PearsonCorrelation

class ignite.metrics.regression.PearsonCorrelation(eps=1e-08, output_transform=<function PearsonCorrelation.<lambda>>, device=device(type='cpu'))

Calculates the Pearson correlation coefficient.

$$r = \frac{\sum_{j=1}^n (P_j-\bar{P})(A_j-\bar{A})} {\max (\sqrt{\sum_{j=1}^n (P_j-\bar{P})^2 \sum_{j=1}^n (A_j-\bar{A})^2}, \epsilon)}, \quad \bar{P}=\frac{1}{n}\sum_{j=1}^n P_j, \quad \bar{A}=\frac{1}{n}\sum_{j=1}^n A_j$$

where $A_j$ is the ground truth and $P_j$ is the predicted value.

Internally uses Welford’s online algorithm for numerically stable computation, avoiding catastrophic cancellation that can occur with the naive sum-of-squares formula in float32.

• update must receive output of the form (y_pred, y) or {'y_pred': y_pred, 'y': y}.

• y and y_pred must be of same shape (N, ) or (N, 1).

Parameters are inherited from Metric.__init__.

Parameters:

• eps (float) – a small value to avoid division by zero. Default: 1e-8

• output_transform (Callable) – a callable that is used to transform the Engine’s process_function’s output into the form expected by the metric. This can be useful if, for example, you have a multi-output model and you want to compute the metric with respect to one of the outputs. By default, metrics require the output as (y_pred, y) or {'y_pred': y_pred, 'y': y}.

• device (str | device) – specifies which device updates are accumulated on. Setting the metric’s device to be the same as your update arguments ensures the update method is non-blocking. By default, CPU.

Examples

To use with Engine and process_function, simply attach the metric instance to the engine. The output of the engine’s process_function needs to be in format of (y_pred, y) or {'y_pred': y_pred, 'y': y, ...}.

from collections import OrderedDict

import torch
from torch import nn, optim

from ignite.engine import *
from ignite.handlers import *
from ignite.metrics import *
from ignite.metrics.clustering import *
from ignite.metrics.fairness import *
from ignite.metrics.rec_sys import *
from ignite.metrics.regression import *
from ignite.utils import *

# create default evaluator for doctests

def eval_step(engine, batch):
    return batch

default_evaluator = Engine(eval_step)

# create default optimizer for doctests

param_tensor = torch.zeros([1], requires_grad=True)
default_optimizer = torch.optim.SGD([param_tensor], lr=0.1)

# create default trainer for doctests
# as handlers could be attached to the trainer,
# each test must define his own trainer using `.. testsetup:`

def get_default_trainer():

    def train_step(engine, batch):
        return batch

    return Engine(train_step)

# create default model for doctests

default_model = nn.Sequential(OrderedDict([
    ('base', nn.Linear(4, 2)),
    ('fc', nn.Linear(2, 1))
]))

manual_seed(666)

metric = PearsonCorrelation()
metric.attach(default_evaluator, 'corr')
y_true = torch.tensor([0., 1., 2., 3., 4., 5.])
y_pred = torch.tensor([0.5, 1.3, 1.9, 2.8, 4.1, 6.0])
state = default_evaluator.run([[y_pred, y_true]])
print(state.metrics['corr'])

0.9768687504744322

Changed in version 0.6.0: Uses Welford’s online algorithm for improved numerical stability.

Methods

compute	Computes the metric based on its accumulated state.
reset	Resets the metric to its initial state.

compute()

Computes the metric based on its accumulated state.

By default, this is called at the end of each epoch.

Returns:

the actual quantity of interest. However, if a Mapping is returned, it will be (shallow) flattened into engine.state.metrics when completed() is called.

Return type:

Any

Raises:

NotComputableError – raised when the metric cannot be computed.

reset()

Resets the metric to its initial state.

By default, this is called at the start of each epoch.

Return type:

None