# logDeterminantConditionalGain.py
# Author: Vishal Kaushal <vishal.kaushal@gmail.com>
import numpy as np
import scipy
from .setFunction import SetFunction
import submodlib_cpp as subcp
from submodlib_cpp import LogDeterminantConditionalGain
from submodlib.helper import create_kernel
[docs]class LogDeterminantConditionalGainFunction(SetFunction):
"""Implementation of the Log Determinant Conditional Gain (LogDetCG) function.
Given a :ref:`functions.conditional-gain` function, Log Determinantn Conditional Gain function is its instantiation using a :class:`~submodlib.functions.logDeterminant.LogDeterminantFunction`.
Let :math:`S_{A, B}` be the cross-similarity matrix between the items in sets :math:`A` and :math:`B`. Also, denote :math:`S_{AB} = S_{A \\cup B}`.
We construct a similarity matrix :math:`S^{\\nu}` (on a base matrix :math:`S`) in such a way that the cross-similarity between :math:`A` and :math:`P` is multiplied by :math:`\\nu` (i.e :math:`S^{\\nu}_{A,P} = \\nu S_{A,P}`) to control the hardness of enforcing privacy constraints. Higher values of :math:`\\nu` ensure stricter privacy constraints, such as in the context of privacy-preserving summarization, i.e., tightening the extent of dissimilarity of the subset from the private set.
Using a similarity matrix defined above and with :math:`f(A) = \\log\\det(S^{\\nu}_{A})`, we have:
.. math::
f(A | P ) = \\log\\det(S_{A} - \\nu^2 S_{A, P}S_{P}^{-1}S_{A, P}^T)
Increasing :math:`\\nu` increases the privacy-irrelevance score, thereby ensuring a stricter privacy-irrelevance constraint.
.. note::
LogDetCG outperforms FLCG and GCCG both in terms of diversity and privacy-irrelevance.
Parameters
----------
n : int
Number of elements in the ground set. Must be > 0.
num_privates : int
Number of private instances in the target.
lambdaVal : float
Addition to :math:`s_{ii} (1)` so that :math:`\\log` doesn't become 0
data_sijs : numpy.ndarray, optional
Similarity kernel between the elements of the ground set. Shape: n X n. When not provided, it is computed using data.
private_sijs : numpy.ndarray, optional
Similarity kernel between the ground set and the private instances. Shape: n X num_privates. When not provided, it is computed using data and privateData.
private_private_sijs : numpy.ndarray, optional
Similarity kernel between the private instances. Shape: num_privates X num_privates. When not provided, it is computed using privateData.
data : numpy.ndarray, optional
Matrix of shape n X num_features containing the ground set data elements. data[i] should contain the num-features dimensional features of element i. Mandatory, if either if data_sijs or private_sijs is not provided. Ignored if both data_sijs and private_sijs are provided.
privateData : numpy.ndarray, optional
Matrix of shape num_privates X num_features containing the private instances. privateData[i] should contain the num-features dimensional features of private instance i. Must be provided if private_sijs is not provided. Ignored if both data_sijs and private_sijs are provided.
metric : str, optional
Similarity metric to be used for computing the similarity kernels. Can be "cosine" for cosine similarity or "euclidean" for similarity based on euclidean distance. Default is "cosine".
privacyHardness : float, optional
Parameter that governs the hardness of the privacy constraint. Default is 1.
"""
def __init__(self, n, num_privates, lambdaVal, data_sijs=None, private_sijs=None, private_private_sijs=None, data=None, privateData=None, metric="cosine", privacyHardness=1):
self.n = n
self.num_privates = num_privates
self.lambdaVal=lambdaVal
self.metric = metric
self.privacyHardness=privacyHardness
self.data_sijs = data_sijs
self.private_sijs = private_sijs
self.private_private_sijs = private_private_sijs
self.data = data
self.privateData = privateData
self.cpp_obj = None
self.cpp_data_sijs = None
self.cpp_private_sijs = None
self.cpp_private_private_sijs = None
self.cpp_content = None
self.cpp_content2 = None
self.effective_ground = None
if self.n <= 0:
raise Exception("ERROR: Number of elements in ground set must be positive")
if self.num_privates < 0:
raise Exception("ERROR: Number of queries must be >= 0")
# if self.metric not in ['euclidean', 'cosine']:
# raise Exception("ERROR: Unsupported metric. Must be 'euclidean' or 'cosine'")
if (type(self.data_sijs) != type(None)) and (type(self.private_sijs) != type(None)) and (type(self.private_private_sijs) != type(None)): # User has provided all three kernels
if type(self.data_sijs) != np.ndarray:
raise Exception("Invalid data kernel type provided, must be ndarray")
if type(self.private_sijs) != np.ndarray:
raise Exception("Invalid private kernel type provided, must be ndarray")
if type(self.private_private_sijs) != np.ndarray:
raise Exception("Invalid private-private kernel type provided, must be ndarray")
if np.shape(self.data_sijs)[0]!=self.n or np.shape(self.data_sijs)[1]!=self.n:
raise Exception("ERROR: data kernel should be n X n")
if np.shape(self.private_sijs)[0]!=self.n or np.shape(self.private_sijs)[1]!=self.num_privates:
raise Exception("ERROR: Private Kernel should be n X num_privates")
if np.shape(self.private_private_sijs)[0]!=self.num_privates or np.shape(self.private_private_sijs)[1]!=self.num_privates:
raise Exception("ERROR: Private-private Kernel should be num_privates X num_privates")
if (type(self.data) != type(None)) or (type(self.privateData) != type(None)):
print("WARNING: similarity kernels found. Provided data and private matrices will be ignored.")
else: #similarity kernels have not been provided
if (type(self.data) == type(None)) or (type(self.privateData) == type(None)):
raise Exception("Since kernels are not provided, data matrices are a must")
if np.shape(self.data)[0]!=self.n:
raise Exception("ERROR: Inconsistentcy between n and no of examples in the given data matrix")
if np.shape(self.privateData)[0]!=self.num_privates:
raise Exception("ERROR: Inconsistentcy between num_privates and no of examples in the given private data matrix")
#construct imageKernel
self.num_neighbors = self.n #Using all data as num_neighbors in case of dense mode
self.cpp_content = np.array(subcp.create_kernel(self.data.tolist(), self.metric, self.num_neighbors))
val = self.cpp_content[0]
row = list(self.cpp_content[1].astype(int))
col = list(self.cpp_content[2].astype(int))
self.data_sijs = np.zeros((self.n,self.n))
self.data_sijs[row,col] = val
#construct privateKernel
self.private_sijs = np.array(subcp.create_kernel_NS(self.privateData.tolist(),self.data.tolist(), self.metric))
#construct privatePrivateKernel
self.num_neighbors2 = self.num_privates #Using all data as num_neighbors in case of dense mode
self.cpp_content2 = np.array(subcp.create_kernel(self.privateData.tolist(), self.metric, self.num_neighbors2))
val2 = self.cpp_content2[0]
row2 = list(self.cpp_content2[1].astype(int))
col2 = list(self.cpp_content2[2].astype(int))
self.private_private_sijs = np.zeros((self.num_privates,self.num_privates))
self.private_private_sijs[row2,col2] = val2
#Breaking similarity matrix to simpler native data structures for implicit pybind11 binding
self.cpp_data_sijs = self.data_sijs.tolist() #break numpy ndarray to native list of list datastructure
if type(self.cpp_data_sijs[0])==int or type(self.cpp_data_sijs[0])==float: #Its critical that we pass a list of list to pybind11
#This condition ensures the same in case of a 1D numpy array (for 1x1 sim matrix)
l=[]
l.append(self.cpp_data_sijs)
self.cpp_data_sijs=l
self.cpp_private_sijs = self.private_sijs.tolist() #break numpy ndarray to native list of list datastructure
if type(self.cpp_private_sijs[0])==int or type(self.cpp_private_sijs[0])==float: #Its critical that we pass a list of list to pybind11
#This condition ensures the same in case of a 1D numpy array (for 1x1 sim matrix)
l=[]
l.append(self.cpp_private_sijs)
self.cpp_private_sijs=l
#Breaking similarity matrix to simpler native data structures for implicit pybind11 binding
self.cpp_private_private_sijs = self.private_private_sijs.tolist() #break numpy ndarray to native list of list datastructure
if type(self.cpp_private_private_sijs[0])==int or type(self.cpp_private_private_sijs[0])==float: #Its critical that we pass a list of list to pybind11
#This condition ensures the same in case of a 1D numpy array (for 1x1 sim matrix)
l=[]
l.append(self.cpp_private_private_sijs)
self.cpp_private_private_sijs=l
self.cpp_obj = LogDeterminantConditionalGain(self.n, self.num_privates, self.cpp_data_sijs, self.cpp_private_sijs, self.cpp_private_private_sijs, self.lambdaVal, self.privacyHardness)
self.effective_ground = set(range(n))