Improve tuning by skipping the first samples + add new experimental tuning method

RELEASE-NOTES.md

@@ -23,6 +23,8 @@
 - The `OrderedMultinomial` distribution has been added for use on ordinal data which are _aggregated_ by trial, like multinomial observations, whereas `OrderedLogistic` only accepts ordinal data in a _disaggregated_ format, like categorical
   observations (see [#4773](https://github.com/pymc-devs/pymc3/pull/4773)).
 - The `Polya-Gamma` distribution has been added (see [#4531](https://github.com/pymc-devs/pymc3/pull/4531)). To make use of this distribution, the [`polyagamma>=1.3.1`](https://pypi.org/project/polyagamma/) library must be installed and available in the user's environment.
+- A small change to the mass matrix tuning methods jitter+adapt_diag (the default) and adapt_diag improves performance early on during tuning for some models. [#5004](https://github.com/pymc-devs/pymc3/pull/5004)
+- New experimental mass matrix tuning method jitter+adapt_diag_grad. [#5004](https://github.com/pymc-devs/pymc3/pull/5004)
 - ...
 
 ### Maintenance

pymc3/sampling.py

@@ -287,25 +287,7 @@ def sample(
         by default. See ``discard_tuned_samples``.
     init : str
         Initialization method to use for auto-assigned NUTS samplers.
-
-        * auto: Choose a default initialization method automatically.
-          Currently, this is ``jitter+adapt_diag``, but this can change in the future.
-          If you depend on the exact behaviour, choose an initialization method explicitly.
-        * adapt_diag: Start with a identity mass matrix and then adapt a diagonal based on the
-          variance of the tuning samples. All chains use the test value (usually the prior mean)
-          as starting point.
-        * jitter+adapt_diag: Same as ``adapt_diag``, but add uniform jitter in [-1, 1] to the
-          starting point in each chain.
-        * advi+adapt_diag: Run ADVI and then adapt the resulting diagonal mass matrix based on the
-          sample variance of the tuning samples.
-        * advi+adapt_diag_grad: Run ADVI and then adapt the resulting diagonal mass matrix based
-          on the variance of the gradients during tuning. This is **experimental** and might be
-          removed in a future release.
-        * advi: Run ADVI to estimate posterior mean and diagonal mass matrix.
-        * advi_map: Initialize ADVI with MAP and use MAP as starting point.
-        * map: Use the MAP as starting point. This is discouraged.
-        * adapt_full: Adapt a dense mass matrix using the sample covariances
-
+        See `pm.init_nuts` for a list of all options.
     step : function or iterable of functions
         A step function or collection of functions. If there are variables without step methods,
         step methods for those variables will be assigned automatically.  By default the NUTS step
@@ -516,6 +498,7 @@ def sample(
                 random_seed=random_seed,
                 progressbar=progressbar,
                 jitter_max_retries=jitter_max_retries,
+                tune=tune,
                 **kwargs,
             )
             if start is None:
@@ -2078,6 +2061,7 @@ def init_nuts(
     random_seed=None,
     progressbar=True,
     jitter_max_retries=10,
+    tune=None,
     **kwargs,
 ):
     """Set up the mass matrix initialization for NUTS.
@@ -2099,11 +2083,11 @@ def init_nuts(
           as starting point.
         * jitter+adapt_diag: Same as ``adapt_diag``, but use test value plus a uniform jitter in
           [-1, 1] as starting point in each chain.
+        * jitter+adapt_diag_grad:
+          An experimental initialization method that uses information from gradients and samples
+          during tuning.
         * advi+adapt_diag: Run ADVI and then adapt the resulting diagonal mass matrix based on the
           sample variance of the tuning samples.
-        * advi+adapt_diag_grad: Run ADVI and then adapt the resulting diagonal mass matrix based
-          on the variance of the gradients during tuning. This is **experimental** and might be
-          removed in a future release.
         * advi: Run ADVI to estimate posterior mean and diagonal mass matrix.
         * advi_map: Initialize ADVI with MAP and use MAP as starting point.
         * map: Use the MAP as starting point. This is discouraged.
@@ -2174,24 +2158,24 @@ def init_nuts(
         var = np.ones_like(mean)
         n = len(var)
         potential = quadpotential.QuadPotentialDiagAdapt(n, mean, var, 10)
-    elif init == "advi+adapt_diag_grad":
-        approx: pm.MeanField = pm.fit(
-            random_seed=random_seed,
-            n=n_init,
-            method="advi",
-            model=model,
-            callbacks=cb,
-            progressbar=progressbar,
-            obj_optimizer=pm.adagrad_window,
+    elif init == "jitter+adapt_diag_grad":
+        start = _init_jitter(model, model.initial_point, chains, jitter_max_retries)
+        mean = np.mean([DictToArrayBijection.map(vals).data for vals in start], axis=0)
+        var = np.ones_like(mean)
+        n = len(var)
+
+        if tune is not None and tune > 250:
+            stop_adaptation = tune - 50
+        else:
+            stop_adaptation = None
+
+        potential = quadpotential.QuadPotentialDiagAdaptExp(
+            n,
+            mean,
+            alpha=0.02,
+            use_grads=True,
+            stop_adaptation=stop_adaptation,
         )
-        start = approx.sample(draws=chains)
-        start = list(start)
-        std_apoint = approx.std.eval()
-        cov = std_apoint ** 2
-        mean = approx.mean.get_value()
-        weight = 50
-        n = len(cov)
-        potential = quadpotential.QuadPotentialDiagAdaptGrad(n, mean, cov, weight)
     elif init == "advi+adapt_diag":
         approx = pm.fit(
             random_seed=random_seed,

pymc3/step_methods/hmc/nuts.py

@@ -253,9 +253,7 @@ def __init__(self, ndim, integrator, start, step_size, Emax):
         self.start_energy = np.array(start.energy)
 
         self.left = self.right = start
-        self.proposal = Proposal(
-            start.q.data, start.q_grad.data, start.energy, 1.0, start.model_logp
-        )
+        self.proposal = Proposal(start.q.data, start.q_grad, start.energy, 1.0, start.model_logp)
         self.depth = 0
         self.log_size = 0
         self.log_weighted_accept_sum = -np.inf
@@ -350,7 +348,7 @@ def _single_step(self, left, epsilon):
                 log_size = -energy_change
                 proposal = Proposal(
                     right.q.data,
-                    right.q_grad.data,
+                    right.q_grad,
                     right.energy,
                     log_p_accept_weighted,
                     right.model_logp,