Source code for ott.problems.quadratic.gw_barycenter

# Copyright OTT-JAX
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import functools
from typing import Any, Dict, Literal, Optional, Sequence, Tuple, Union

import jax
import jax.numpy as jnp

from ott.geometry import costs, geometry, pointcloud, segment
from ott.math import utils as mu
from ott.problems.linear import barycenter_problem
from ott.problems.quadratic import quadratic_costs, quadratic_problem

__all__ = ["GWBarycenterProblem"]

# TODO(michalk8): better abstraction (common superclass for Wasserstein bary)
[docs]@jax.tree_util.register_pytree_node_class class GWBarycenterProblem(barycenter_problem.FreeBarycenterProblem): """(Fused) Gromov-Wasserstein barycenter problem :cite:`peyre:16,vayer:19`. Args: y: Array of shape ``[num_total_points, ndim]`` merging the points of all measures. Alternatively, already segmented array of shape ``[num_measures, max_measure_size, ndim]`` can be passed. See also :func:`~ott.geometry.segment.segment_point_cloud`. b: Array of shape ``[num_total_points,]`` containing the weights of all the points within the measures that define the barycenter problem. Same as ``y``, pre-segmented array of weights of shape ``[num_measures, max_measure_size]`` can be passed. If ``y`` is already pre-segmented, this array must be passed. weights: Array of shape ``[num_measures,]`` containing the weights of the barycenter problem. costs: Alternative to ``y``, an array of shape ``[num_measures, max_measure_size, max_measure_size]`` that defines padded cost matrices for each measure. Used in the quadratic term. Only one of ``y`` and ``cost`` can be specified. y_fused: Array of shape ``[num_total_points, ndim_fused]`` containing the data of the points of all measures used to define the linear term in the fused case. Same as ``y``, it can be specified as a pre-segmented array of shape ``[num_measures, max_measure_size, ndim_fused]``. gw_loss: Gromov-Wasserstein loss. fused_penalty: Multiplier of the linear term. Only used when ``y_fused != None``. scale_cost: Scaling of cost matrices passed to geometries. kwargs: Keyword arguments for :class:`~ott.problems.linear.barycenter_problem.BarycenterProblem`. """ def __init__( self, y: Optional[jnp.ndarray] = None, b: Optional[jnp.ndarray] = None, weights: Optional[jnp.ndarray] = None, costs: Optional[jnp.ndarray] = None, y_fused: Optional[jnp.ndarray] = None, fused_penalty: float = 1.0, gw_loss: Literal["sqeucl", "kl"] = "sqeucl", scale_cost: Union[int, float, Literal["mean", "max_cost"]] = 1.0, **kwargs: Any, ): assert y is None or costs is None, "Cannot specify both `y` and `costs`." y = y if costs is None else costs super().__init__(y=y, b=b, weights=weights, **kwargs) self._y_fused = y_fused self.fused_penalty = fused_penalty self._loss_name = gw_loss self.scale_cost = scale_cost self._y_as_costs = costs is not None if self._y_as_costs: # (num_measures, max_measure_size, max_measure_size) _, n, m = self._y.shape assert n == m, "Cost matrices must be square." if self.is_fused: seg_y = self._is_segmented seg_fused = self._y_fused.ndim == 3 if seg_y and seg_fused: # (num_measures, max_measure_size, ndim_fused) # (num_measures, max_measure_size, ndim) assert self._y_fused.shape[:2] == self._y.shape[:2] if not seg_y and not seg_fused: # (num_total_points, ndim_fused), (num_total_points, ndim) assert self._y_fused.shape[0] == self._y.shape[0] # TODO(michalk8): in the future, consider checking the other 2 cases # using `segmented_y` and `segmented_y_fused`?
[docs] def update_barycenter( self, transports: jnp.ndarray, a: jnp.ndarray ) -> jnp.ndarray: """Update the barycenter cost matrix. Uses the eq. 14 and 15 of :cite:`peyre:16`. Args: transports: Transport maps of shape ``[num_measures, bar_size, max_measure_size]``. a: Barycenter weights of shape ``[bar_size,]``. Returns: Update cost matrix of shape ``[bar_size, bar_size]``. """ @functools.partial(jax.vmap, in_axes=[0, 0, 0, None]) def project( y: jnp.ndarray, b: jnp.ndarray, transport: jnp.ndarray, fn: Optional[quadratic_costs.Loss], ) -> jnp.ndarray: geom = self._create_y_geometry(y, mask=b > 0.) fn, lin = (None, True) if fn is None else (fn.func, fn.is_linear) tmp = geom.apply_cost( transport.T, axis=0, fn=fn, is_linear=lin, ) return transport @ tmp fn = None if self._loss_name == "sqeucl" else self.gw_loss.h2 y, b = self.segmented_y_b weights = self.weights[:, None, None] barycenter = jnp.sum(weights * project(y, b, transports, fn), axis=0) inv_a = jnp.where(a > 0, 1.0 / a, 1.0) barycenter = (barycenter * inv_a[None, :]) * inv_a[:, None] # TODO(michalk8): in future, use `isinstanceof(self.gw_loss, ...)` # once refactoring has been done if self._loss_name == "kl": return jnp.exp(barycenter) return barycenter
[docs] def update_features(self, transports: jnp.ndarray, a: jnp.ndarray) -> Optional[jnp.ndarray]: """Update the barycenter features in the fused case :cite:`vayer:19`. Uses :cite:`cuturi:14` eq. 8, and is implemented only for the :class:`~ott.geometry.costs.SqEuclidean` cost. Args: transports: Transport maps of shape ``[num_measures, bar_size, max_measure_size]``. a: Barycenter weights of shape ``[bar_size,]``. Returns: Updated features of shape ``[bar_size, ndim_fused]``. """ if not self.is_fused: raise RuntimeError( "Updating features is available only in the fused case." ) y_fused = self.segmented_y_fused weights = self.weights[:, None, None] inv_a = jnp.where(a > 0, 1.0 / a, 1.0) transports = transports * inv_a[None, :, None] if self._loss_name == "sqeucl": cost_fn = costs.SqEuclidean() return jnp.sum( weights * mu.barycentric_projection(transports, y_fused, cost_fn), axis=0 ) raise NotImplementedError(self._loss_name)
def _create_bary_geometry( self, cost_matrix: jnp.ndarray, mask: Optional[jnp.ndarray] = None ) -> geometry.Geometry: return geometry.Geometry( cost_matrix=cost_matrix, src_mask=mask, tgt_mask=mask, epsilon=self.epsilon, scale_cost=self.scale_cost ) def _create_y_geometry( self, y: jnp.ndarray, mask: Optional[jnp.ndarray] = None ) -> geometry.Geometry: if self._y_as_costs: assert y.shape[0] == y.shape[1], y.shape return geometry.Geometry( y, epsilon=self.epsilon, scale_cost=self.scale_cost, src_mask=mask, tgt_mask=mask ) return pointcloud.PointCloud( y, epsilon=self.epsilon, scale_cost=self.scale_cost, cost_fn=self.cost_fn, src_mask=mask, tgt_mask=mask ) def _create_fused_geometry( self, x: jnp.ndarray, y: jnp.ndarray, src_mask: Optional[jnp.ndarray] = None, tgt_mask: Optional[jnp.ndarray] = None ) -> pointcloud.PointCloud: return pointcloud.PointCloud( x, y, cost_fn=self.cost_fn, epsilon=self.epsilon, scale_cost=self.scale_cost, src_mask=src_mask, tgt_mask=tgt_mask ) def _create_problem( self, state: "GWBarycenterState", # noqa: F821 y: jnp.ndarray, b: jnp.ndarray, f: Optional[jnp.ndarray] = None ) -> quadratic_problem.QuadraticProblem: # TODO(michalk8): in future, mask in the problem for convenience? bary_mask = state.a > 0. y_mask = b > 0. geom_xx = self._create_bary_geometry(state.cost, mask=bary_mask) geom_yy = self._create_y_geometry(y, mask=y_mask) if self.is_fused: assert f is not None assert state.x.shape[1] == f.shape[1] geom_xy = self._create_fused_geometry( state.x, f, src_mask=bary_mask, tgt_mask=y_mask ) else: geom_xy = None return quadratic_problem.QuadraticProblem( geom_xx=geom_xx, geom_yy=geom_yy, geom_xy=geom_xy, a=state.a, b=b, fused_penalty=self.fused_penalty, ) @property def is_fused(self) -> bool: """Whether the problem is fused.""" return self._y_fused is not None @property def segmented_y_fused(self) -> Optional[jnp.ndarray]: """Feature array of shape used in the fused case.""" if not self.is_fused or self._y_fused.ndim == 3: return self._y_fused y_fused, _ = segment.segment_point_cloud( x=self._y_fused, padding_vector=self.cost_fn._padder(self.ndim_fused), **self._kwargs ) return y_fused @property def ndim(self) -> Optional[int]: # noqa: D102 return None if self._y_as_costs else self._y.shape[-1] @property def ndim_fused(self) -> Optional[int]: """Number of dimensions of the fused term.""" return self._y_fused.shape[-1] if self.is_fused else None @property def gw_loss(self) -> quadratic_costs.GWLoss: """Gromov-Wasserstein loss.""" # TODO(michalk8): custom losses would require inverting some fns; # ` some fns; # Writing_custom_interpreters_in_Jax.html#your-first-interpreter-invert` # might be useful if self._loss_name == "sqeucl": return quadratic_costs.make_square_loss() if self._loss_name == "kl": return quadratic_costs.make_kl_loss() raise NotImplementedError( f"Loss `{self._loss_name}` is not yet implemented." ) def tree_flatten(self) -> Tuple[Sequence[Any], Dict[str, Any]]: # noqa: D102 (y, b, weights), aux = super().tree_flatten() if self._y_as_costs: children = [None, b, weights, y] else: children = [y, b, weights, None] aux["fused_penalty"] = self.fused_penalty aux["gw_loss"] = self._loss_name aux["scale_cost"] = self.scale_cost return children + [self._y_fused], aux @classmethod def tree_unflatten( # noqa: D102 cls, aux_data: Dict[str, Any], children: Sequence[Any] ) -> "GWBarycenterProblem": y, b, weights, costs, y_fused = children return cls( y=y, b=b, weights=weights, costs=costs, y_fused=y_fused, **aux_data )