-
Notifications
You must be signed in to change notification settings - Fork 387
/
pearson.py
212 lines (176 loc) · 8.18 KB
/
pearson.py
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
# Copyright The Lightning team.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
from typing import Any, List, Optional, Sequence, Tuple, Union
import torch
from torch import Tensor
from torchmetrics.functional.regression.pearson import _pearson_corrcoef_compute, _pearson_corrcoef_update
from torchmetrics.metric import Metric
from torchmetrics.utilities.imports import _MATPLOTLIB_AVAILABLE
from torchmetrics.utilities.plot import _AX_TYPE, _PLOT_OUT_TYPE
if not _MATPLOTLIB_AVAILABLE:
__doctest_skip__ = ["PearsonCorrCoef.plot"]
def _final_aggregation(
means_x: Tensor,
means_y: Tensor,
vars_x: Tensor,
vars_y: Tensor,
corrs_xy: Tensor,
nbs: Tensor,
) -> Tuple[Tensor, Tensor, Tensor, Tensor, Tensor, Tensor]:
"""Aggregate the statistics from multiple devices.
Formula taken from here: `Aggregate the statistics from multiple devices`_
"""
if len(means_x) == 1:
return means_x[0], means_y[0], vars_x[0], vars_y[0], corrs_xy[0], nbs[0]
mx1, my1, vx1, vy1, cxy1, n1 = means_x[0], means_y[0], vars_x[0], vars_y[0], corrs_xy[0], nbs[0]
for i in range(1, len(means_x)):
mx2, my2, vx2, vy2, cxy2, n2 = means_x[i], means_y[i], vars_x[i], vars_y[i], corrs_xy[i], nbs[i]
nb = n1 + n2
mean_x = (n1 * mx1 + n2 * mx2) / nb
mean_y = (n1 * my1 + n2 * my2) / nb
# var_x
element_x1 = (n1 + 1) * mean_x - n1 * mx1
vx1 += (element_x1 - mx1) * (element_x1 - mean_x) - (element_x1 - mean_x) ** 2
element_x2 = (n2 + 1) * mean_x - n2 * mx2
vx2 += (element_x2 - mx2) * (element_x2 - mean_x) - (element_x2 - mean_x) ** 2
var_x = vx1 + vx2
# var_y
element_y1 = (n1 + 1) * mean_y - n1 * my1
vy1 += (element_y1 - my1) * (element_y1 - mean_y) - (element_y1 - mean_y) ** 2
element_y2 = (n2 + 1) * mean_y - n2 * my2
vy2 += (element_y2 - my2) * (element_y2 - mean_y) - (element_y2 - mean_y) ** 2
var_y = vy1 + vy2
# corr
cxy1 += (element_x1 - mx1) * (element_y1 - mean_y) - (element_x1 - mean_x) * (element_y1 - mean_y)
cxy2 += (element_x2 - mx2) * (element_y2 - mean_y) - (element_x2 - mean_x) * (element_y2 - mean_y)
corr_xy = cxy1 + cxy2
mx1, my1, vx1, vy1, cxy1, n1 = mean_x, mean_y, var_x, var_y, corr_xy, nb
return mean_x, mean_y, var_x, var_y, corr_xy, nb
class PearsonCorrCoef(Metric):
r"""Compute `Pearson Correlation Coefficient`_.
.. math::
P_{corr}(x,y) = \frac{cov(x,y)}{\sigma_x \sigma_y}
Where :math:`y` is a tensor of target values, and :math:`x` is a tensor of predictions.
As input to ``forward`` and ``update`` the metric accepts the following input:
- ``preds`` (:class:`~torch.Tensor`): either single output float tensor with shape ``(N,)``
or multioutput float tensor of shape ``(N,d)``
- ``target`` (:class:`~torch.Tensor`): either single output tensor with shape ``(N,)``
or multioutput tensor of shape ``(N,d)``
As output of ``forward`` and ``compute`` the metric returns the following output:
- ``pearson`` (:class:`~torch.Tensor`): A tensor with the Pearson Correlation Coefficient
Args:
num_outputs: Number of outputs in multioutput setting
kwargs: Additional keyword arguments, see :ref:`Metric kwargs` for more info.
Example (single output regression):
>>> from torchmetrics.regression import PearsonCorrCoef
>>> target = torch.tensor([3, -0.5, 2, 7])
>>> preds = torch.tensor([2.5, 0.0, 2, 8])
>>> pearson = PearsonCorrCoef()
>>> pearson(preds, target)
tensor(0.9849)
Example (multi output regression):
>>> from torchmetrics.regression import PearsonCorrCoef
>>> target = torch.tensor([[3, -0.5], [2, 7]])
>>> preds = torch.tensor([[2.5, 0.0], [2, 8]])
>>> pearson = PearsonCorrCoef(num_outputs=2)
>>> pearson(preds, target)
tensor([1., 1.])
"""
is_differentiable: bool = True
higher_is_better: Optional[bool] = None # both -1 and 1 are optimal
full_state_update: bool = True
plot_lower_bound: float = -1.0
plot_upper_bound: float = 1.0
preds: List[Tensor]
target: List[Tensor]
mean_x: Tensor
mean_y: Tensor
var_x: Tensor
var_y: Tensor
corr_xy: Tensor
n_total: Tensor
def __init__(
self,
num_outputs: int = 1,
**kwargs: Any,
) -> None:
super().__init__(**kwargs)
if not isinstance(num_outputs, int) and num_outputs < 1:
raise ValueError("Expected argument `num_outputs` to be an int larger than 0, but got {num_outputs}")
self.num_outputs = num_outputs
self.add_state("mean_x", default=torch.zeros(self.num_outputs), dist_reduce_fx=None)
self.add_state("mean_y", default=torch.zeros(self.num_outputs), dist_reduce_fx=None)
self.add_state("var_x", default=torch.zeros(self.num_outputs), dist_reduce_fx=None)
self.add_state("var_y", default=torch.zeros(self.num_outputs), dist_reduce_fx=None)
self.add_state("corr_xy", default=torch.zeros(self.num_outputs), dist_reduce_fx=None)
self.add_state("n_total", default=torch.zeros(self.num_outputs), dist_reduce_fx=None)
def update(self, preds: Tensor, target: Tensor) -> None:
"""Update state with predictions and targets."""
self.mean_x, self.mean_y, self.var_x, self.var_y, self.corr_xy, self.n_total = _pearson_corrcoef_update(
preds,
target,
self.mean_x,
self.mean_y,
self.var_x,
self.var_y,
self.corr_xy,
self.n_total,
self.num_outputs,
)
def compute(self) -> Tensor:
"""Compute pearson correlation coefficient over state."""
if (self.num_outputs == 1 and self.mean_x.numel() > 1) or (self.num_outputs > 1 and self.mean_x.ndim > 1):
# multiple devices, need further reduction
_, _, var_x, var_y, corr_xy, n_total = _final_aggregation(
self.mean_x, self.mean_y, self.var_x, self.var_y, self.corr_xy, self.n_total
)
else:
var_x = self.var_x
var_y = self.var_y
corr_xy = self.corr_xy
n_total = self.n_total
return _pearson_corrcoef_compute(var_x, var_y, corr_xy, n_total)
def plot(
self, val: Optional[Union[Tensor, Sequence[Tensor]]] = None, ax: Optional[_AX_TYPE] = None
) -> _PLOT_OUT_TYPE:
"""Plot a single or multiple values from the metric.
Args:
val: Either a single result from calling `metric.forward` or `metric.compute` or a list of these results.
If no value is provided, will automatically call `metric.compute` and plot that result.
ax: An matplotlib axis object. If provided will add plot to that axis
Returns:
Figure and Axes object
Raises:
ModuleNotFoundError:
If `matplotlib` is not installed
.. plot::
:scale: 75
>>> from torch import randn
>>> # Example plotting a single value
>>> from torchmetrics.regression import PearsonCorrCoef
>>> metric = PearsonCorrCoef()
>>> metric.update(randn(10,), randn(10,))
>>> fig_, ax_ = metric.plot()
.. plot::
:scale: 75
>>> from torch import randn
>>> # Example plotting multiple values
>>> from torchmetrics.regression import PearsonCorrCoef
>>> metric = PearsonCorrCoef()
>>> values = []
>>> for _ in range(10):
... values.append(metric(randn(10,), randn(10,)))
>>> fig, ax = metric.plot(values)
"""
return self._plot(val, ax)