Porting kroneckernormal distribution to v4 (#4774)

Co-authored-by: Ricardo <ricardo.vieira1994@gmail.com>

Co-authored-by: Ricardo <ricardo.vieira1994@gmail.com>

Author: kc611

pymc3/distributions/multivariate.py

@@ -17,6 +17,8 @@
 
 import warnings
 
+from functools import reduce
+
 import aesara
 import aesara.tensor as at
 import numpy as np
@@ -45,7 +47,7 @@
 from pymc3.distributions.continuous import ChiSquared, Normal, assert_negative_support
 from pymc3.distributions.dist_math import bound, factln, logpow, multigammaln
 from pymc3.distributions.distribution import Continuous, Discrete
-from pymc3.math import kron_diag, kron_dot, kron_solve_lower, kronecker
+from pymc3.math import kron_diag, kron_dot
 
 __all__ = [
     "MvNormal",
@@ -1702,6 +1704,32 @@ def _distr_parameters_for_repr(self):
         return ["mu", "row" + mapping[self._rowcov_type], "col" + mapping[self._colcov_type]]
 
 
+class KroneckerNormalRV(RandomVariable):
+    name = "kroneckernormal"
+    ndim_supp = 2
+    ndims_params = [1, 0, 2]
+    dtype = "floatX"
+    _print_name = ("KroneckerNormal", "\\operatorname{KroneckerNormal}")
+
+    def _shape_from_params(self, dist_params, rep_param_idx=0, param_shapes=None):
+        return default_shape_from_params(1, dist_params, rep_param_idx, param_shapes)
+
+    def rng_fn(self, rng, mu, sigma, *covs, size=None):
+        size = size if size else covs[-1]
+        covs = covs[:-1] if covs[-1] == size else covs
+
+        cov = reduce(linalg.kron, covs)
+
+        if sigma:
+            cov = cov + sigma ** 2 * np.eye(cov.shape[0])
+
+        x = multivariate_normal.rng_fn(rng=rng, mean=mu, cov=cov, size=size)
+        return x
+
+
+kroneckernormal = KroneckerNormalRV()
+
+
 class KroneckerNormal(Continuous):
     r"""
     Multivariate normal log-likelihood with Kronecker-structured covariance.
@@ -1790,160 +1818,79 @@ class KroneckerNormal(Continuous):
     ----------
     .. [1] Saatchi, Y. (2011). "Scalable inference for structured Gaussian process models"
     """
+    rv_op = kroneckernormal
 
-    def __init__(self, mu, covs=None, chols=None, evds=None, sigma=None, *args, **kwargs):
-        self._setup(covs, chols, evds, sigma)
-        super().__init__(*args, **kwargs)
-        self.mu = at.as_tensor_variable(mu)
-        self.mean = self.median = self.mode = self.mu
+    @classmethod
+    def dist(cls, mu, covs=None, chols=None, evds=None, sigma=None, *args, **kwargs):
 
-    def _setup(self, covs, chols, evds, sigma):
-        self.cholesky = Cholesky(lower=True, on_error="raise")
         if len([i for i in [covs, chols, evds] if i is not None]) != 1:
             raise ValueError(
                 "Incompatible parameterization. Specify exactly one of covs, chols, or evds."
             )
-        self._isEVD = False
-        self.sigma = sigma
-        self.is_noisy = self.sigma is not None and self.sigma != 0
-        if covs is not None:
-            self._cov_type = "cov"
-            self.covs = covs
-            if self.is_noisy:
-                # Noise requires eigendecomposition
-                eigh_map = map(eigh, covs)
-                self._setup_evd(eigh_map)
-            else:
-                # Otherwise use cholesky as usual
-                self.chols = list(map(self.cholesky, self.covs))
-                self.chol_diags = list(map(at.diag, self.chols))
-                self.sizes = at.as_tensor_variable([chol.shape[0] for chol in self.chols])
-                self.N = at.prod(self.sizes)
-        elif chols is not None:
-            self._cov_type = "chol"
-            if self.is_noisy:  # A strange case...
-                # Noise requires eigendecomposition
-                covs = [at.dot(chol, chol.T) for chol in chols]
-                eigh_map = map(eigh, covs)
-                self._setup_evd(eigh_map)
-            else:
-                self.chols = chols
-                self.chol_diags = list(map(at.diag, self.chols))
-                self.sizes = at.as_tensor_variable([chol.shape[0] for chol in self.chols])
-                self.N = at.prod(self.sizes)
-        else:
-            self._cov_type = "evd"
-            self._setup_evd(evds)
 
-    def _setup_evd(self, eigh_iterable):
-        self._isEVD = True
-        eigs_sep, Qs = zip(*eigh_iterable)  # Unzip
-        self.Qs = list(map(at.as_tensor_variable, Qs))
-        self.QTs = list(map(at.transpose, self.Qs))
-
-        self.eigs_sep = list(map(at.as_tensor_variable, eigs_sep))
-        self.eigs = kron_diag(*self.eigs_sep)  # Combine separate eigs
-        if self.is_noisy:
-            self.eigs += self.sigma ** 2
-        self.N = self.eigs.shape[0]
-
-    def _setup_random(self):
-        if not hasattr(self, "mv_params"):
-            self.mv_params = {"mu": self.mu}
-            if self._cov_type == "cov":
-                cov = kronecker(*self.covs)
-                if self.is_noisy:
-                    cov = cov + self.sigma ** 2 * at.identity_like(cov)
-                self.mv_params["cov"] = cov
-            elif self._cov_type == "chol":
-                if self.is_noisy:
-                    covs = []
-                    for eig, Q in zip(self.eigs_sep, self.Qs):
-                        cov_i = at.dot(Q, at.dot(at.diag(eig), Q.T))
-                        covs.append(cov_i)
-                    cov = kronecker(*covs)
-                    if self.is_noisy:
-                        cov = cov + self.sigma ** 2 * at.identity_like(cov)
-                    self.mv_params["chol"] = self.cholesky(cov)
-                else:
-                    self.mv_params["chol"] = kronecker(*self.chols)
-            elif self._cov_type == "evd":
-                covs = []
-                for eig, Q in zip(self.eigs_sep, self.Qs):
-                    cov_i = at.dot(Q, at.dot(at.diag(eig), Q.T))
-                    covs.append(cov_i)
-                cov = kronecker(*covs)
-                if self.is_noisy:
-                    cov = cov + self.sigma ** 2 * at.identity_like(cov)
-                self.mv_params["cov"] = cov
+        sigma = sigma if sigma else 0
 
-    def random(self, point=None, size=None):
+        if chols is not None:
+            covs = [chol.dot(chol.T) for chol in chols]
+        elif evds is not None:
+            eigh_iterable = evds
+            covs = []
+            eigs_sep, Qs = zip(*eigh_iterable)  # Unzip
+            for eig, Q in zip(eigs_sep, Qs):
+                cov_i = at.dot(Q, at.dot(at.diag(eig), Q.T))
+                covs.append(cov_i)
+
+        mu = at.as_tensor_variable(mu)
+
+        # mean = median = mode = mu
+        return super().dist([mu, sigma, *covs], **kwargs)
+
+    def logp(value, mu, sigma, *covs):
         """
-        Draw random values from Multivariate Normal distribution
-        with Kronecker-structured covariance.
+        Calculate log-probability of Multivariate Normal distribution
+        with Kronecker-structured covariance at specified value.
 
         Parameters
         ----------
-        point: dict, optional
-            Dict of variable values on which random values are to be
-            conditioned (uses default point if not specified).
-        size: int, optional
-            Desired size of random sample (returns one sample if not
-            specified).
+        value: numeric
+            Value for which log-probability is calculated.
 
         Returns
         -------
-        array
+        TensorVariable
         """
-        # Expand params into terms MvNormal can understand to force consistency
-        self._setup_random()
-        self.mv_params["shape"] = self.shape
-        dist = MvNormal.dist(**self.mv_params)
-        return dist.random(point, size)
-
-    def _quaddist(self, value):
-        """Computes the quadratic (x-mu)^T @ K^-1 @ (x-mu) and log(det(K))"""
+        # Computes the quadratic (x-mu)^T @ K^-1 @ (x-mu) and log(det(K))
         if value.ndim > 2 or value.ndim == 0:
-            raise ValueError("Invalid dimension for value: %s" % value.ndim)
+            raise ValueError(f"Invalid dimension for value: {value.ndim}")
         if value.ndim == 1:
             onedim = True
             value = value[None, :]
         else:
             onedim = False
 
-        delta = value - self.mu
-        if self._isEVD:
-            sqrt_quad = kron_dot(self.QTs, delta.T)
-            sqrt_quad = sqrt_quad / at.sqrt(self.eigs[:, None])
-            logdet = at.sum(at.log(self.eigs))
-        else:
-            sqrt_quad = kron_solve_lower(self.chols, delta.T)
-            logdet = 0
-            for chol_size, chol_diag in zip(self.sizes, self.chol_diags):
-                logchol = at.log(chol_diag) * self.N / chol_size
-                logdet += at.sum(2 * logchol)
+        delta = value - mu
+
+        eigh_iterable = map(eigh, covs)
+        eigs_sep, Qs = zip(*eigh_iterable)  # Unzip
+        Qs = list(map(at.as_tensor_variable, Qs))
+        QTs = list(map(at.transpose, Qs))
+
+        eigs_sep = list(map(at.as_tensor_variable, eigs_sep))
+        eigs = kron_diag(*eigs_sep)  # Combine separate eigs
+        eigs += sigma ** 2
+        N = eigs.shape[0]
+
+        sqrt_quad = kron_dot(QTs, delta.T)
+        sqrt_quad = sqrt_quad / at.sqrt(eigs[:, None])
+        logdet = at.sum(at.log(eigs))
+
         # Square each sample
         quad = at.batched_dot(sqrt_quad.T, sqrt_quad.T)
         if onedim:
             quad = quad[0]
-        return quad, logdet
 
-    def logp(self, value):
-        """
-        Calculate log-probability of Multivariate Normal distribution
-        with Kronecker-structured covariance at specified value.
-
-        Parameters
-        ----------
-        value: numeric
-            Value for which log-probability is calculated.
-
-        Returns
-        -------
-        TensorVariable
-        """
-        quad, logdet = self._quaddist(value)
-        return -(quad + logdet + self.N * at.log(2 * np.pi)) / 2.0
+        a = -(quad + logdet + N * at.log(2 * np.pi)) / 2.0
+        return a
 
     def _distr_parameters_for_repr(self):
         return ["mu"]

pymc3/tests/test_distributions.py

@@ -388,19 +388,19 @@ def matrix_normal_logpdf_chol(value, mu, rowchol, colchol):
     )
 
 
-def kron_normal_logpdf_cov(value, mu, covs, sigma):
+def kron_normal_logpdf_cov(value, mu, covs, sigma, size=None):
     cov = kronecker(*covs).eval()
     if sigma is not None:
         cov += sigma ** 2 * np.eye(*cov.shape)
     return scipy.stats.multivariate_normal.logpdf(value, mu, cov).sum()
 
 
-def kron_normal_logpdf_chol(value, mu, chols, sigma):
+def kron_normal_logpdf_chol(value, mu, chols, sigma, size=None):
     covs = [np.dot(chol, chol.T) for chol in chols]
     return kron_normal_logpdf_cov(value, mu, covs, sigma=sigma)
 
 
-def kron_normal_logpdf_evd(value, mu, evds, sigma):
+def kron_normal_logpdf_evd(value, mu, evds, sigma, size=None):
     covs = []
     for eigs, Q in evds:
         try:
@@ -1943,8 +1943,7 @@ def test_matrixnormal(self, n):
 
     @pytest.mark.parametrize("n", [2, 3])
     @pytest.mark.parametrize("m", [3])
-    @pytest.mark.parametrize("sigma", [None, 1.0])
-    @pytest.mark.xfail(reason="Distribution not refactored yet")
+    @pytest.mark.parametrize("sigma", [None, 1])
     def test_kroneckernormal(self, n, m, sigma):
         np.random.seed(5)
         N = n * m
@@ -1990,6 +1989,9 @@ def test_kroneckernormal(self, n, m, sigma):
         )
 
         dom = Domain([np.random.randn(2, N) * 0.1], edges=(None, None), shape=(2, N))
+        cov_args["size"] = 2
+        chol_args["size"] = 2
+        evd_args["size"] = 2
 
         self.check_logp(
             KroneckerNormal,