Allow multivariate components to share latent states (#558)

* Add shared_state argument to LevelTrendComponent

* Add shared_state argument to TimeSeasonality

* Add shared_state argument to CycleComponent

* Add shared_state argument to FrequencySeasonality

* Add shared_state argument to RegressionComponent

* Add shared_state argument to AutoregressiveComponent

* Add shared_state argument to MeasurementError

* Pass `share_states` to `super` calls

* Add shared_states flag in core.py

* Fix cycle tests after param renaming

---------

Co-authored-by: Jonathan Dekermanjian <Jonathan.Dekermanjian@gmail.com>
Co-authored-by: Alexandre Andorra <andorra.alexandre@gmail.com>

Author: 3 people

pymc_extras/statespace/models/structural/components/autoregressive.py

@@ -23,6 +23,11 @@ class AutoregressiveComponent(Component):
     observed_state_names: list[str] | None, default None
         List of strings for observed state labels. If None, defaults to ["data"].
 
+    share_states: bool, default False
+        Whether latent states are shared across the observed states. If True, there will be only one set of latent
+        states, which are observed by all observed states. If False, each observed state has its own set of
+        latent states. This argument has no effect if `k_endog` is 1.
+
     Notes
     -----
     An autoregressive component can be thought of as a way o introducing serially correlated errors into the model.
@@ -73,45 +78,59 @@ def __init__(
         order: int = 1,
         name: str = "auto_regressive",
         observed_state_names: list[str] | None = None,
+        share_states: bool = False,
     ):
         if observed_state_names is None:
             observed_state_names = ["data"]
 
-        k_posdef = k_endog = len(observed_state_names)
+        k_endog = len(observed_state_names)
+        k_endog_effective = k_posdef = 1 if share_states else k_endog
 
         order = order_to_mask(order)
         ar_lags = np.flatnonzero(order).ravel().astype(int) + 1
         k_states = len(order)
 
+        self.share_states = share_states
         self.order = order
         self.ar_lags = ar_lags
 
         super().__init__(
             name=name,
             k_endog=k_endog,
-            k_states=k_states * k_endog,
+            k_states=k_states * k_endog_effective,
             k_posdef=k_posdef,
             measurement_error=True,
             combine_hidden_states=True,
             observed_state_names=observed_state_names,
-            obs_state_idxs=np.tile(np.r_[[1.0], np.zeros(k_states - 1)], k_endog),
+            obs_state_idxs=np.tile(np.r_[[1.0], np.zeros(k_states - 1)], k_endog_effective),
+            share_states=share_states,
         )
 
     def populate_component_properties(self):
-        k_states = self.k_states // self.k_endog  # this is also the number of AR lags
+        k_endog = self.k_endog
+        k_endog_effective = 1 if self.share_states else k_endog
 
-        self.state_names = [
-            f"L{i + 1}[{state_name}]"
-            for state_name in self.observed_state_names
-            for i in range(k_states)
-        ]
+        k_states = self.k_states // k_endog_effective  # this is also the number of AR lags
+        base_names = [f"L{i + 1}_{self.name}" for i in range(k_states)]
+
+        if self.share_states:
+            self.state_names = [f"{name}[shared]" for name in base_names]
+            self.shock_names = [f"{self.name}[shared]"]
+        else:
+            self.state_names = [
+                f"{name}[{state_name}]"
+                for state_name in self.observed_state_names
+                for name in base_names
+            ]
+            self.shock_names = [
+                f"{self.name}[{obs_name}]" for obs_name in self.observed_state_names
+            ]
 
-        self.shock_names = [f"{self.name}[{obs_name}]" for obs_name in self.observed_state_names]
         self.param_names = [f"params_{self.name}", f"sigma_{self.name}"]
         self.param_dims = {f"params_{self.name}": (f"lag_{self.name}",)}
         self.coords = {f"lag_{self.name}": self.ar_lags.tolist()}
 
-        if self.k_endog > 1:
+        if k_endog_effective > 1:
             self.param_dims[f"params_{self.name}"] = (
                 f"endog_{self.name}",
                 f"lag_{self.name}",
@@ -140,26 +159,29 @@ def populate_component_properties(self):
 
     def make_symbolic_graph(self) -> None:
         k_endog = self.k_endog
-        k_states = self.k_states // k_endog
+        k_endog_effective = 1 if self.share_states else k_endog
+
+        k_states = self.k_states // k_endog_effective
         k_posdef = self.k_posdef
 
         k_nonzero = int(sum(self.order))
         ar_params = self.make_and_register_variable(
-            f"params_{self.name}", shape=(k_nonzero,) if k_endog == 1 else (k_endog, k_nonzero)
+            f"params_{self.name}",
+            shape=(k_nonzero,) if k_endog_effective == 1 else (k_endog_effective, k_nonzero),
         )
         sigma_ar = self.make_and_register_variable(
-            f"sigma_{self.name}", shape=() if k_endog == 1 else (k_endog,)
+            f"sigma_{self.name}", shape=() if k_endog_effective == 1 else (k_endog_effective,)
         )
 
-        if k_endog == 1:
+        if k_endog_effective == 1:
             T = pt.eye(k_states, k=-1)
             ar_idx = (np.zeros(k_nonzero, dtype="int"), np.nonzero(self.order)[0])
             T = T[ar_idx].set(ar_params)
 
         else:
             transition_matrices = []
 
-            for i in range(k_endog):
+            for i in range(k_endog_effective):
                 T = pt.eye(k_states, k=-1)
                 ar_idx = (np.zeros(k_nonzero, dtype="int"), np.nonzero(self.order)[0])
                 T = T[ar_idx].set(ar_params[i])
@@ -171,18 +193,21 @@ def make_symbolic_graph(self) -> None:
         self.ssm["transition", :, :] = T
 
         R = np.eye(k_states)
-        R_mask = np.full((k_states), False)
+        R_mask = np.full((k_states,), False)
         R_mask[0] = True
         R = R[:, R_mask]
 
         self.ssm["selection", :, :] = pt.specify_shape(
-            pt.linalg.block_diag(*[R for _ in range(k_endog)]), (self.k_states, self.k_posdef)
+            pt.linalg.block_diag(*[R for _ in range(k_endog_effective)]), (self.k_states, k_posdef)
         )
 
-        Z = pt.zeros((1, k_states))[0, 0].set(1.0)
-        self.ssm["design", :, :] = pt.specify_shape(
-            pt.linalg.block_diag(*[Z for _ in range(k_endog)]), (self.k_endog, self.k_states)
-        )
+        Zs = [pt.zeros((1, k_states))[0, 0].set(1.0) for _ in range(k_endog)]
+
+        if self.share_states:
+            Z = pt.join(0, *Zs)
+        else:
+            Z = pt.linalg.block_diag(*Zs)
+        self.ssm["design", :, :] = pt.specify_shape(Z, (k_endog, self.k_states))
 
         cov_idx = ("state_cov", *np.diag_indices(k_posdef))
         self.ssm[cov_idx] = sigma_ar**2

pymc_extras/statespace/models/structural/components/cycle.py

@@ -43,6 +43,11 @@ class CycleComponent(Component):
         Names of the observed state variables. For univariate time series, defaults to ``["data"]``.
         For multivariate time series, specify a list of names for each endogenous variable.
 
+    share_states: bool, default False
+        Whether latent states are shared across the observed states. If True, there will be only one set of latent
+        states, which are observed by all observed states. If False, each observed state has its own set of
+        latent states. This argument has no effect if `k_endog` is 1.
+
     Notes
     -----
     The cycle component is very similar in implementation to the frequency domain seasonal component, expect that it
@@ -155,6 +160,7 @@ def __init__(
         dampen: bool = False,
         innovations: bool = True,
         observed_state_names: list[str] | None = None,
+        share_states: bool = False,
     ):
         if observed_state_names is None:
             observed_state_names = ["data"]
@@ -167,6 +173,7 @@ def __init__(
             cycle = int(cycle_length) if cycle_length is not None else "Estimate"
             name = f"Cycle[s={cycle}, dampen={dampen}, innovations={innovations}]"
 
+        self.share_states = share_states
         self.estimate_cycle_length = estimate_cycle_length
         self.cycle_length = cycle_length
         self.innovations = innovations
@@ -175,8 +182,8 @@ def __init__(
 
         k_endog = len(observed_state_names)
 
-        k_states = 2 * k_endog
-        k_posdef = 2 * k_endog
+        k_states = 2 if share_states else 2 * k_endog
+        k_posdef = 2 if share_states else 2 * k_endog
 
         obs_state_idx = np.zeros(k_states)
         obs_state_idx[slice(0, k_states, 2)] = 1
@@ -190,21 +197,26 @@ def __init__(
             combine_hidden_states=True,
             obs_state_idxs=obs_state_idx,
             observed_state_names=observed_state_names,
+            share_states=share_states,
         )
 
     def make_symbolic_graph(self) -> None:
+        k_endog = self.k_endog
+        k_endog_effective = 1 if self.share_states else k_endog
+
         Z = np.array([1.0, 0.0]).reshape((1, -1))
-        design_matrix = block_diag(*[Z for _ in range(self.k_endog)])
+        design_matrix = block_diag(*[Z for _ in range(k_endog_effective)])
         self.ssm["design", :, :] = pt.as_tensor_variable(design_matrix)
 
         # selection matrix R defines structure of innovations (always identity for cycle components)
         # when innovations=False, state cov Q=0, hence R @ Q @ R.T = 0
         R = np.eye(2)  # 2x2 identity for each cycle component
-        selection_matrix = block_diag(*[R for _ in range(self.k_endog)])
+        selection_matrix = block_diag(*[R for _ in range(k_endog_effective)])
         self.ssm["selection", :, :] = pt.as_tensor_variable(selection_matrix)
 
         init_state = self.make_and_register_variable(
-            f"params_{self.name}", shape=(self.k_endog, 2) if self.k_endog > 1 else (self.k_states,)
+            f"params_{self.name}",
+            shape=(k_endog_effective, 2) if k_endog_effective > 1 else (self.k_states,),
         )
         self.ssm["initial_state", :] = init_state.ravel()
 
@@ -219,37 +231,45 @@ def make_symbolic_graph(self) -> None:
             rho = 1
 
         T = rho * _frequency_transition_block(lamb, j=1)
-        transition = block_diag(*[T for _ in range(self.k_endog)])
+        transition = block_diag(*[T for _ in range(k_endog_effective)])
         self.ssm["transition"] = pt.specify_shape(transition, (self.k_states, self.k_states))
 
         if self.innovations:
-            if self.k_endog == 1:
+            if k_endog_effective == 1:
                 sigma_cycle = self.make_and_register_variable(f"sigma_{self.name}", shape=())
                 self.ssm["state_cov", :, :] = pt.eye(self.k_posdef) * sigma_cycle**2
             else:
                 sigma_cycle = self.make_and_register_variable(
-                    f"sigma_{self.name}", shape=(self.k_endog,)
+                    f"sigma_{self.name}", shape=(k_endog_effective,)
                 )
                 state_cov = block_diag(
-                    *[pt.eye(2) * sigma_cycle[i] ** 2 for i in range(self.k_endog)]
+                    *[pt.eye(2) * sigma_cycle[i] ** 2 for i in range(k_endog_effective)]
                 )
                 self.ssm["state_cov"] = pt.specify_shape(state_cov, (self.k_states, self.k_states))
         else:
             # explicitly set state cov to 0 when no innovations
             self.ssm["state_cov", :, :] = pt.zeros((self.k_posdef, self.k_posdef))
 
     def populate_component_properties(self):
-        self.state_names = [
-            f"{f}_{self.name}[{var_name}]" if self.k_endog > 1 else f"{f}_{self.name}"
-            for var_name in self.observed_state_names
-            for f in ["Cos", "Sin"]
-        ]
+        k_endog = self.k_endog
+        k_endog_effective = 1 if self.share_states else k_endog
+
+        base_names = [f"{f}_{self.name}" for f in ["Cos", "Sin"]]
+
+        if self.share_states:
+            self.state_names = [f"{name}[shared]" for name in base_names]
+        else:
+            self.state_names = [
+                f"{name}[{var_name}]" if k_endog_effective > 1 else name
+                for var_name in self.observed_state_names
+                for name in base_names
+            ]
 
         self.param_names = [f"params_{self.name}"]
 
-        if self.k_endog == 1:
+        if k_endog_effective == 1:
             self.param_dims = {f"params_{self.name}": (f"state_{self.name}",)}
-            self.coords = {f"state_{self.name}": self.state_names}
+            self.coords = {f"state_{self.name}": base_names}
             self.param_info = {
                 f"params_{self.name}": {
                     "shape": (2,),
@@ -265,7 +285,7 @@ def populate_component_properties(self):
             }
             self.param_info = {
                 f"params_{self.name}": {
-                    "shape": (self.k_endog, 2),
+                    "shape": (k_endog_effective, 2),
                     "constraints": None,
                     "dims": (f"endog_{self.name}", f"state_{self.name}"),
                 }
@@ -274,22 +294,22 @@ def populate_component_properties(self):
         if self.estimate_cycle_length:
             self.param_names += [f"length_{self.name}"]
             self.param_info[f"length_{self.name}"] = {
-                "shape": () if self.k_endog == 1 else (self.k_endog,),
+                "shape": () if k_endog_effective == 1 else (k_endog_effective,),
                 "constraints": "Positive, non-zero",
-                "dims": None if self.k_endog == 1 else (f"endog_{self.name}",),
+                "dims": None if k_endog_effective == 1 else (f"endog_{self.name}",),
             }
 
         if self.dampen:
             self.param_names += [f"dampening_factor_{self.name}"]
             self.param_info[f"dampening_factor_{self.name}"] = {
-                "shape": () if self.k_endog == 1 else (self.k_endog,),
+                "shape": () if k_endog_effective == 1 else (k_endog_effective,),
                 "constraints": "0 < x ≤ 1",
-                "dims": None if self.k_endog == 1 else (f"endog_{self.name}",),
+                "dims": None if k_endog_effective == 1 else (f"endog_{self.name}",),
             }
 
         if self.innovations:
             self.param_names += [f"sigma_{self.name}"]
-            if self.k_endog == 1:
+            if k_endog_effective == 1:
                 self.param_info[f"sigma_{self.name}"] = {
                     "shape": (),
                     "constraints": "Positive",
@@ -298,7 +318,7 @@ def populate_component_properties(self):
             else:
                 self.param_dims[f"sigma_{self.name}"] = (f"endog_{self.name}",)
                 self.param_info[f"sigma_{self.name}"] = {
-                    "shape": (self.k_endog,),
+                    "shape": (k_endog_effective,),
                     "constraints": "Positive",
                     "dims": (f"endog_{self.name}",),
                 }