Merge pull request #28 from simon-hirsch/correct_names_for_link_deriv…

…atives Correct names for link derivatives
simon-hirsch · Nov 19, 2024 · a6e65a4 · a6e65a4
2 parents 2147be3 + 412a0b3
commit a6e65a4
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diff --git a/docs/links.md b/docs/links.md
@@ -8,6 +8,7 @@ For all link functions, we implement
 
 - the link \(g(x)\)
 - the inverse \(g^{-1}(x)\)
+- the derivative of the link function $\frac{\partial g(x)}{\partial x}$.
 - the first derivative _of the inverse_ of the link function \(\frac{\partial g(x)^{-1}}{\partial x}\). The choice of the inverse is justified by Equation (7) in Hirsch, Berrisch & Ziel ([2024](https://github.com/simon-hirsch/rolch/blob/main/paper.pdf)). 
 
 The link functions implemented in `ROLCH` implemenent these as class methods each. Currently, we have implemented the identity-link, log-link and  shifted log-link functions.

diff --git a/src/rolch/abc.py b/src/rolch/abc.py
@@ -33,8 +33,13 @@ def inverse(self, x: np.ndarray) -> np.ndarray:
         """Calculate the inverse of the link function"""
 
     @abstractmethod
-    def derivative(self, x: np.ndarray) -> np.ndarray:
+    def link_derivative(self, x: np.ndarray) -> np.ndarray:
         """Calculate the first derivative of the link function"""
+        raise NotImplementedError("Currently not implemented. Will be needed for GLMs")
+
+    @abstractmethod
+    def inverse_derivative(self, x: np.ndarray) -> np.ndarray:
+        """Calculate the first derivative for the inverse link function"""
 
 
 class Distribution(ABC):
@@ -66,9 +71,13 @@ def link_inverse(self, y: np.ndarray, param: int = 0) -> np.ndarray:
         """Apply the inverse of the link function for param on y."""
 
     @abstractmethod
-    def link_derivative(self, y: np.ndarray, param: int = 0) -> np.ndarray:
+    def link_function_derivative(self, y: np.ndarray, param: int = 0) -> np.ndarray:
         """Apply the derivative of the link function for param on y."""
 
+    @abstractmethod
+    def link_inverse_derivative(self, y: np.ndarray, param: int = 0) -> np.ndarray:
+        """Apply the derivative of the inverse link function for param on y."""
+
     @abstractmethod
     def initial_values(
         self, y: np.ndarray, param: int = 0, axis: int = None

diff --git a/src/rolch/distributions/gamma.py b/src/rolch/distributions/gamma.py
@@ -113,8 +113,11 @@ def link_function(self, y, param=0):
     def link_inverse(self, y, param=0):
         return self.links[param].inverse(y)
 
-    def link_derivative(self, y, param=0):
-        return self.links[param].derivative(y)
+    def link_function_derivative(self, y: np.ndarray, param: int = 0) -> np.ndarray:
+        return self.links[param].link_derivative(y)
+
+    def link_inverse_derivative(self, y: np.ndarray, param: int = 0) -> np.ndarray:
+        return self.links[param].inverse_derivative(y)
 
     def initial_values(self, y, param=0, axis=None):
         if param == 0:

diff --git a/src/rolch/distributions/johnsonsu.py b/src/rolch/distributions/johnsonsu.py
@@ -184,8 +184,11 @@ def link_function(self, y, param=0):
     def link_inverse(self, y, param=0):
         return self.links[param].inverse(y)
 
-    def link_derivative(self, y, param=0):
-        return self.links[param].derivative(y)
+    def link_function_derivative(self, y: np.ndarray, param: int = 0) -> np.ndarray:
+        return self.links[param].link_derivative(y)
+
+    def link_inverse_derivative(self, y: np.ndarray, param: int = 0) -> np.ndarray:
+        return self.links[param].inverse_derivative(y)
 
     def initial_values(self, y, param=0, axis=None):
         if param == 0:

diff --git a/src/rolch/distributions/normal.py b/src/rolch/distributions/normal.py
@@ -49,8 +49,11 @@ def link_function(self, y, param=0):
     def link_inverse(self, y, param=0):
         return self.links[param].inverse(y)
 
-    def link_derivative(self, y, param=0):
-        return self.links[param].derivative(y)
+    def link_function_derivative(self, y: np.ndarray, param: int = 0) -> np.ndarray:
+        return self.links[param].link_derivative(y)
+
+    def link_inverse_derivative(self, y: np.ndarray, param: int = 0) -> np.ndarray:
+        return self.links[param].inverse_derivative(y)
 
     def initial_values(self, y, param=0, axis=None):
         if param == 0:

diff --git a/src/rolch/distributions/studentt.py b/src/rolch/distributions/studentt.py
@@ -95,8 +95,11 @@ def link_function(self, y, param=0):
     def link_inverse(self, y, param=0):
         return self.links[param].inverse(y)
 
-    def link_derivative(self, y, param=0):
-        return self.links[param].derivative(y)
+    def link_function_derivative(self, y: np.ndarray, param: int = 0) -> np.ndarray:
+        return self.links[param].link_derivative(y)
+
+    def link_inverse_derivative(self, y: np.ndarray, param: int = 0) -> np.ndarray:
+        return self.links[param].inverse_derivative(y)
 
     def initial_values(self, y, param=0, axis=None):
         if param == 0:

diff --git a/src/rolch/link.py b/src/rolch/link.py
@@ -17,18 +17,21 @@ class LogLink(LinkFunction):
     def __init__(self):
         pass
 
-    def link(self, x):
+    def link(self, x: np.ndarray) -> np.ndarray:
         return np.log(np.fmax(x, LOG_LOWER_BOUND))
 
-    def inverse(self, x):
+    def inverse(self, x: np.ndarray) -> np.ndarray:
         return np.fmax(
             np.exp(np.fmin(x, EXP_UPPER_BOUND)),
             LOG_LOWER_BOUND,
         )
 
-    def derivative(self, x):
+    def inverse_derivative(self, x: np.ndarray) -> np.ndarray:
         return np.exp(np.fmin(x, EXP_UPPER_BOUND))
 
+    def link_derivative(self, x: np.ndarray) -> np.ndarray:
+        return 1 / x
+
 
 class IdentityLink(LinkFunction):
     """
@@ -40,13 +43,16 @@ class IdentityLink(LinkFunction):
     def __init__(self):
         pass
 
-    def link(self, x):
+    def link(self, x: np.ndarray) -> np.ndarray:
         return x
 
-    def inverse(self, x):
+    def inverse(self, x: np.ndarray) -> np.ndarray:
         return x
 
-    def derivative(self, x):
+    def inverse_derivative(self, x: np.ndarray) -> np.ndarray:
+        return np.ones_like(x)
+
+    def link_derivative(self, x: np.ndarray) -> np.ndarray:
         return np.ones_like(x)
 
 
@@ -60,20 +66,23 @@ class LogShiftValueLink(LinkFunction):
     don't fall below 2, hence ensuring that the variance exists.
     """
 
-    def __init__(self, value):
+    def __init__(self, value: float):
         self.value = value
 
-    def link(self, x):
+    def link(self, x: np.ndarray) -> np.ndarray:
         return np.log(x - self.value + LOG_LOWER_BOUND)
 
-    def inverse(self, x):
+    def inverse(self, x: np.ndarray) -> np.ndarray:
         return self.value + np.fmax(
             np.exp(np.fmin(x, EXP_UPPER_BOUND)), LOG_LOWER_BOUND
         )
 
-    def derivative(self, x):
+    def inverse_derivative(self, x: np.ndarray) -> np.ndarray:
         return np.fmax(np.exp(np.fmin(x, EXP_UPPER_BOUND)), LOG_LOWER_BOUND)
 
+    def link_derivative(self, x: np.ndarray) -> np.ndarray:
+        return super().link_derivative(x)
+
 
 class LogShiftTwoLink(LogShiftValueLink):
     """
@@ -99,15 +108,18 @@ class SqrtLink(LinkFunction):
     def __init__(self):
         pass
 
-    def link(self, x):
+    def link(self, x: np.ndarray) -> np.ndarray:
         return np.sqrt(x)
 
-    def inverse(self, x):
+    def inverse(self, x: np.ndarray) -> np.ndarray:
         return np.power(x, 2)
 
-    def derivative(self, x):
+    def inverse_derivative(self, x: np.ndarray) -> np.ndarray:
         return 2 * x
 
+    def link_derivative(self, x: np.ndarray) -> np.ndarray:
+        return 1 / (2 * np.sqrt(x))
+
 
 class SqrtShiftValueLink(LinkFunction):
     """
@@ -119,18 +131,21 @@ class SqrtShiftValueLink(LinkFunction):
     don't fall below 2, hence ensuring that the variance exists.
     """
 
-    def __init__(self, value):
+    def __init__(self, value: float):
         self.value = value
 
-    def link(self, x):
+    def link(self, x: np.ndarray) -> np.ndarray:
         return np.sqrt(x - self.value + LOG_LOWER_BOUND)
 
-    def inverse(self, x):
+    def inverse(self, x: np.ndarray) -> np.ndarray:
         return self.value + np.power(np.fmin(x, EXP_UPPER_BOUND), 2)
 
-    def derivative(self, x):
+    def inverse_derivative(self, x: np.ndarray) -> np.ndarray:
         return 2 * x
 
+    def link_derivative(self, x: np.ndarray) -> np.ndarray:
+        return super().link_derivative(x)
+
 
 class SqrtShiftTwoLink(SqrtShiftValueLink):
     """
@@ -158,15 +173,18 @@ class LogIdentLink(LinkFunction):
     def __init__(self):
         pass
 
-    def link(self, x: np.ndarray):
+    def link(self, x: np.ndarray) -> np.ndarray:
         return np.where(x <= 1, np.log(x), x - 1)
 
-    def inverse(self, x: np.ndarray):
+    def inverse(self, x: np.ndarray) -> np.ndarray:
         return np.where(x <= 0, np.exp(x), x + 1)
 
-    def derivative(self, x: np.ndarray):
+    def inverse_derivative(self, x: np.ndarray) -> np.ndarray:
         return np.where(x <= 0, np.exp(x), 1)
 
+    def link_derivative(self, x: np.ndarray) -> np.ndarray:
+        return super().link_derivative(x)
+
 
 __all__ = [
     "LogLink",

diff --git a/src/rolch/online_gamlss.py b/src/rolch/online_gamlss.py
@@ -696,7 +696,7 @@ def _inner_fit(
             iteration_inner += 1
             eta = self.distribution.link_function(fv[:, param], param=param)
             # if iteration == 1:
-            dr = 1 / self.distribution.link_derivative(eta, param=param)
+            dr = 1 / self.distribution.link_inverse_derivative(eta, param=param)
             # mu, sigma, nu vs. fv?
             dl1dp1 = self.distribution.dl1_dp1(y, fv, param=param)
             dl2dp2 = self.distribution.dl2_dp2(y, fv, param=param)
@@ -806,7 +806,7 @@ def _inner_update(
 
             iteration_inner += 1
             eta = self.distribution.link_function(fv[:, param], param=param)
-            dr = 1 / self.distribution.link_derivative(eta, param=param)
+            dr = 1 / self.distribution.link_inverse_derivative(eta, param=param)
             # mu, sigma, nu vs. fv?
             dl1dp1 = self.distribution.dl1_dp1(y, fv, param=param)
             dl2dp2 = self.distribution.dl2_dp2(y, fv, param=param)

diff --git a/tests/test_link_functions.py b/tests/test_link_functions.py
@@ -34,7 +34,7 @@ def test_link_positive_line(linkfun):
 
 @pytest.mark.parametrize("linkfun", SHIFTED_LINKS)
 @pytest.mark.parametrize("value", VALUES)
-def test_link_positive_line(linkfun, value):
+def test_link_positive_shifted_line(linkfun, value):
     """Test links that are shifted. This changes the domain of the links."""
     instance = linkfun(value)
     x = np.linspace(value, 100 + value, M)