Marginalapprox fix (#6076)

* switch from using DensityDist to using Potential

* increase tolerance on flaky tests, add test using find_MAP

* refactor MarginalApprox tests

* run precommit

* address comments, pass approx arg correctly, improve docstrings

* fix comments, make pass jitter through correctly, get rid of is_observed arg

pymc/gp/gp.py

@@ -685,18 +685,13 @@ def __init__(self, approx="VFE", *, mean_func=Zero(), cov_func=Constant(0.0)):
         super().__init__(mean_func=mean_func, cov_func=cov_func)
 
     def __add__(self, other):
-        # new_gp will default to FITC approx
         new_gp = super().__add__(other)
-        # make sure new gp has correct approx
         if not self.approx == other.approx:
             raise TypeError("Cannot add GPs with different approximations")
         new_gp.approx = self.approx
         return new_gp
 
-    # Use y as first argument, so that we can use functools.partial
-    # in marginal_likelihood instead of lambda. This makes pickling
-    # possible.
-    def _build_marginal_likelihood_logp(self, y, X, Xu, sigma, jitter):
+    def _build_marginal_likelihood_loglik(self, y, X, Xu, sigma, jitter):
         sigma2 = at.square(sigma)
         Kuu = self.cov_func(Xu)
         Kuf = self.cov_func(Xu, X)
@@ -725,9 +720,7 @@ def _build_marginal_likelihood_logp(self, y, X, Xu, sigma, jitter):
         quadratic = 0.5 * (at.dot(r, r_l) - at.dot(c, c))
         return -1.0 * (constant + logdet + quadratic + trace)
 
-    def marginal_likelihood(
-        self, name, X, Xu, y, noise=None, is_observed=True, jitter=JITTER_DEFAULT, **kwargs
-    ):
+    def marginal_likelihood(self, name, X, Xu, y, noise=None, jitter=JITTER_DEFAULT, **kwargs):
         R"""
         Returns the approximate marginal likelihood distribution, given the input
         locations `X`, inducing point locations `Xu`, data `y`, and white noise
@@ -747,9 +740,6 @@ def marginal_likelihood(
             noise.  Must have shape `(n, )`.
         noise: scalar, Variable
             Standard deviation of the Gaussian noise.
-        is_observed: bool
-            Whether to set `y` as an `observed` variable in the `model`.
-            Default is `True`.
         jitter: scalar
             A small correction added to the diagonal of positive semi-definite
             covariance matrices to ensure numerical stability.
@@ -767,38 +757,8 @@ def marginal_likelihood(
         else:
             self.sigma = noise
 
-        if is_observed:
-            return pm.DensityDist(
-                name,
-                X,
-                Xu,
-                self.sigma,
-                jitter,
-                logp=self._build_marginal_likelihood_logp,
-                observed=y,
-                ndims_params=[2, 2, 0],
-                size=X.shape[0],
-                **kwargs,
-            )
-        else:
-            warnings.warn(
-                "The 'is_observed' argument has been deprecated.  If the GP is "
-                "unobserved use gp.Latent instead.",
-                FutureWarning,
-            )
-            return pm.DensityDist(
-                name,
-                X,
-                Xu,
-                self.sigma,
-                jitter,
-                logp=self._build_marginal_likelihood_logp,
-                observed=y,
-                ndims_params=[2, 2, 0],
-                # ndim_supp=1,
-                size=X.shape[0],
-                **kwargs,
-            )
+        approx_loglik = self._build_marginal_likelihood_loglik(y, X, Xu, noise, jitter)
+        pm.Potential(f"marginalapprox_loglik_{name}", approx_loglik, **kwargs)
 
     def _build_conditional(
         self, Xnew, pred_noise, diag, X, Xu, y, sigma, cov_total, mean_total, jitter

pymc/tests/test_gp.py

@@ -846,63 +846,71 @@ def testLatent2(self):
 
 class TestMarginalVsMarginalApprox:
     R"""
-    Compare logp of models Marginal and MarginalApprox.
-    Should be nearly equal when inducing points are same as inputs.
+    Compare test fits of models Marginal and MarginalApprox.
     """
 
     def setup_method(self):
-        X = np.random.randn(50, 3)
-        y = np.random.randn(50)
-        Xnew = np.random.randn(60, 3)
-        pnew = np.random.randn(60)
-        with pm.Model() as model:
-            cov_func = pm.gp.cov.ExpQuad(3, [0.1, 0.2, 0.3])
-            mean_func = pm.gp.mean.Constant(0.5)
-            gp = pm.gp.Marginal(mean_func=mean_func, cov_func=cov_func)
-            sigma = 0.1
-            f = gp.marginal_likelihood("f", X, y, noise=sigma)
-            p = gp.conditional("p", Xnew)
-        self.logp = model.compile_logp()({"p": pnew})
-        self.X = X
-        self.Xnew = Xnew
-        self.y = y
-        self.sigma = sigma
-        self.pnew = pnew
-        self.gp = gp
+        self.sigma = 0.1
+        self.x = np.linspace(-5, 5, 30)
+        self.y = np.random.normal(0.25 * self.x, self.sigma)
+        with pm.Model() as model:
+            cov_func = pm.gp.cov.Linear(1, c=0.0)
+            c = pm.Normal("c", mu=20.0, sigma=100.0)  # far from true value
+            mean_func = pm.gp.mean.Constant(c)
+            self.gp = pm.gp.Marginal(mean_func=mean_func, cov_func=cov_func)
+            sigma = pm.HalfNormal("sigma", sigma=100)
+            self.gp.marginal_likelihood("lik", self.x[:, None], self.y, sigma)
+            self.map_full = pm.find_MAP(method="bfgs")  # bfgs seems to work much better than lbfgsb
+
+        self.x_new = np.linspace(-6, 6, 20)
+
+        # Include additive Gaussian noise, return diagonal of predicted covariance matrix
+        with model:
+            self.pred_mu, self.pred_var = self.gp.predict(
+                self.x_new[:, None], point=self.map_full, pred_noise=True, diag=True
+            )
 
-    @pytest.mark.parametrize("approx", ["FITC", "VFE", "DTC"])
-    def testApproximations(self, approx):
-        with pm.Model() as model:
-            cov_func = pm.gp.cov.ExpQuad(3, [0.1, 0.2, 0.3])
-            mean_func = pm.gp.mean.Constant(0.5)
-            gp = pm.gp.MarginalApprox(mean_func=mean_func, cov_func=cov_func, approx=approx)
-            f = gp.marginal_likelihood("f", self.X, self.X, self.y, self.sigma)
-            p = gp.conditional("p", self.Xnew)
-        approx_logp = model.compile_logp()({"p": self.pnew})
-        npt.assert_allclose(approx_logp, self.logp, atol=0, rtol=1e-2)
+        # Dont include additive Gaussian noise, return full predicted covariance matrix
+        with model:
+            self.pred_mu, self.pred_covar = self.gp.predict(
+                self.x_new[:, None], point=self.map_full, pred_noise=False, diag=False
+            )
 
     @pytest.mark.parametrize("approx", ["FITC", "VFE", "DTC"])
-    def testPredictVar(self, approx):
+    def test_fits_and_preds(self, approx):
+        """Get MAP estimate for GP approximation, compare results and predictions to what's returned
+        by an unapproximated GP.  The tolerances are fairly wide, but narrow relative to initial
+        values of the unknown parameters.
+        """
+
         with pm.Model() as model:
-            cov_func = pm.gp.cov.ExpQuad(3, [0.1, 0.2, 0.3])
-            mean_func = pm.gp.mean.Constant(0.5)
+            cov_func = pm.gp.cov.Linear(1, c=0.0)
+            c = pm.Normal("c", mu=20.0, sigma=100.0, initval=-500.0)
+            mean_func = pm.gp.mean.Constant(c)
             gp = pm.gp.MarginalApprox(mean_func=mean_func, cov_func=cov_func, approx=approx)
-            f = gp.marginal_likelihood("f", self.X, self.X, self.y, self.sigma)
-            mu1, var1 = self.gp.predict(self.Xnew, diag=True)
-            mu2, var2 = gp.predict(self.Xnew, diag=True)
-        npt.assert_allclose(mu1, mu2, atol=0, rtol=1e-3)
-        npt.assert_allclose(var1, var2, atol=0, rtol=1e-3)
+            sigma = pm.HalfNormal("sigma", sigma=100, initval=50.0)
+            gp.marginal_likelihood("lik", self.x[:, None], self.x[:, None], self.y, sigma)
+            map_approx = pm.find_MAP(method="bfgs")
+
+        # Check MAP gets approximately correct result
+        npt.assert_allclose(self.map_full["c"], map_approx["c"], atol=0.01, rtol=0.1)
+        npt.assert_allclose(self.map_full["sigma"], map_approx["sigma"], atol=0.01, rtol=0.1)
+
+        # Check that predict (and conditional) work, include noise, with diagonal non-full pred var.
+        with model:
+            pred_mu_approx, pred_var_approx = gp.predict(
+                self.x_new[:, None], point=map_approx, pred_noise=True, diag=True
+            )
+        npt.assert_allclose(self.pred_mu, pred_mu_approx, atol=0.0, rtol=0.1)
+        npt.assert_allclose(self.pred_var, pred_var_approx, atol=0.0, rtol=0.1)
 
-    def testPredictCov(self):
-        with pm.Model() as model:
-            cov_func = pm.gp.cov.ExpQuad(3, [0.1, 0.2, 0.3])
-            mean_func = pm.gp.mean.Constant(0.5)
-            gp = pm.gp.MarginalApprox(mean_func=mean_func, cov_func=cov_func, approx="DTC")
-            f = gp.marginal_likelihood("f", self.X, self.X, self.y, self.sigma)
-            mu1, cov1 = self.gp.predict(self.Xnew, pred_noise=True)
-            mu2, cov2 = gp.predict(self.Xnew, pred_noise=True)
-        npt.assert_allclose(mu1, mu2, atol=0, rtol=1e-3)
-        npt.assert_allclose(cov1, cov2, atol=0, rtol=1e-3)
+        # Check that predict (and conditional) work, no noise, full pred covariance.
+        with model:
+            pred_mu_approx, pred_var_approx = gp.predict(
+                self.x_new[:, None], point=map_approx, pred_noise=True, diag=True
+            )
+        npt.assert_allclose(self.pred_mu, pred_mu_approx, atol=0.0, rtol=0.1)
+        npt.assert_allclose(self.pred_var, pred_var_approx, atol=0.0, rtol=0.1)
 
 
 class TestGPAdditive: