Source code for submodlib.functions.logDeterminantConditionalMutualInformation

# logDeterminantConditionalMutualInformation.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 LogDeterminantConditionalMutualInformation 
from submodlib.helper import create_kernel

[docs]class LogDeterminantConditionalMutualInformationFunction(SetFunction): """Implementation of the Log Determinant Conditional Mutual Information (LogDetCMI) function. Given a :ref:`functions.conditional-mutual-information` function, Log Determinant Conditional Mutual Information 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^{\\eta,\\nu}` (on a base matrix :math:`S`) in such a way that the cross-similarity between :math:`A` and :math:`Q` is multiplied by :math:`\\eta` (i.e :math:`S^{\\eta}_{A,Q} = \\eta S_{A,Q}`) to control the query-relevance and diversity trade-off and 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. Using a similarity matrix defined above and with :math:`f(A) = \\log\\det(S^{\\nu}_{A})`, we have: .. math:: I_f(A; Q|P ) = \\log \\frac{\\det(I - S_{P}^{-1} S_{P, Q} S_{Q}^{-1} S_{P, Q}^T)}{\\det(I - S_{A P}^{-1} S_{A P, Q} S_{Q}^{-1} S_{A P, Q}^T)} .. note:: LogDetCMI favors query-relevance and privacy-irrelevance over query-coverage and diversity. Parameters ---------- n : int Number of elements in the ground set. Must be > 0. num_queries : int Number of query points in the target. 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. query_sijs : numpy.ndarray, optional Similarity kernel between the ground set and the queries. Shape: n X num_queries. When not provided, it is computed using data, queryData and metric. query_query_sijs : numpy.ndarray, optional Similarity kernel between the query points. Shape: num_queries X num_queries. When not provided, it is computed using queryData. 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. query_private_sijs : numpy.ndarray, optional Similarity kernel between the query instances and the private instances. Shape: num_queries X num_privates. When not provided, it is computed using queryData and 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. queryData : numpy.ndarray, optional Matrix of shape num_queries X num_features containing the query elements. queryData[i] should contain the num-features dimensional features of query i. It is optional (and is ignored if provided) if query_sijs has been 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". magnificationEta : float, optional The value of the query-relevance vs diversity trade-off. Increasing :math:`\eta` tends to increase query-relevance while reducing query-coverage and diversity. Default is 1. privacyHardness : float, optional Parameter that governs the hardness of the privacy constraint. Default is 1. """ def __init__(self, n, num_queries, num_privates, lambdaVal, data_sijs=None, query_sijs=None, query_query_sijs=None, private_sijs=None, private_private_sijs=None, query_private_sijs=None, data=None, queryData=None, privateData=None, metric="cosine", magnificationEta=1, privacyHardness=1): self.n = n self.num_queries = num_queries self.num_privates = num_privates self.lambdaVal=lambdaVal self.metric = metric self.magnificationEta=magnificationEta self.privacyHardness=privacyHardness self.data_sijs = data_sijs self.query_sijs = query_sijs self.query_query_sijs = query_query_sijs self.private_sijs = private_sijs self.private_private_sijs = private_private_sijs self.query_private_sijs = query_private_sijs self.data = data self.queryData = queryData self.privateData = privateData self.cpp_obj = None self.cpp_data_sijs = None self.cpp_query_sijs = None self.cpp_query_query_sijs = None self.cpp_private_sijs = None self.cpp_private_private_sijs = None self.cpp_query_private_sijs = None self.cpp_content = None self.cpp_content2 = None self.cpp_content3 = None self.effective_ground = None if self.n <= 0: raise Exception("ERROR: Number of elements in ground set must be positive") if self.num_queries < 0: raise Exception("ERROR: Number of queries must be >= 0") 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.query_sijs) != type(None)) and (type(self.query_query_sijs) != type(None)) and (type(self.private_sijs) != type(None)) and (type(self.private_private_sijs) != type(None)) and (type(self.query_private_sijs) != type(None)): # User has provided all required kernels if type(self.data_sijs) != np.ndarray: raise Exception("Invalid data kernel type provided, must be ndarray") if type(self.query_sijs) != np.ndarray: raise Exception("Invalid query kernel type provided, must be ndarray") if type(self.query_query_sijs) != np.ndarray: raise Exception("Invalid query-query 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 type(self.query_private_sijs) != np.ndarray: raise Exception("Invalid query-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.query_sijs)[0]!=self.n or np.shape(self.query_sijs)[1]!=self.num_queries: raise Exception("ERROR: Query Kernel should be n X num_queries") if np.shape(self.query_query_sijs)[0]!=self.num_queries or np.shape(self.query_query_sijs)[1]!=self.num_queries: raise Exception("ERROR: Query-query Kernel should be num_queries X num_queries") 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 np.shape(self.query_private_sijs)[0]!=self.num_queries or np.shape(self.query_private_sijs)[1]!=self.num_privates: raise Exception("ERROR: Query-private Kernel should be num_queries X num_privates") if (type(self.data) != type(None)) or (type(self.queryData) != type(None)) or (type(self.privateData) != type(None)): print("WARNING: similarity kernels found. Provided data, query and private matrices will be ignored.") else: #similarity kernels have not been provided if (type(self.data) == type(None)) or (type(self.queryData) == 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.queryData)[0]!=self.num_queries: raise Exception("ERROR: Inconsistentcy between num_queries and no of examples in the given query 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 queryKernel self.query_sijs = np.array(subcp.create_kernel_NS(self.queryData.tolist(),self.data.tolist(), self.metric)) #construct queryQueryKernel self.num_neighbors2 = self.num_queries #Using all data as num_neighbors in case of dense mode self.cpp_content2 = np.array(subcp.create_kernel(self.queryData.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.query_query_sijs = np.zeros((self.num_queries,self.num_queries)) self.query_query_sijs[row2,col2] = val2 #construct privateKernel self.private_sijs = np.array(subcp.create_kernel_NS(self.privateData.tolist(),self.data.tolist(), self.metric)) #construct privatePrivateKernel self.num_neighbors3 = self.num_privates #Using all data as num_neighbors in case of dense mode self.cpp_content3 = np.array(subcp.create_kernel(self.privateData.tolist(), self.metric, self.num_neighbors3)) val3 = self.cpp_content3[0] row3 = list(self.cpp_content3[1].astype(int)) col3 = list(self.cpp_content3[2].astype(int)) self.private_private_sijs = np.zeros((self.num_privates,self.num_privates)) self.private_private_sijs[row3,col3] = val3 #construct queryPrivateKernel self.query_private_sijs = np.array(subcp.create_kernel_NS(self.privateData.tolist(),self.queryData.tolist(), self.metric)) #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_query_sijs = self.query_sijs.tolist() #break numpy ndarray to native list of list datastructure if type(self.cpp_query_sijs[0])==int or type(self.cpp_query_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_query_sijs) self.cpp_query_sijs=l self.cpp_query_query_sijs = self.query_query_sijs.tolist() #break numpy ndarray to native list of list datastructure if type(self.cpp_query_query_sijs[0])==int or type(self.cpp_query_query_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_query_query_sijs) self.cpp_query_query_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 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_query_private_sijs = self.query_private_sijs.tolist() #break numpy ndarray to native list of list datastructure if type(self.cpp_query_private_sijs[0])==int or type(self.cpp_query_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_query_private_sijs) self.cpp_query_private_sijs=l self.cpp_obj = LogDeterminantConditionalMutualInformation(self.n, self.num_queries, self.num_privates, self.cpp_data_sijs, self.cpp_query_sijs, self.cpp_query_query_sijs, self.cpp_private_sijs, self.cpp_private_private_sijs,self.cpp_query_private_sijs, self.lambdaVal, self.magnificationEta, self.privacyHardness) self.effective_ground = set(range(n))