from typing import Iterable
import numpy as np
import torch
from sklearn.linear_model import LogisticRegression
from inFairness.distances import SensitiveSubspaceDistance
from inFairness.utils import datautils, validationutils
[docs]
class LogisticRegSensitiveSubspace(SensitiveSubspaceDistance):
"""Implements the Softmax Regression model based fair metric as defined in Appendix B.1
of "Training individually fair ML models with sensitive subspace robustness" paper.
This metric assumes that the sensitive attributes are discrete and observed for a small subset
of training data. Assuming data of the form :math:`(X_i, K_i, Y_i)` where :math:`K_i` is the
sensitive attribute of the i-th subject, the model fits a softmax regression model to the data as:
.. math:: \mathbb{P}(K_i = l\\mid X_i) = \\frac{\exp(a_l^TX_i+b_l)}{\\sum_{l=1}^k \\exp(a_l^TX_i+b_l)},\\ l=1,\\ldots,k
Using the span of the matrix :math:`A=[a_1, \cdots, a_k]`, the fair metric is trained as:
.. math:: d_x(x_1,x_2)^2 = (x_1 - x_2)^T(I - P_{\\text{ran}(A)})(x_1 - x_2)
References
-------------
`Yurochkin, Mikhail, Amanda Bower, and Yuekai Sun. "Training individually fair
ML models with sensitive subspace robustness." arXiv preprint arXiv:1907.00020 (2019).`
"""
def __init__(self):
super().__init__()
self.basis_vectors_ = None
self._logreg_models = None
@property
def logistic_regression_models(self):
"""Logistic Regression models trained by the metric to predict each sensitive attribute
given inputs. The property is a list of logistic regression models each corresponding to
:math:`\mathbb{P}(K_i = l\\mid X_i)`. This property can be used to measure the performance
of the logistic regression models.
"""
return self._logreg_models
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def fit(
self,
data_X: torch.Tensor,
data_SensitiveAttrs: torch.Tensor = None,
protected_idxs: Iterable[int] = None,
keep_protected_idxs: bool = True,
autoinfer_device: bool = True,
):
"""Fit Logistic Regression Sensitive Subspace distance metric
Parameters
--------------
data_X: torch.Tensor
Input data corresponding to either :math:`X_i` or :math:`(X_i, K_i)` in the equation above.
If the variable corresponds to :math:`X_i`, then the `y_train` parameter should be specified.
If the variable corresponds to :math:`(X_i, K_i)` then the `protected_idxs` parameter
should be specified to indicate the sensitive attributes.
data_SensitiveAttrs: torch.Tensor
Represents the sensitive attributes ( :math:`K_i` ) and is used when the `X_train` parameter
represents :math:`X_i` from the equation above. **Note**: This parameter is mutually exclusive
with the `protected_idxs` parameter. Specififying both the `data_SensitiveAttrs` and `protected_idxs`
parameters will raise an error
protected_idxs: Iterable[int]
If the `X_train` parameter above represents :math:`(X_i, K_i)`, then this parameter is used
to provide the indices of sensitive attributes in `X_train`. **Note**: This parameter is mutually exclusive
with the `protected_idxs` parameter. Specififying both the `data_SensitiveAttrs` and `protected_idxs`
parameters will raise an error
keep_protected_indices: bool
True, if while training the model, protected attributes will be part of the training data
Set to False, if for training the model, protected attributes will be excluded
Default = True
autoinfer_device: bool
Should the distance metric be automatically moved to an appropriate
device (CPU / GPU) or not? If set to True, it moves the metric
to the same device `X_train` is on. If set to False, keeps the metric
on CPU.
"""
if data_SensitiveAttrs is not None and protected_idxs is None:
basis_vectors_ = self.compute_basis_vectors_data(
X_train=data_X, y_train=data_SensitiveAttrs
)
elif data_SensitiveAttrs is None and protected_idxs is not None:
basis_vectors_ = self.compute_basis_vectors_protected_idxs(
data_X,
protected_idxs=protected_idxs,
keep_protected_idxs=keep_protected_idxs,
)
else:
raise AssertionError(
"Parameters `y_train` and `protected_idxs` are exclusive. Either of these two parameters should be None, and cannot be set to non-None values simultaneously."
)
super().fit(basis_vectors_)
self.basis_vectors_ = basis_vectors_
if autoinfer_device:
device = datautils.get_device(data_X)
super().to(device)
[docs]
def compute_basis_vectors_protected_idxs(
self, data, protected_idxs, keep_protected_idxs=True
):
dtype = data.dtype
data = datautils.convert_tensor_to_numpy(data)
basis_vectors_ = []
num_attr = data.shape[1]
# Get input data excluding the protected attributes
protected_idxs = sorted(protected_idxs)
free_idxs = [idx for idx in range(num_attr) if idx not in protected_idxs]
X_train = data[:, free_idxs]
Y_train = data[:, protected_idxs]
self.__assert_sensitiveattrs_binary__(Y_train)
self._logreg_models = [
LogisticRegression(solver="liblinear", penalty="l1")
.fit(X_train, Y_train[:, idx])
for idx in range(len(protected_idxs))
]
coefs = np.array(
[
self._logreg_models[idx].coef_.squeeze()
for idx in range(len(protected_idxs))
]
) # ( |protected_idxs|, |free_idxs| )
if keep_protected_idxs:
# To keep protected indices, we add two basis vectors
# First, with logistic regression coefficients with 0 in
# protected indices. Second, with one-hot vectors with 1 in
# protected indices.
basis_vectors_ = np.empty(shape=(2 * len(protected_idxs), num_attr))
for i, protected_idx in enumerate(protected_idxs):
protected_basis_vector = np.zeros(shape=(num_attr))
protected_basis_vector[protected_idx] = 1.0
unprotected_basis_vector = np.zeros(shape=(num_attr))
np.put_along_axis(
unprotected_basis_vector, np.array(free_idxs), coefs[i], axis=0
)
basis_vectors_[2 * i] = unprotected_basis_vector
basis_vectors_[2 * i + 1] = protected_basis_vector
else:
# Protected indices are to be discarded. Therefore, we can
# simply return back the logistic regression coefficients
basis_vectors_ = coefs
basis_vectors_ = torch.tensor(basis_vectors_, dtype=dtype).T
basis_vectors_ = basis_vectors_.detach()
return basis_vectors_
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def compute_basis_vectors_data(self, X_train, y_train):
dtype = X_train.dtype
X_train = datautils.convert_tensor_to_numpy(X_train)
y_train = datautils.convert_tensor_to_numpy(y_train)
self.__assert_sensitiveattrs_binary__(y_train)
basis_vectors_ = []
outdim = y_train.shape[-1]
self._logreg_models = [
LogisticRegression(solver="liblinear", penalty="l1")
.fit(X_train, y_train[:, idx])
for idx in range(outdim)
]
basis_vectors_ = np.array(
[
self._logreg_models[idx].coef_.squeeze()
for idx in range(outdim)
]
)
basis_vectors_ = torch.tensor(basis_vectors_, dtype=dtype).T
basis_vectors_ = basis_vectors_.detach()
return basis_vectors_
def __assert_sensitiveattrs_binary__(self, sensitive_attrs):
assert validationutils.is_tensor_binary(
sensitive_attrs
), "Sensitive attributes are required to be binary to learn the metric. Please binarize these attributes before fitting the metric."