key = jax.random.split(rng_key)
+samples = run_adjusted_mclmc(
+    logdensity_fn=lambda x: -0.5 * jnp.sum(jnp.square(x)),
+    num_steps=1000,
+    initial_position=jnp.ones((1000,)),
+    key=sample_key,
+)
+plt.scatter(x=samples[:, 0], y=samples[:, 1], alpha=0.1)
+plt.axis("equal")
+plt.title("Scatter Plot of Samples")
+```
+
+```{code-cell}
+# run the algorithm on a high dimensional gaussian, and show two of the dimensions
+
+sample_key, rng_key = jax.random.split(rng_key)
+samples = run_adjusted_mclmc(
+    logdensity_fn=lambda x: -0.5 * jnp.sum(jnp.square(x)),
+    num_steps=1000,
+    initial_position=jnp.ones((1000,)),
+    key=sample_key,
+    random_trajectory_length=False,
+    L_proposal_factor=1.25,
+)
+plt.scatter(x=samples[:, 0], y=samples[:, 1], alpha=0.1)
+plt.axis("equal")
+plt.title("Scatter Plot of Samples")
+```
+
 ```{bibliography}
 :filter: docname in docnames
 ```
 
 
+```
+
+```{code-cell}
+
 ```
diff --git a/algorithms/mclmc.html b/algorithms/mclmc.html
index b053ee6..2916e34 100644
--- a/algorithms/mclmc.html
+++ b/algorithms/mclmc.html
@@ -386,6 +386,7 @@ <h2> Contents </h2>
 <li class="toc-h1 nav-item toc-entry"><a class="reference internal nav-link" href="#how-to-analyze-the-results-of-your-mclmc-run">How to analyze the results of your MCLMC run</a><ul class="visible nav section-nav flex-column">
 <li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#validate-the-choice-of-epsilon">Validate the choice of <span class="math notranslate nohighlight">\(\epsilon\)</span></a></li>
 <li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#a-more-complex-example">A more complex example</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#adjusted-mclmc">Adjusted MCLMC</a></li>
 </ul>
 </li>
 </ul>
@@ -455,7 +456,7 @@ <h2>How to run MCLMC in BlackJax<a class="headerlink" href="#how-to-run-mclmc-in
 </div>
 </div>
 <div class="cell_output docutils container">
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/opt/hostedtoolcache/Python/3.11.10/x64/lib/python3.11/site-packages/tqdm/auto.py:21: TqdmWarning: IProgress not found. Please update jupyter and ipywidgets. See https://ipywidgets.readthedocs.io/en/stable/user_install.html
+<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/opt/hostedtoolcache/Python/3.11.11/x64/lib/python3.11/site-packages/tqdm/auto.py:21: TqdmWarning: IProgress not found. Please update jupyter and ipywidgets. See https://ipywidgets.readthedocs.io/en/stable/user_install.html
   from .autonotebook import tqdm as notebook_tqdm
 </pre></div>
 </div>
@@ -557,7 +558,7 @@ <h2>How to run MCLMC in BlackJax<a class="headerlink" href="#how-to-run-mclmc-in
       <progress value='10000' class='' max='10000' style='width:300px; height:20px; vertical-align: middle;'></progress>
       100.00% [10000/10000 00:00&lt;?]
     </div>
-    </div><div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Array(0.00264662, dtype=float32)
+    </div><div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Array(0.00752303, dtype=float32)
 </pre></div>
 </div>
 </div>
@@ -574,7 +575,7 @@ <h2>How to run MCLMC in BlackJax<a class="headerlink" href="#how-to-run-mclmc-in
 <div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Text(0.5, 1.0, &#39;Scatter Plot of Samples&#39;)
 </pre></div>
 </div>
-<img alt="../_images/0ec1b4434d7309896a76cee60b2f67a770c5ddaeb10603670ec5fa8f8e14d4c1.png" src="../_images/0ec1b4434d7309896a76cee60b2f67a770c5ddaeb10603670ec5fa8f8e14d4c1.png" />
+<img alt="../_images/f58a28d8bafef836b4f2d1ea0216cb04e354440f8ce63a6016047a6e39295bf5.png" src="../_images/f58a28d8bafef836b4f2d1ea0216cb04e354440f8ce63a6016047a6e39295bf5.png" />
 </div>
 </div>
 <div class="cell docutils container">
@@ -599,7 +600,7 @@ <h2>How to run MCLMC in BlackJax<a class="headerlink" href="#how-to-run-mclmc-in
 </div>
 </div>
 <div class="cell_output docutils container">
-<img alt="../_images/d1c7d7b84b3a6ac445ac29b9c2056d5ff847bed88f6d4718a6a5d831289668c4.png" src="../_images/d1c7d7b84b3a6ac445ac29b9c2056d5ff847bed88f6d4718a6a5d831289668c4.png" />
+<img alt="../_images/f872d80acedc9f464f69f4829103b9c5bb0b73d3fe8a5c463eee4cc45be0f044.png" src="../_images/f872d80acedc9f464f69f4829103b9c5bb0b73d3fe8a5c463eee4cc45be0f044.png" />
 </div>
 </div>
 </section>
@@ -662,7 +663,7 @@ <h2>Validate the choice of <span class="math notranslate nohighlight">\(\epsilon
       <progress value='20000' class='' max='20000' style='width:300px; height:20px; vertical-align: middle;'></progress>
       100.00% [20000/20000 00:00&lt;?]
     </div>
-    </div><img alt="../_images/38d0c9943edeadd2477f421372f67a01eb1b0f4f12fc3a057b3f5a05794aac96.png" src="../_images/38d0c9943edeadd2477f421372f67a01eb1b0f4f12fc3a057b3f5a05794aac96.png" />
+    </div><img alt="../_images/94d18d3d4664c09e29ac2a9f661585be3ea67e4043777c3f339077f031456486.png" src="../_images/94d18d3d4664c09e29ac2a9f661585be3ea67e4043777c3f339077f031456486.png" />
 </div>
 </div>
 <p>So here the change has little effect in this case.</p>
@@ -671,8 +672,8 @@ <h2>Validate the choice of <span class="math notranslate nohighlight">\(\epsilon
 <h2>A more complex example<a class="headerlink" href="#a-more-complex-example" title="Link to this heading">#</a></h2>
 <p>We now consider a more complex model, of stock volatility.</p>
 <p>The returns <span class="math notranslate nohighlight">\(r_n\)</span> are modeled by a Student’s-t distribution whose scale (volatility) <span class="math notranslate nohighlight">\(R_n\)</span> is time varying and unknown. The prior for <span class="math notranslate nohighlight">\(\log R_n\)</span> is a Gaussian random walk, with an exponential distribution of the random walk step-size <span class="math notranslate nohighlight">\(\sigma\)</span>. An exponential prior is also taken for the Student’s-t degrees of freedom <span class="math notranslate nohighlight">\(\nu\)</span>. The generative process of the data is:</p>
-<div class="amsmath math notranslate nohighlight" id="equation-75e344c6-890b-4ed0-85f3-e78b87abaf89">
-<span class="eqno">(1)<a class="headerlink" href="#equation-75e344c6-890b-4ed0-85f3-e78b87abaf89" title="Permalink to this equation">#</a></span>\[\begin{align}
+<div class="amsmath math notranslate nohighlight" id="equation-dca724b5-5e5e-4c47-9720-94146bf5eb05">
+<span class="eqno">(1)<a class="headerlink" href="#equation-dca724b5-5e5e-4c47-9720-94146bf5eb05" title="Permalink to this equation">#</a></span>\[\begin{align}
     &amp;r_n / R_n \sim \text{Student's-t}(\nu) \qquad
     &amp;&amp;\nu \sim \text{Exp}(\lambda = 1/10) \\ \nonumber
     &amp;\log R_n \sim \mathcal{N}(\log R_{n-1}, \sigma) \qquad
@@ -716,12 +717,10 @@ <h2>A more complex example<a class="headerlink" href="#a-more-complex-example" t
 </div>
 <div class="cell_output docutils container">
 <div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Downloading - https://d2hg8soec8ck9v.cloudfront.net/datasets/SP500.csv.
+Download complete.
 </pre></div>
 </div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Download complete.
-</pre></div>
-</div>
-<img alt="../_images/f7fd34fb893d79efc3e37fb858a4589d8551017b468c16da4ac5f51a3ad224d1.png" src="../_images/f7fd34fb893d79efc3e37fb858a4589d8551017b468c16da4ac5f51a3ad224d1.png" />
+<img alt="../_images/007875a6641d5f45dcd208adcadda104db098d0a2c3a6adc8ab9a549a3ea8194.png" src="../_images/007875a6641d5f45dcd208adcadda104db098d0a2c3a6adc8ab9a549a3ea8194.png" />
 </div>
 </div>
 <div class="cell docutils container">
@@ -808,7 +807,7 @@ <h2>A more complex example<a class="headerlink" href="#a-more-complex-example" t
       <progress value='20000' class='' max='20000' style='width:300px; height:20px; vertical-align: middle;'></progress>
       100.00% [20000/20000 00:00&lt;?]
     </div>
-    </div><img alt="../_images/0a70760fa6e9e436f76686fc34a0a16b4091cbcd9d13b793090929596eff7b8e.png" src="../_images/0a70760fa6e9e436f76686fc34a0a16b4091cbcd9d13b793090929596eff7b8e.png" />
+    </div><img alt="../_images/c80fb9135c61b29129499d74efabdb728d01e90f1b18055728d11bf698744b5c.png" src="../_images/c80fb9135c61b29129499d74efabdb728d01e90f1b18055728d11bf698744b5c.png" />
 </div>
 </div>
 <div class="cell docutils container">
@@ -870,7 +869,7 @@ <h2>A more complex example<a class="headerlink" href="#a-more-complex-example" t
       <progress value='40000' class='' max='40000' style='width:300px; height:20px; vertical-align: middle;'></progress>
       100.00% [40000/40000 00:00&lt;?]
     </div>
-    </div><img alt="../_images/50b50a28029252f98e42ed1b367172bcd81c5ebe172126bb0c87553f87976245.png" src="../_images/50b50a28029252f98e42ed1b367172bcd81c5ebe172126bb0c87553f87976245.png" />
+    </div><img alt="../_images/adaeffd1cf285dd63535c2c781fb1286bb3bd072812b80b4aadc4cc675736d3a.png" src="../_images/adaeffd1cf285dd63535c2c781fb1286bb3bd072812b80b4aadc4cc675736d3a.png" />
 </div>
 </div>
 <p>Here, we have again inspected the effect of halving <span class="math notranslate nohighlight">\(\epsilon\)</span>. This looks OK, but suppose we are interested in the hierarchial parameters in particular, which tend to be harder to infer. We now inspect the marginal of a hierarchical parameter:</p>
@@ -895,10 +894,149 @@ <h2>A more complex example<a class="headerlink" href="#a-more-complex-example" t
 </div>
 </div>
 <div class="cell_output docutils container">
-<img alt="../_images/7a204e67bf4cd962187cf778534ae56bbaeb4dbc1bbf19681183439da815d942.png" src="../_images/7a204e67bf4cd962187cf778534ae56bbaeb4dbc1bbf19681183439da815d942.png" />
+<img alt="../_images/71464f41a600b82a21fb8145d6da6372716a1d658eb09b075628598c1ca0c2c6.png" src="../_images/71464f41a600b82a21fb8145d6da6372716a1d658eb09b075628598c1ca0c2c6.png" />
 </div>
 </div>
 <p>If we care about this parameter in particular, we should reduce step size further, until the difference disappears.</p>
+</section>
+<section id="adjusted-mclmc">
+<h2>Adjusted MCLMC<a class="headerlink" href="#adjusted-mclmc" title="Link to this heading">#</a></h2>
+<p>Blackjax also provides an adjusted version of the algorithm. This also has two hyperparameters, <code class="docutils literal notranslate"><span class="pre">step_size</span></code> and <code class="docutils literal notranslate"><span class="pre">L</span></code>. <code class="docutils literal notranslate"><span class="pre">L</span></code> is related to the <code class="docutils literal notranslate"><span class="pre">L</span></code> parameter of the unadjusted version, but not identical. The tuning algorithm is also similar, but uses a dual averaging scheme to tune the step size. We find in practice that a target MH acceptance rate of 0.9 is a good choice.</p>
+<div class="cell docutils container">
+<div class="cell_input docutils container">
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">blackjax.mcmc.adjusted_mclmc</span> <span class="kn">import</span> <span class="n">rescale</span>
+<span class="kn">from</span> <span class="nn">blackjax.util</span> <span class="kn">import</span> <span class="n">run_inference_algorithm</span>
+
+<span class="k">def</span> <span class="nf">run_adjusted_mclmc</span><span class="p">(</span>
+    <span class="n">logdensity_fn</span><span class="p">,</span>
+    <span class="n">num_steps</span><span class="p">,</span>
+    <span class="n">initial_position</span><span class="p">,</span>
+    <span class="n">key</span><span class="p">,</span>
+    <span class="n">transform</span><span class="o">=</span><span class="k">lambda</span> <span class="n">state</span><span class="p">,</span> <span class="n">_</span> <span class="p">:</span> <span class="n">state</span><span class="o">.</span><span class="n">position</span><span class="p">,</span>
+    <span class="n">diagonal_preconditioning</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span>
+    <span class="n">random_trajectory_length</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span>
+    <span class="n">L_proposal_factor</span><span class="o">=</span><span class="n">jnp</span><span class="o">.</span><span class="n">inf</span>
+<span class="p">):</span>
+
+    <span class="n">init_key</span><span class="p">,</span> <span class="n">tune_key</span><span class="p">,</span> <span class="n">run_key</span> <span class="o">=</span> <span class="n">jax</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">split</span><span class="p">(</span><span class="n">key</span><span class="p">,</span> <span class="mi">3</span><span class="p">)</span>
+
+    <span class="n">initial_state</span> <span class="o">=</span> <span class="n">blackjax</span><span class="o">.</span><span class="n">mcmc</span><span class="o">.</span><span class="n">adjusted_mclmc</span><span class="o">.</span><span class="n">init</span><span class="p">(</span>
+        <span class="n">position</span><span class="o">=</span><span class="n">initial_position</span><span class="p">,</span>
+        <span class="n">logdensity_fn</span><span class="o">=</span><span class="n">logdensity_fn</span><span class="p">,</span>
+        <span class="n">random_generator_arg</span><span class="o">=</span><span class="n">init_key</span><span class="p">,</span>
+    <span class="p">)</span>
+
+    <span class="k">if</span> <span class="n">random_trajectory_length</span><span class="p">:</span>
+        <span class="n">integration_steps_fn</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">avg_num_integration_steps</span><span class="p">:</span> <span class="k">lambda</span> <span class="n">k</span><span class="p">:</span> <span class="n">jnp</span><span class="o">.</span><span class="n">ceil</span><span class="p">(</span>
+            <span class="n">jax</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">uniform</span><span class="p">(</span><span class="n">k</span><span class="p">)</span> <span class="o">*</span> <span class="n">rescale</span><span class="p">(</span><span class="n">avg_num_integration_steps</span><span class="p">))</span>
+    <span class="k">else</span><span class="p">:</span>
+        <span class="n">integration_steps_fn</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">avg_num_integration_steps</span><span class="p">:</span> <span class="k">lambda</span> <span class="n">_</span><span class="p">:</span> <span class="n">jnp</span><span class="o">.</span><span class="n">ceil</span><span class="p">(</span><span class="n">avg_num_integration_steps</span><span class="p">)</span>
+
+    <span class="n">kernel</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">rng_key</span><span class="p">,</span> <span class="n">state</span><span class="p">,</span> <span class="n">avg_num_integration_steps</span><span class="p">,</span> <span class="n">step_size</span><span class="p">,</span> <span class="n">sqrt_diag_cov</span><span class="p">:</span> <span class="n">blackjax</span><span class="o">.</span><span class="n">mcmc</span><span class="o">.</span><span class="n">adjusted_mclmc</span><span class="o">.</span><span class="n">build_kernel</span><span class="p">(</span>
+        <span class="n">integration_steps_fn</span><span class="o">=</span><span class="n">integration_steps_fn</span><span class="p">(</span><span class="n">avg_num_integration_steps</span><span class="p">),</span>
+        <span class="n">sqrt_diag_cov</span><span class="o">=</span><span class="n">sqrt_diag_cov</span><span class="p">,</span>
+    <span class="p">)(</span>
+        <span class="n">rng_key</span><span class="o">=</span><span class="n">rng_key</span><span class="p">,</span>
+        <span class="n">state</span><span class="o">=</span><span class="n">state</span><span class="p">,</span>
+        <span class="n">step_size</span><span class="o">=</span><span class="n">step_size</span><span class="p">,</span>
+        <span class="n">logdensity_fn</span><span class="o">=</span><span class="n">logdensity_fn</span><span class="p">,</span>
+        <span class="n">L_proposal_factor</span><span class="o">=</span><span class="n">L_proposal_factor</span><span class="p">,</span>
+    <span class="p">)</span>
+
+    <span class="n">target_acc_rate</span> <span class="o">=</span> <span class="mf">0.9</span> <span class="c1"># our recommendation</span>
+
+    <span class="p">(</span>
+        <span class="n">blackjax_state_after_tuning</span><span class="p">,</span>
+        <span class="n">blackjax_mclmc_sampler_params</span><span class="p">,</span>
+    <span class="p">)</span> <span class="o">=</span> <span class="n">blackjax</span><span class="o">.</span><span class="n">adjusted_mclmc_find_L_and_step_size</span><span class="p">(</span>
+        <span class="n">mclmc_kernel</span><span class="o">=</span><span class="n">kernel</span><span class="p">,</span>
+        <span class="n">num_steps</span><span class="o">=</span><span class="n">num_steps</span><span class="p">,</span>
+        <span class="n">state</span><span class="o">=</span><span class="n">initial_state</span><span class="p">,</span>
+        <span class="n">rng_key</span><span class="o">=</span><span class="n">tune_key</span><span class="p">,</span>
+        <span class="n">target</span><span class="o">=</span><span class="n">target_acc_rate</span><span class="p">,</span>
+        <span class="n">frac_tune1</span><span class="o">=</span><span class="mf">0.1</span><span class="p">,</span>
+        <span class="n">frac_tune2</span><span class="o">=</span><span class="mf">0.1</span><span class="p">,</span>
+        <span class="n">frac_tune3</span><span class="o">=</span><span class="mf">0.0</span><span class="p">,</span> <span class="c1"># our recommendation</span>
+        <span class="n">diagonal_preconditioning</span><span class="o">=</span><span class="n">diagonal_preconditioning</span><span class="p">,</span>
+    <span class="p">)</span>
+
+    <span class="n">step_size</span> <span class="o">=</span> <span class="n">blackjax_mclmc_sampler_params</span><span class="o">.</span><span class="n">step_size</span>
+    <span class="n">L</span> <span class="o">=</span> <span class="n">blackjax_mclmc_sampler_params</span><span class="o">.</span><span class="n">L</span>
+
+    <span class="n">alg</span> <span class="o">=</span> <span class="n">blackjax</span><span class="o">.</span><span class="n">adjusted_mclmc</span><span class="p">(</span>
+        <span class="n">logdensity_fn</span><span class="o">=</span><span class="n">logdensity_fn</span><span class="p">,</span>
+        <span class="n">step_size</span><span class="o">=</span><span class="n">step_size</span><span class="p">,</span>
+        <span class="n">integration_steps_fn</span><span class="o">=</span><span class="k">lambda</span> <span class="n">key</span><span class="p">:</span> <span class="n">jnp</span><span class="o">.</span><span class="n">ceil</span><span class="p">(</span>
+            <span class="n">jax</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">uniform</span><span class="p">(</span><span class="n">key</span><span class="p">)</span> <span class="o">*</span> <span class="n">rescale</span><span class="p">(</span><span class="n">L</span> <span class="o">/</span> <span class="n">step_size</span><span class="p">)</span>
+        <span class="p">),</span>
+        <span class="n">sqrt_diag_cov</span><span class="o">=</span><span class="n">blackjax_mclmc_sampler_params</span><span class="o">.</span><span class="n">sqrt_diag_cov</span><span class="p">,</span>
+        <span class="n">L_proposal_factor</span><span class="o">=</span><span class="n">L_proposal_factor</span><span class="p">,</span>
+    <span class="p">)</span>
+
+    <span class="n">_</span><span class="p">,</span> <span class="n">out</span> <span class="o">=</span> <span class="n">run_inference_algorithm</span><span class="p">(</span>
+        <span class="n">rng_key</span><span class="o">=</span><span class="n">run_key</span><span class="p">,</span>
+        <span class="n">initial_state</span><span class="o">=</span><span class="n">blackjax_state_after_tuning</span><span class="p">,</span>
+        <span class="n">inference_algorithm</span><span class="o">=</span><span class="n">alg</span><span class="p">,</span>
+        <span class="n">num_steps</span><span class="o">=</span><span class="n">num_steps</span><span class="p">,</span>
+        <span class="n">transform</span><span class="o">=</span><span class="n">transform</span><span class="p">,</span>
+        <span class="n">progress_bar</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span>
+    <span class="p">)</span>
+
+    <span class="k">return</span> <span class="n">out</span>
+</pre></div>
+</div>
+</div>
+</div>
+<div class="cell docutils container">
+<div class="cell_input docutils container">
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="c1"># run the algorithm on a high dimensional gaussian, and show two of the dimensions</span>
+
+<span class="n">sample_key</span><span class="p">,</span> <span class="n">rng_key</span> <span class="o">=</span> <span class="n">jax</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">split</span><span class="p">(</span><span class="n">rng_key</span><span class="p">)</span>
+<span class="n">samples</span> <span class="o">=</span> <span class="n">run_adjusted_mclmc</span><span class="p">(</span>
+    <span class="n">logdensity_fn</span><span class="o">=</span><span class="k">lambda</span> <span class="n">x</span><span class="p">:</span> <span class="o">-</span><span class="mf">0.5</span> <span class="o">*</span> <span class="n">jnp</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">jnp</span><span class="o">.</span><span class="n">square</span><span class="p">(</span><span class="n">x</span><span class="p">)),</span>
+    <span class="n">num_steps</span><span class="o">=</span><span class="mi">1000</span><span class="p">,</span>
+    <span class="n">initial_position</span><span class="o">=</span><span class="n">jnp</span><span class="o">.</span><span class="n">ones</span><span class="p">((</span><span class="mi">1000</span><span class="p">,)),</span>
+    <span class="n">key</span><span class="o">=</span><span class="n">sample_key</span><span class="p">,</span>
+<span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">scatter</span><span class="p">(</span><span class="n">x</span><span class="o">=</span><span class="n">samples</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">y</span><span class="o">=</span><span class="n">samples</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">],</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.1</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">axis</span><span class="p">(</span><span class="s2">&quot;equal&quot;</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s2">&quot;Scatter Plot of Samples&quot;</span><span class="p">)</span>
+</pre></div>
+</div>
+</div>
+<div class="cell_output docutils container">
+<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Text(0.5, 1.0, &#39;Scatter Plot of Samples&#39;)
+</pre></div>
+</div>
+<img alt="../_images/9ac388bb73a2903fcc26a9e56d67334a38b7217f1d9fb9fe422768ea6419656d.png" src="../_images/9ac388bb73a2903fcc26a9e56d67334a38b7217f1d9fb9fe422768ea6419656d.png" />
+</div>
+</div>
+<div class="cell docutils container">
+<div class="cell_input docutils container">
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="c1"># run the algorithm on a high dimensional gaussian, and show two of the dimensions</span>
+
+<span class="n">sample_key</span><span class="p">,</span> <span class="n">rng_key</span> <span class="o">=</span> <span class="n">jax</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">split</span><span class="p">(</span><span class="n">rng_key</span><span class="p">)</span>
+<span class="n">samples</span> <span class="o">=</span> <span class="n">run_adjusted_mclmc</span><span class="p">(</span>
+    <span class="n">logdensity_fn</span><span class="o">=</span><span class="k">lambda</span> <span class="n">x</span><span class="p">:</span> <span class="o">-</span><span class="mf">0.5</span> <span class="o">*</span> <span class="n">jnp</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">jnp</span><span class="o">.</span><span class="n">square</span><span class="p">(</span><span class="n">x</span><span class="p">)),</span>
+    <span class="n">num_steps</span><span class="o">=</span><span class="mi">1000</span><span class="p">,</span>
+    <span class="n">initial_position</span><span class="o">=</span><span class="n">jnp</span><span class="o">.</span><span class="n">ones</span><span class="p">((</span><span class="mi">1000</span><span class="p">,)),</span>
+    <span class="n">key</span><span class="o">=</span><span class="n">sample_key</span><span class="p">,</span>
+    <span class="n">random_trajectory_length</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span>
+    <span class="n">L_proposal_factor</span><span class="o">=</span><span class="mf">1.25</span><span class="p">,</span>
+<span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">scatter</span><span class="p">(</span><span class="n">x</span><span class="o">=</span><span class="n">samples</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">y</span><span class="o">=</span><span class="n">samples</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">],</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.1</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">axis</span><span class="p">(</span><span class="s2">&quot;equal&quot;</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s2">&quot;Scatter Plot of Samples&quot;</span><span class="p">)</span>
+</pre></div>
+</div>
+</div>
+<div class="cell_output docutils container">
+<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Text(0.5, 1.0, &#39;Scatter Plot of Samples&#39;)
+</pre></div>
+</div>
+<img alt="../_images/ce341e7b5e15603176fe4c01cc9731b1255965a6276c12e0db0cf60fa40c380e.png" src="../_images/ce341e7b5e15603176fe4c01cc9731b1255965a6276c12e0db0cf60fa40c380e.png" />
+</div>
+</div>
 <div class="docutils container" id="id3">
 <div role="list" class="citation-list">
 <div class="citation" id="id23" role="doc-biblioentry">
@@ -912,6 +1050,8 @@ <h2>A more complex example<a class="headerlink" href="#a-more-complex-example" t
 </div>
 </div>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span>
+```{code-cell}
+
 </pre></div>
 </div>
 </section>
@@ -989,6 +1129,7 @@ <h2>A more complex example<a class="headerlink" href="#a-more-complex-example" t
 <li class="toc-h1 nav-item toc-entry"><a class="reference internal nav-link" href="#how-to-analyze-the-results-of-your-mclmc-run">How to analyze the results of your MCLMC run</a><ul class="visible nav section-nav flex-column">
 <li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#validate-the-choice-of-epsilon">Validate the choice of <span class="math notranslate nohighlight">\(\epsilon\)</span></a></li>
 <li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#a-more-complex-example">A more complex example</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#adjusted-mclmc">Adjusted MCLMC</a></li>
 </ul>
 </li>
 </ul>
diff --git a/searchindex.js b/searchindex.js
index 7e80acb..f724f3d 100644
--- a/searchindex.js
+++ b/searchindex.js
@@ -1 +1 @@
-Search.setIndex({"alltitles": {"A more complex example": [[5, "a-more-complex-example"]], "Adaptation": [[9, null]], "Algorithms": [[7, null]], "Arviz Plots": [[12, "arviz-plots"]], "Banana Density": [[0, "banana-density"]], "Bayesian Logistic Regression": [[14, null]], "Bayesian Logistic Regression With Latent Gaussian Sampler": [[10, null]], "Bayesian Regression With Latent Gaussian Sampler": [[9, null]], "Bibliography": [[17, "bibliography"]], "Change of Variable": [[12, "change-of-variable"]], "Change of Variable in HMC": [[12, null]], "Comparison": [[15, "comparison"]], "Conclusion": [[16, "conclusion"]], "Contour stochastic gradient Langevin dynamics": [[3, null]], "Cyclical SGLD": [[4, null], [4, "id2"]], "Cyclical schedule": [[4, "cyclical-schedule"]], "Data": [[13, "data"]], "Data Preparation": [[15, "data-preparation"]], "Diagnostics": [[8, "diagnostics"], [9, "diagnostics"]], "Ellipsis": [[0, "ellipsis"]], "Ellipsis + IAF": [[0, "ellipsis-iaf"]], "Example: Auxiliary Metropolis-Adjusted Langevin Algorithm (MALA)": [[9, "example-auxiliary-metropolis-adjusted-langevin-algorithm-mala"]], "Experimental Setup": [[1, "experimental-setup"], [1, "id1"]], "Exploring uncertainty": [[15, "exploring-uncertainty"]], "Fit Separate MLPs, One Per Task": [[13, "fit-separate-mlps-one-per-task"]], "Gaussian Mixture model": [[3, "gaussian-mixture-model"]], "Gaussian Regression with the Elliptical Slice Sampler": [[8, null]], "German credit dataset": [[17, "german-credit-dataset"]], "HMC Sampler": [[1, "hmc-sampler"]], "Hierarchical Bayesian Neural Networks": [[13, null]], "Hierarchical Model": [[13, "hierarchical-model"]], "How does Contour SGLD work?": [[3, "how-does-contour-sgld-work"]], "How to analyze the results of your MCLMC run": [[5, "how-to-analyze-the-results-of-your-mclmc-run"]], "How to run MCLMC in BlackJax": [[5, "how-to-run-mclmc-in-blackjax"]], "Hyperparameters": [[13, "hyperparameters"]], "IRMH tuning the covariance matrix.": [[2, "irmh-tuning-the-covariance-matrix"]], "IRMH tuning the diagonal of the covariance matrix": [[2, "irmh-tuning-the-diagonal-of-the-covariance-matrix"]], "IRMH without tuning": [[2, "irmh-without-tuning"]], "Imports": [[1, "imports"]], "Initial State and Sampler Parameters": [[0, "initial-state-and-sampler-parameters"]], "Latent Gaussian Models": [[9, "latent-gaussian-models"]], "Log-posterior densities via ProbDiffEq": [[16, "log-posterior-densities-via-probdiffeq"]], "MEADS": [[17, "meads"]], "MLP classifier": [[15, null]], "McLachlan": [[0, "mclachlan"]], "Microcanonical Langevin Monte Carlo": [[5, null]], "Models": [[7, null], [17, "models"]], "Motivation: Auxiliary Metropolis-Hastings samplers": [[9, "motivation-auxiliary-metropolis-hastings-samplers"]], "Multi-layer Perceptron": [[15, "multi-layer-perceptron"]], "NUTS Sampler": [[1, "nuts-sampler"]], "Parameter estimation in ODE models with a probabilistic ODE solver": [[16, null]], "Pathfinder": [[6, null]], "Pathfinder as a Variational Inference Method": [[6, "pathfinder-as-a-variational-inference-method"]], "Pathfinder as an Initialization Tool for MCMC Kernels": [[6, "pathfinder-as-an-initialization-tool-for-mcmc-kernels"]], "Pathfinder: Parallel Quasi-Newton Variational Inference": [[6, "pathfinder-parallel-quasi-newton-variational-inference"]], "Periodic Orbital MCMC": [[0, null]], "Posterior Sampling": [[12, "posterior-sampling"], [14, "posterior-sampling"]], "Posterior sampling": [[10, "posterior-sampling"]], "Predictive Distribution": [[14, "predictive-distribution"]], "Predictive distribution": [[10, "predictive-distribution"]], "Problem setting": [[16, "problem-setting"]], "Regime switching Hidden Markov model": [[11, null]], "Results": [[13, "results"], [13, "id1"]], "SGLD": [[4, "sgld"]], "Sample From the Posterior Distribution of the MLP\u2019s Weights": [[15, "sample-from-the-posterior-distribution-of-the-mlp-s-weights"]], "Sample with Contour SGLD": [[3, "sample-with-contour-sgld"]], "Sample with HMC": [[1, "sample-with-hmc"]], "Sample with NUTS": [[1, "sample-with-nuts"]], "Sampler Overview": [[9, "sampler-overview"]], "Sampling": [[8, "sampling"], [9, "sampling"]], "Sampling From a Bimodal Potential": [[1, "sampling-from-a-bimodal-potential"]], "Sampling from the Rastrigin Potential": [[1, "sampling-from-the-rastrigin-potential"]], "Sampling with BlackJAX": [[16, "sampling-with-blackjax"]], "Sampling with SGHMC": [[15, "sampling-with-sghmc"]], "Setup": [[13, "setup"]], "Some Caveats": [[6, "some-caveats"]], "Some Utility Functions": [[0, "some-utility-functions"]], "Sparse regression": [[17, null]], "Step function": [[4, "step-function"]], "TL;DR": [[16, "tl-dr"]], "Technical setup": [[16, "technical-setup"]], "Tempered SMC with HMC Kernel": [[1, "tempered-smc-with-hmc-kernel"], [1, "id2"]], "The Data": [[6, "the-data"], [14, "the-data"]], "The Model": [[6, "the-model"], [14, "the-model"]], "The Sampling Book Project": [[7, null]], "The data": [[10, "the-data"]], "The model": [[10, "the-model"]], "Tuning inner kernel parameters of SMC": [[2, null]], "Use Tempered SMC to Improve Exploration of MCMC Methods.": [[1, null]], "Using a PPL": [[12, "using-a-ppl"]], "Utility Functions for Training and Testing": [[13, "utility-functions-for-training-and-testing"]], "Validate the choice of \\epsilon": [[5, "validate-the-choice-of-epsilon"]], "Velocity Verlet": [[0, "velocity-verlet"]], "Visualisation": [[16, "visualisation"]], "What\u2019s next": [[16, "what-s-next"]], "Yoshida": [[0, "yoshida"]]}, "docnames": ["algorithms/PeriodicOrbitalMCMC", "algorithms/TemperedSMC", "algorithms/TemperedSMCWithOptimizedInnerKernel", "algorithms/contour_sgld", "algorithms/cyclical_sgld", "algorithms/mclmc", "algorithms/pathfinder", "index", "models/GP_EllipticalSliceSampler", "models/GP_Marginal", "models/LogisticRegressionWithLatentGaussianSampler", "models/RegimeSwitchingModel", "models/change_of_variable_hmc", "models/hierarchical_bnn", "models/logistic_regression", "models/mlp", "models/probabilistic_ode_solver_parameter_estimation", "models/sparse_regression"], "envversion": {"sphinx": 62, "sphinx.domains.c": 3, "sphinx.domains.changeset": 1, "sphinx.domains.citation": 1, "sphinx.domains.cpp": 9, "sphinx.domains.index": 1, "sphinx.domains.javascript": 3, "sphinx.domains.math": 2, "sphinx.domains.python": 4, "sphinx.domains.rst": 2, "sphinx.domains.std": 2, "sphinx.ext.intersphinx": 1, "sphinxcontrib.bibtex": 9}, "filenames": ["algorithms/PeriodicOrbitalMCMC.md", "algorithms/TemperedSMC.md", "algorithms/TemperedSMCWithOptimizedInnerKernel.md", "algorithms/contour_sgld.md", "algorithms/cyclical_sgld.md", "algorithms/mclmc.md", "algorithms/pathfinder.md", "index.md", "models/GP_EllipticalSliceSampler.md", "models/GP_Marginal.md", "models/LogisticRegressionWithLatentGaussianSampler.md", "models/RegimeSwitchingModel.md", "models/change_of_variable_hmc.md", "models/hierarchical_bnn.md", "models/logistic_regression.md", "models/mlp.md", 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\ No newline at end of file