Пример #1
0
    def testScale(self):
        """
        Look at the scales of the unnormalised gradients. 
        """

        m = 100
        n = 400
        k = 3
        X = SparseUtils.generateSparseBinaryMatrix((m, n), k, csarray=True)

        w = 0.1
        eps = 0.001
        learner = MaxAUCTanh(k, w)
        learner.normalise = False
        learner.lmbdaU = 1.0
        learner.lmbdaV = 1.0
        learner.rho = 1.0
        learner.numAucSamples = 100

        indPtr, colInds = SparseUtils.getOmegaListPtr(X)
        r = numpy.random.rand(m)

        U = numpy.random.rand(X.shape[0], k)
        V = numpy.random.rand(X.shape[1], k)

        gi = numpy.random.rand(m)
        gi /= gi.sum()
        gp = numpy.random.rand(n)
        gp /= gp.sum()
        gq = numpy.random.rand(n)
        gq /= gq.sum()

        permutedRowInds = numpy.array(numpy.random.permutation(m),
                                      numpy.uint32)
        permutedColInds = numpy.array(numpy.random.permutation(n),
                                      numpy.uint32)

        maxLocalAuc = MaxLocalAUC(k, w)
        normGp, normGq = maxLocalAuc.computeNormGpq(indPtr, colInds, gp, gq, m)

        normDui = 0
        for i in range(m):
            du = learner.derivativeUi(indPtr, colInds, U, V, r, gi, gp, gq, i)
            normDui += numpy.linalg.norm(du)

        normDui /= float(m)
        print(normDui)

        normDvi = 0

        for i in range(n):
            dv = learner.derivativeVi(indPtr, colInds, U, V, r, gi, gp, gq, i)
            normDvi += numpy.linalg.norm(dv)

        normDvi /= float(n)
        print(normDvi)
Пример #2
0
    def testScale(self): 
        """
        Look at the scales of the unnormalised gradients. 
        """        
        
        m = 100 
        n = 400 
        k = 3 
        X = SparseUtils.generateSparseBinaryMatrix((m, n), k, csarray=True)
        
        w = 0.1
        eps = 0.001
        learner = MaxAUCTanh(k, w)
        learner.normalise = False
        learner.lmbdaU = 1.0
        learner.lmbdaV = 1.0
        learner.rho = 1.0
        learner.numAucSamples = 100
        
        indPtr, colInds = SparseUtils.getOmegaListPtr(X)
        r = numpy.random.rand(m)

        U = numpy.random.rand(X.shape[0], k)
        V = numpy.random.rand(X.shape[1], k)
        
        gi = numpy.random.rand(m)
        gi /= gi.sum()        
        gp = numpy.random.rand(n)
        gp /= gp.sum()        
        gq = numpy.random.rand(n)
        gq /= gq.sum()     
        
        permutedRowInds = numpy.array(numpy.random.permutation(m), numpy.uint32)
        permutedColInds = numpy.array(numpy.random.permutation(n), numpy.uint32)
        
        maxLocalAuc = MaxLocalAUC(k, w)
        normGp, normGq = maxLocalAuc.computeNormGpq(indPtr, colInds, gp, gq, m)
        
        normDui = 0
        for i in range(m): 
            du = learner.derivativeUi(indPtr, colInds, U, V, r, gi, gp, gq, i) 
            normDui += numpy.linalg.norm(du)
            
        normDui /= float(m)
        print(normDui)        
        
        normDvi = 0         
        
        for i in range(n): 
            dv = learner.derivativeVi(indPtr, colInds, U, V, r, gi, gp, gq, i) 
            normDvi += numpy.linalg.norm(dv)
            
        normDvi /= float(n)
        print(normDvi)
Пример #3
0
    def testObjectiveApprox(self):
        """
        We'll test the case in which we apprormate using a large number of samples 
        for the AUC and see if we get close to the exact objective 
        """
        m = 20
        n = 30
        k = 3
        X = SparseUtils.generateSparseBinaryMatrix((m, n), k, csarray=True)

        w = 0.1
        learner = MaxAUCTanh(k, w)
        learner.normalise = False
        learner.lmbdaU = 0
        learner.lmbdaV = 0
        learner.rho = 1.0
        learner.numAucSamples = n

        indPtr, colInds = SparseUtils.getOmegaListPtr(X)

        U = numpy.random.rand(X.shape[0], k)
        V = numpy.random.rand(X.shape[1], k)

        numRuns = 100
        numTests = 5

        gp = numpy.random.rand(n)
        gp /= gp.sum()
        gq = numpy.random.rand(n)
        gq /= gq.sum()
        #gi = numpy.ones(m)
        #gp = numpy.ones(n)
        #gq = numpy.ones(n)

        #Let's compare against using the exact derivative
        for i in range(numTests):
            obj = 0

            for j in range(numRuns):
                obj += learner.objectiveApprox(indPtr, colInds, indPtr,
                                               colInds, U, V, gp, gq)
            obj /= numRuns

            obj2 = learner.objective(indPtr, colInds, indPtr, colInds, U, V,
                                     gp, gq)
            self.assertAlmostEquals(obj, obj2, 2)

        learner.rho = 0.2

        for i in range(numTests):
            obj = 0
            for j in range(numRuns):
                obj += learner.objectiveApprox(indPtr, colInds, indPtr,
                                               colInds, U, V, gp, gq)
            obj /= numRuns

            obj2 = learner.objective(indPtr, colInds, indPtr, colInds, U, V,
                                     gp, gq)
            self.assertAlmostEquals(obj, obj2, 2)

        learner.lmbdaV = 0.2

        for i in range(numTests):
            obj = 0
            for j in range(numRuns):
                obj += learner.objectiveApprox(indPtr, colInds, indPtr,
                                               colInds, U, V, gp, gq)
            obj /= numRuns

            obj2 = learner.objective(indPtr, colInds, indPtr, colInds, U, V,
                                     gp, gq)
            self.assertAlmostEquals(obj, obj2, 2)

        #Check full and summary versions are the same
        obj = learner.objective(indPtr, colInds, indPtr, colInds, U, V, gp, gq)
        obj2 = learner.objective(indPtr, colInds, indPtr, colInds, U, V, gp,
                                 gq)
        self.assertAlmostEquals(obj, obj2, 2)
Пример #4
0
    def testDerivativeViApprox(self):
        """
        We'll test the case in which we apprormate using a large number of samples 
        for the AUC and see if we get close to the exact derivative 
        """
        m = 20
        n = 30
        k = 3
        X = SparseUtils.generateSparseBinaryMatrix((m, n), k, csarray=True)

        for i in range(m):
            X[i, 0] = 1
            X[i, 1] = 0

        w = 0.1
        eps = 0.001
        learner = MaxAUCTanh(k, w)
        learner.normalise = False
        learner.lmbdaU = 0
        learner.lmbdaV = 0
        learner.numAucSamples = n

        indPtr, colInds = SparseUtils.getOmegaListPtr(X)

        U = numpy.random.rand(X.shape[0], k)
        V = numpy.random.rand(X.shape[1], k)

        gp = numpy.random.rand(n)
        gp /= gp.sum()
        gq = numpy.random.rand(n)
        gq /= gq.sum()

        permutedRowInds = numpy.array(numpy.random.permutation(m),
                                      numpy.uint32)
        permutedColInds = numpy.array(numpy.random.permutation(n),
                                      numpy.uint32)

        maxLocalAuc = MaxLocalAUC(k, w)
        normGp, normGq = maxLocalAuc.computeNormGpq(indPtr, colInds, gp, gq, m)

        numRuns = 100
        numTests = 5

        #Let's compare against using the exact derivative
        for i in numpy.random.permutation(m)[0:numTests]:
            U = numpy.random.rand(X.shape[0], k)
            V = numpy.random.rand(X.shape[1], k)
            dv1 = numpy.zeros(k)
            for j in range(numRuns):
                dv1 += learner.derivativeViApprox(indPtr, colInds, U, V, gp,
                                                  gq, normGp, normGq,
                                                  permutedRowInds,
                                                  permutedColInds, i)
            dv1 /= numRuns
            dv2 = learner.derivativeVi(indPtr, colInds, U, V, gp, gq, i)

            dv3 = numpy.zeros(k)
            for j in range(k):
                eps = 10**-6
                tempV = V.copy()
                tempV[i, j] += eps
                obj1 = learner.objective(indPtr, colInds, indPtr, colInds, U,
                                         tempV, gp, gq)

                tempV = V.copy()
                tempV[i, j] -= eps
                obj2 = learner.objective(indPtr, colInds, indPtr, colInds, U,
                                         tempV, gp, gq)

                dv3[j] = (obj1 - obj2) / (2 * eps)

            print(dv1, dv2, dv3)

            nptst.assert_array_almost_equal(dv1, dv2, 2)

        learner.lmbdaV = 0.5
        learner.rho = 0.5

        for i in numpy.random.permutation(m)[0:numTests]:
            U = numpy.random.rand(X.shape[0], k)
            V = numpy.random.rand(X.shape[1], k)

            dv1 = numpy.zeros(k)
            for j in range(numRuns):
                dv1 += learner.derivativeViApprox(indPtr, colInds, U, V, gp,
                                                  gq, normGp, normGq,
                                                  permutedRowInds,
                                                  permutedColInds, i)
            dv1 /= numRuns
            dv2 = learner.derivativeVi(indPtr, colInds, U, V, gp, gq, i)
            print(dv1, dv2)
            nptst.assert_array_almost_equal(dv1, dv2, 2)

        learner.numRowSamples = 10
        numRuns = 1000

        for i in numpy.random.permutation(m)[0:numTests]:
            U = numpy.random.rand(X.shape[0], k)
            V = numpy.random.rand(X.shape[1], k)

            dv1 = numpy.zeros(k)
            for j in range(numRuns):
                dv1 += learner.derivativeViApprox(indPtr, colInds, U, V, gp,
                                                  gq, normGp, normGq,
                                                  permutedRowInds,
                                                  permutedColInds, i)
            dv1 /= numRuns
            dv2 = learner.derivativeVi(indPtr, colInds, U, V, gp, gq, i)
            print(dv1, dv2)
            #nptst.assert_array_almost_equal(dv1, dv2, 3)

        maxLocalAuc.numRowSamples = m
        maxLocalAuc.numAucSamples = 20
        maxLocalAuc.lmbdaV = 0
        numRuns = 1000
        print("Final test")

        #for i in numpy.random.permutation(m)[0:numTests]:
        for i in range(m):
            U = numpy.random.rand(X.shape[0], k)
            V = numpy.random.rand(X.shape[1], k)

            dv1 = numpy.zeros(k)
            for j in range(numRuns):
                dv1 += learner.derivativeViApprox(indPtr, colInds, U, V, gp,
                                                  gq, normGp, normGq,
                                                  permutedRowInds,
                                                  permutedColInds, i)
            dv1 /= numRuns
            #dv1 = learner.derivativeVi(indPtr, colInds, U, V, gp, gq, i)
            dv2 = learner.derivativeVi(indPtr, colInds, U, V, gp, gq, i)

            print(i, dv1, dv2)
            nptst.assert_array_almost_equal(dv1, dv2, 2)
Пример #5
0
    def testDerivativeV(self):
        m = 10
        n = 20
        nnzPerRow = 5
        X = SparseUtils.generateSparseBinaryMatrix((m, n),
                                                   nnzPerRow,
                                                   csarray=True)

        for i in range(m):
            X[i, 0] = 1
            X[i, 1] = 0

        k = 5
        u = 0.1
        w = 1 - u
        eps = 0.05
        learner = MaxAUCTanh(k, w)
        learner.normalise = False
        learner.lmbdaU = 0
        learner.lmbdaV = 0
        learner.rho = 1.0
        learner.numAucSamples = 100

        numRuns = 20
        indPtr, colInds = SparseUtils.getOmegaListPtr(X)

        gp = numpy.random.rand(n)
        gp /= gp.sum()
        gq = numpy.random.rand(n)
        gq /= gq.sum()

        for s in range(numRuns):
            U = numpy.random.randn(m, k)
            V = numpy.random.randn(n, k)

            deltaV = numpy.zeros(V.shape)
            for j in range(n):
                deltaV[j, :] = learner.derivativeVi(indPtr, colInds, U, V, gp,
                                                    gq, j)

            deltaV2 = numpy.zeros(V.shape)

            eps = 0.00001

            for i in range(n):
                for j in range(k):
                    tempV = V.copy()
                    tempV[i, j] += eps
                    obj1 = learner.objective(indPtr, colInds, indPtr, colInds,
                                             U, tempV, gp, gq)

                    tempV = V.copy()
                    tempV[i, j] -= eps
                    obj2 = learner.objective(indPtr, colInds, indPtr, colInds,
                                             U, tempV, gp, gq)

                    deltaV2[i, j] = (obj1 - obj2) / (2 * eps)
                #deltaV2[i,:] = deltaV2[i,:]/numpy.linalg.norm(deltaV2[i,:])

            #print(deltaV*100)
            #print(deltaV2*100)
            nptst.assert_almost_equal(deltaV, deltaV2, 3)

        #Try r != 0 and rho > 0
        for s in range(numRuns):
            U = numpy.random.randn(m, k)
            V = numpy.random.randn(n, k)
            learner.rho = 0.5

            deltaV = numpy.zeros(V.shape)
            for j in range(n):
                deltaV[j, :] = learner.derivativeVi(indPtr, colInds, U, V, gp,
                                                    gq, j)

            deltaV2 = numpy.zeros(V.shape)

            for i in range(n):
                for j in range(k):
                    tempV = V.copy()
                    tempV[i, j] += eps
                    obj1 = learner.objective(indPtr, colInds, indPtr, colInds,
                                             U, tempV, gp, gq)

                    tempV = V.copy()
                    tempV[i, j] -= eps
                    obj2 = learner.objective(indPtr, colInds, indPtr, colInds,
                                             U, tempV, gp, gq)

                    deltaV2[i, j] = (obj1 - obj2) / (2 * eps)
                #deltaV2[i,:] = deltaV2[i,:]/numpy.linalg.norm(deltaV2[i,:])

            nptst.assert_almost_equal(deltaV, deltaV2, 3)

        #Try r != 0 and rho > 0
        for s in range(numRuns):
            U = numpy.random.randn(m, k)
            V = numpy.random.randn(n, k)

            learner.lmbdaV = 100

            deltaV = numpy.zeros(V.shape)
            for j in range(n):
                deltaV[j, :] = learner.derivativeVi(indPtr, colInds, U, V, gp,
                                                    gq, j)

            deltaV2 = numpy.zeros(V.shape)

            for i in range(n):
                for j in range(k):
                    tempV = V.copy()
                    tempV[i, j] += eps
                    obj1 = learner.objective(indPtr, colInds, indPtr, colInds,
                                             U, tempV, gp, gq)

                    tempV = V.copy()
                    tempV[i, j] -= eps
                    obj2 = learner.objective(indPtr, colInds, indPtr, colInds,
                                             U, tempV, gp, gq)

                    deltaV2[i, j] = (obj1 - obj2) / (2 * eps)
                #deltaV2[i,:] = deltaV2[i,:]/numpy.linalg.norm(deltaV2[i,:])

            nptst.assert_almost_equal(deltaV, deltaV2, 3)
Пример #6
0
    def testDerivativeU(self):
        m = 10
        n = 20
        nnzPerRow = 5
        X = SparseUtils.generateSparseBinaryMatrix((m, n),
                                                   nnzPerRow,
                                                   csarray=True)

        k = 5
        u = 0.1
        w = 1 - u
        eps = 0.05
        learner = MaxAUCTanh(k, w)
        learner.normalise = False
        learner.lmbdaU = 0
        learner.lmbdaV = 0
        learner.rho = 1.0
        learner.numAucSamples = n

        numRuns = 20
        r = numpy.zeros(m)
        gi = numpy.random.rand(m)
        gi /= gi.sum()
        gp = numpy.random.rand(n)
        gp /= gp.sum()
        gq = numpy.random.rand(n)
        gq /= gq.sum()

        indPtr, colInds = SparseUtils.getOmegaListPtr(X)

        for s in range(numRuns):
            U = numpy.random.randn(m, k)
            V = numpy.random.randn(n, k)
            deltaU = numpy.zeros(U.shape)
            for i in range(X.shape[0]):
                deltaU[i, :] = learner.derivativeUi(indPtr, colInds, U, V, gp,
                                                    gq, i)

            deltaU2 = numpy.zeros(U.shape)
            eps = 10**-8

            for i in range(m):
                for j in range(k):
                    tempU = U.copy()
                    tempU[i, j] += eps
                    obj1 = learner.objective(indPtr, colInds, indPtr, colInds,
                                             tempU, V, gp, gq)

                    tempU = U.copy()
                    tempU[i, j] -= eps
                    obj2 = learner.objective(indPtr, colInds, indPtr, colInds,
                                             tempU, V, gp, gq)

                    deltaU2[i, j] = (obj1 - obj2) / (2 * eps)

                #deltaU2[i,:] = deltaU2[i,:]/numpy.linalg.norm(deltaU2[i,:])

            #print(deltaU*100)
            #print(deltaU2*100)
            nptst.assert_almost_equal(deltaU, deltaU2, 3)

        #Try r != 0 and rho > 0
        for s in range(numRuns):
            U = numpy.random.randn(m, k)
            V = numpy.random.randn(n, k)
            learner.rho = 0.1

            deltaU = numpy.zeros(U.shape)
            for i in range(X.shape[0]):
                deltaU[i, :] = learner.derivativeUi(indPtr, colInds, U, V, gp,
                                                    gq, i)

            deltaU2 = numpy.zeros(U.shape)
            eps = 10**-9

            for i in range(m):
                for j in range(k):
                    tempU = U.copy()
                    tempU[i, j] += eps
                    obj1 = learner.objective(indPtr, colInds, indPtr, colInds,
                                             tempU, V, gp, gq)

                    tempU = U.copy()
                    tempU[i, j] -= eps
                    obj2 = learner.objective(indPtr, colInds, indPtr, colInds,
                                             tempU, V, gp, gq)

                    deltaU2[i, j] = (obj1 - obj2) / (2 * eps)

            nptst.assert_almost_equal(deltaU, deltaU2, 3)

        #Try lmbda > 0

        for s in range(numRuns):
            U = numpy.random.randn(m, k)
            V = numpy.random.randn(n, k)
            learner.lmbdaU = 0.5

            deltaU = numpy.zeros(U.shape)
            for i in range(X.shape[0]):
                deltaU[i, :] = learner.derivativeUi(indPtr, colInds, U, V, gp,
                                                    gq, i)

            deltaU2 = numpy.zeros(U.shape)
            eps = 10**-9

            for i in range(m):
                for j in range(k):
                    tempU = U.copy()
                    tempU[i, j] += eps
                    obj1 = learner.objective(indPtr, colInds, indPtr, colInds,
                                             tempU, V, gp, gq)

                    tempU = U.copy()
                    tempU[i, j] -= eps
                    obj2 = learner.objective(indPtr, colInds, indPtr, colInds,
                                             tempU, V, gp, gq)

                    deltaU2[i, j] = (obj1 - obj2) / (2 * eps)

            nptst.assert_almost_equal(deltaU, deltaU2, 3)
Пример #7
0
    def testDerivativeUiApprox(self):
        """
        We'll test the case in which we apprormate using a large number of samples 
        for the AUC and see if we get close to the exact derivative 
        """
        m = 20
        n = 30
        k = 3
        X = SparseUtils.generateSparseBinaryMatrix((m, n), k, csarray=True)

        w = 0.1
        learner = MaxAUCTanh(k, w)
        learner.normalise = False
        learner.lmbdaU = 0
        learner.lmbdaV = 0
        learner.rho = 1.0
        learner.numAucSamples = 100

        U = numpy.random.rand(X.shape[0], k)
        V = numpy.random.rand(X.shape[1], k)

        gp = numpy.random.rand(n)
        gp /= gp.sum()
        gq = numpy.random.rand(n)
        gq /= gq.sum()

        numRuns = 200
        numTests = 5

        indPtr, colInds = SparseUtils.getOmegaListPtr(X)
        permutedColInds = numpy.arange(n, dtype=numpy.uint32)

        #Test with small number of AUC samples, but normalise
        learner.numAucSamples = n
        numRuns = 1000

        for i in numpy.random.permutation(m)[0:numTests]:
            U = numpy.random.rand(X.shape[0], k)
            V = numpy.random.rand(X.shape[1], k)

            du1 = numpy.zeros(k)
            for j in range(numRuns):
                du1 += learner.derivativeUiApprox(indPtr, colInds, U, V, gp,
                                                  gq, permutedColInds, i)
            du1 /= numRuns
            du2 = learner.derivativeUi(indPtr, colInds, U, V, gp, gq, i)
            #print(du1, du2)
            print(du1 / numpy.linalg.norm(du1), du2 / numpy.linalg.norm(du2))
            #print(numpy.linalg.norm(du1 - du2)/numpy.linalg.norm(du1))
            self.assertTrue(
                numpy.linalg.norm(du1 - du2) / numpy.linalg.norm(du1) < 0.5)

        #Let's compare against using the exact derivative
        for i in numpy.random.permutation(m)[0:numTests]:
            U = numpy.random.rand(X.shape[0], k)
            V = numpy.random.rand(X.shape[1], k)

            du1 = numpy.zeros(k)
            for j in range(numRuns):
                du1 += learner.derivativeUiApprox(indPtr, colInds, U, V, gp,
                                                  gq, permutedColInds, i)
            du1 /= numRuns
            du2 = learner.derivativeUi(indPtr, colInds, U, V, gp, gq, i)

            print(du1 / numpy.linalg.norm(du1), du2 / numpy.linalg.norm(du2))
            nptst.assert_array_almost_equal(du1, du2, 2)

        learner.lmbdaV = 0.5
        learner.rho = 0.5

        for i in numpy.random.permutation(m)[0:numTests]:
            U = numpy.random.rand(X.shape[0], k)
            V = numpy.random.rand(X.shape[1], k)

            du1 = numpy.zeros(k)
            for j in range(numRuns):
                du1 += learner.derivativeUiApprox(indPtr, colInds, U, V, gp,
                                                  gq, permutedColInds, i)
            du1 /= numRuns
            du2 = learner.derivativeUi(indPtr, colInds, U, V, gp, gq, i)
            nptst.assert_array_almost_equal(du1, du2, 2)
            print(du1 / numpy.linalg.norm(du1), du2 / numpy.linalg.norm(du2))
Пример #8
0
    def testObjectiveApprox(self): 
        """
        We'll test the case in which we apprormate using a large number of samples 
        for the AUC and see if we get close to the exact objective 
        """
        m = 20 
        n = 30 
        k = 3 
        X = SparseUtils.generateSparseBinaryMatrix((m, n), k, csarray=True)
        
        w = 0.1
        learner = MaxAUCTanh(k, w)
        learner.normalise = False
        learner.lmbdaU = 0
        learner.lmbdaV = 0
        learner.rho = 1.0
        learner.numAucSamples = n
        
        indPtr, colInds = SparseUtils.getOmegaListPtr(X)
        
        U = numpy.random.rand(X.shape[0], k)
        V = numpy.random.rand(X.shape[1], k)
        
        numRuns = 100 
        numTests = 5
             
        gp = numpy.random.rand(n)
        gp /= gp.sum()        
        gq = numpy.random.rand(n)
        gq /= gq.sum()
        #gi = numpy.ones(m)
        #gp = numpy.ones(n)
        #gq = numpy.ones(n)

        #Let's compare against using the exact derivative 
        for i in range(numTests): 
            obj = 0

            for j in range(numRuns): 
                obj += learner.objectiveApprox(indPtr, colInds, indPtr, colInds, U, V, gp, gq)
            obj /= numRuns

            obj2 = learner.objective(indPtr, colInds, indPtr, colInds, U, V, gp, gq)    
            self.assertAlmostEquals(obj, obj2, 2)
            
        learner.rho = 0.2

        for i in range(numTests): 
            obj = 0
            for j in range(numRuns): 
                obj += learner.objectiveApprox(indPtr, colInds, indPtr, colInds, U, V, gp, gq)
            obj /= numRuns
            
            obj2 = learner.objective(indPtr, colInds, indPtr, colInds, U, V, gp, gq)    
            self.assertAlmostEquals(obj, obj2, 2)

        learner.lmbdaV = 0.2

        for i in range(numTests): 
            obj = 0
            for j in range(numRuns): 
                obj += learner.objectiveApprox(indPtr, colInds, indPtr, colInds, U, V, gp, gq)
            obj /= numRuns
            
            obj2 = learner.objective(indPtr, colInds, indPtr, colInds, U, V, gp, gq)    
            self.assertAlmostEquals(obj, obj2, 2)
        
        #Check full and summary versions are the same 
        obj = learner.objective(indPtr, colInds, indPtr, colInds, U, V, gp, gq) 
        obj2 = learner.objective(indPtr, colInds, indPtr, colInds, U, V, gp, gq) 
        self.assertAlmostEquals(obj, obj2, 2)
Пример #9
0
    def testDerivativeViApprox(self): 
        """
        We'll test the case in which we apprormate using a large number of samples 
        for the AUC and see if we get close to the exact derivative 
        """
        m = 20 
        n = 30 
        k = 3 
        X = SparseUtils.generateSparseBinaryMatrix((m, n), k, csarray=True)
        
        for i in range(m):
            X[i, 0] = 1
            X[i, 1] = 0
        
        w = 0.1
        eps = 0.001
        learner = MaxAUCTanh(k, w)
        learner.normalise = False
        learner.lmbdaU = 0
        learner.lmbdaV = 0
        learner.numAucSamples = n
        
        indPtr, colInds = SparseUtils.getOmegaListPtr(X)

        U = numpy.random.rand(X.shape[0], k)
        V = numpy.random.rand(X.shape[1], k)
             
        gp = numpy.random.rand(n)
        gp /= gp.sum()        
        gq = numpy.random.rand(n)
        gq /= gq.sum()     
        
        permutedRowInds = numpy.array(numpy.random.permutation(m), numpy.uint32)
        permutedColInds = numpy.array(numpy.random.permutation(n), numpy.uint32)
        
        maxLocalAuc = MaxLocalAUC(k, w)
        normGp, normGq = maxLocalAuc.computeNormGpq(indPtr, colInds, gp, gq, m)
        
        numRuns = 100 
        numTests = 5

        #Let's compare against using the exact derivative 
        for i in numpy.random.permutation(m)[0:numTests]: 
            U = numpy.random.rand(X.shape[0], k)
            V = numpy.random.rand(X.shape[1], k)
            dv1 = numpy.zeros(k)
            for j in range(numRuns): 
                dv1 += learner.derivativeViApprox(indPtr, colInds, U, V, gp, gq, normGp, normGq, permutedRowInds, permutedColInds, i)
            dv1 /= numRuns
            dv2 = learner.derivativeVi(indPtr, colInds, U, V, gp, gq, i)   
            
            
            dv3 = numpy.zeros(k)
            for j in range(k): 
                eps = 10**-6
                tempV = V.copy() 
                tempV[i,j] += eps
                obj1 = learner.objective(indPtr, colInds, indPtr, colInds, U, tempV, gp, gq)
                
                tempV = V.copy() 
                tempV[i,j] -= eps
                obj2 = learner.objective(indPtr, colInds, indPtr, colInds, U, tempV, gp, gq)
                
                dv3[j] = (obj1-obj2)/(2*eps)            
            
            print(dv1, dv2, dv3)
            
            nptst.assert_array_almost_equal(dv1, dv2, 2)
            
        learner.lmbdaV = 0.5 
        learner.rho = 0.5 
        
        for i in numpy.random.permutation(m)[0:numTests]: 
            U = numpy.random.rand(X.shape[0], k)
            V = numpy.random.rand(X.shape[1], k)            
    
            dv1 = numpy.zeros(k)
            for j in range(numRuns): 
                dv1 += learner.derivativeViApprox(indPtr, colInds, U, V,  gp, gq, normGp, normGq, permutedRowInds, permutedColInds, i)
            dv1 /= numRuns
            dv2 = learner.derivativeVi(indPtr, colInds, U, V, gp, gq, i) 
            print(dv1, dv2)
            nptst.assert_array_almost_equal(dv1, dv2, 2)
            
        learner.numRowSamples = 10 
        numRuns = 1000
        
        for i in numpy.random.permutation(m)[0:numTests]: 
            U = numpy.random.rand(X.shape[0], k)
            V = numpy.random.rand(X.shape[1], k)            
            
            dv1 = numpy.zeros(k)
            for j in range(numRuns): 
                dv1 += learner.derivativeViApprox(indPtr, colInds, U, V, gp, gq, normGp, normGq, permutedRowInds, permutedColInds, i)
            dv1 /= numRuns
            dv2 = learner.derivativeVi(indPtr, colInds, U, V, gp, gq, i)  
            print(dv1, dv2)
            #nptst.assert_array_almost_equal(dv1, dv2, 3)

        maxLocalAuc.numRowSamples = m 
        maxLocalAuc.numAucSamples = 20 
        maxLocalAuc.lmbdaV = 0
        numRuns = 1000
        print("Final test")
        
        #for i in numpy.random.permutation(m)[0:numTests]: 
        for i in range(m): 
            U = numpy.random.rand(X.shape[0], k)
            V = numpy.random.rand(X.shape[1], k)            
            
            dv1 = numpy.zeros(k)
            for j in range(numRuns): 
                dv1 += learner.derivativeViApprox(indPtr, colInds, U, V, gp, gq, normGp, normGq, permutedRowInds, permutedColInds, i)
            dv1 /= numRuns
            #dv1 = learner.derivativeVi(indPtr, colInds, U, V, gp, gq, i) 
            dv2 = learner.derivativeVi(indPtr, colInds, U, V, gp, gq, i)   
                      
            
            print(i, dv1, dv2)
            nptst.assert_array_almost_equal(dv1, dv2, 2)
Пример #10
0
    def testDerivativeV(self): 
        m = 10 
        n = 20 
        nnzPerRow = 5 
        X = SparseUtils.generateSparseBinaryMatrix((m, n), nnzPerRow, csarray=True)
        
        for i in range(m):
            X[i, 0] = 1
            X[i, 1] = 0
        
        k = 5
        u = 0.1
        w = 1-u
        eps = 0.05
        learner = MaxAUCTanh(k, w)
        learner.normalise = False
        learner.lmbdaU = 0
        learner.lmbdaV = 0
        learner.rho = 1.0
        learner.numAucSamples = 100

        numRuns = 20
        indPtr, colInds = SparseUtils.getOmegaListPtr(X)
            
        gp = numpy.random.rand(n)
        gp /= gp.sum()        
        gq = numpy.random.rand(n)
        gq /= gq.sum()            
        
        for s in range(numRuns):
            U = numpy.random.randn(m, k)
            V = numpy.random.randn(n, k)            
            
            deltaV = numpy.zeros(V.shape)
            for j in range(n): 
                deltaV[j, :] = learner.derivativeVi(indPtr, colInds, U, V, gp, gq, j)   
            
            deltaV2 = numpy.zeros(V.shape)    
            
            eps = 0.00001        
            
            for i in range(n): 
                for j in range(k):
                    tempV = V.copy() 
                    tempV[i,j] += eps
                    obj1 = learner.objective(indPtr, colInds, indPtr, colInds, U, tempV, gp, gq)
                    
                    tempV = V.copy() 
                    tempV[i,j] -= eps
                    obj2 = learner.objective(indPtr, colInds, indPtr, colInds, U, tempV, gp, gq)
                    
                    deltaV2[i,j] = (obj1-obj2)/(2*eps)
                #deltaV2[i,:] = deltaV2[i,:]/numpy.linalg.norm(deltaV2[i,:])                   
                        
            #print(deltaV*100)
            #print(deltaV2*100)
            nptst.assert_almost_equal(deltaV, deltaV2, 3)

        #Try r != 0 and rho > 0
        for s in range(numRuns):
            U = numpy.random.randn(m, k)
            V = numpy.random.randn(n, k)   
            learner.rho = 0.5  
            
            deltaV = numpy.zeros(V.shape)
            for j in range(n): 
                deltaV[j, :] = learner.derivativeVi(indPtr, colInds, U, V, gp, gq, j)    
            
            deltaV2 = numpy.zeros(V.shape)
            
            for i in range(n): 
                for j in range(k):
                    tempV = V.copy() 
                    tempV[i,j] += eps
                    obj1 = learner.objective(indPtr, colInds, indPtr, colInds, U, tempV, gp, gq)
                    
                    tempV = V.copy() 
                    tempV[i,j] -= eps
                    obj2 = learner.objective(indPtr, colInds, indPtr, colInds, U, tempV, gp, gq)
                    
                    deltaV2[i,j] = (obj1-obj2)/(2*eps)
                #deltaV2[i,:] = deltaV2[i,:]/numpy.linalg.norm(deltaV2[i,:])
                           
            nptst.assert_almost_equal(deltaV, deltaV2, 3)
        
        
        #Try r != 0 and rho > 0
        for s in range(numRuns):
            U = numpy.random.randn(m, k)
            V = numpy.random.randn(n, k)              
            
            learner.lmbdaV = 100    
            
            deltaV = numpy.zeros(V.shape)
            for j in range(n): 
                deltaV[j, :] = learner.derivativeVi(indPtr, colInds, U, V, gp, gq, j)
            
            deltaV2 = numpy.zeros(V.shape)
            
            for i in range(n): 
                for j in range(k):
                    tempV = V.copy() 
                    tempV[i,j] += eps
                    obj1 = learner.objective(indPtr, colInds, indPtr, colInds, U, tempV, gp, gq)
                    
                    tempV = V.copy() 
                    tempV[i,j] -= eps
                    obj2 = learner.objective(indPtr, colInds, indPtr, colInds, U, tempV,  gp, gq)
                    
                    deltaV2[i,j] = (obj1-obj2)/(2*eps)
                #deltaV2[i,:] = deltaV2[i,:]/numpy.linalg.norm(deltaV2[i,:])
              
            nptst.assert_almost_equal(deltaV, deltaV2, 3)         
Пример #11
0
    def testDerivativeU(self): 
        m = 10 
        n = 20 
        nnzPerRow = 5 
        X = SparseUtils.generateSparseBinaryMatrix((m, n), nnzPerRow, csarray=True)
        
        k = 5
        u = 0.1
        w = 1-u
        eps = 0.05
        learner = MaxAUCTanh(k, w)
        learner.normalise = False
        learner.lmbdaU = 0
        learner.lmbdaV = 0
        learner.rho = 1.0
        learner.numAucSamples = n
        
         

        numRuns = 20
        r = numpy.zeros(m)
        gi = numpy.random.rand(m)
        gi /= gi.sum()        
        gp = numpy.random.rand(n)
        gp /= gp.sum()        
        gq = numpy.random.rand(n)
        gq /= gq.sum()     
        
        indPtr, colInds = SparseUtils.getOmegaListPtr(X)

        for s in range(numRuns):
            U = numpy.random.randn(m, k)
            V = numpy.random.randn(n, k)
            deltaU = numpy.zeros(U.shape)
            for i in range(X.shape[0]): 
                deltaU[i, :] = learner.derivativeUi(indPtr, colInds, U, V, gp, gq, i)      
    
            deltaU2 = numpy.zeros(U.shape) 
            eps = 10**-8         
            
            for i in range(m): 
                for j in range(k):
                    tempU = U.copy() 
                    tempU[i,j] += eps
                    obj1 = learner.objective(indPtr, colInds, indPtr, colInds, tempU, V, gp, gq)
                    
                    tempU = U.copy() 
                    tempU[i,j] -= eps
                    obj2 = learner.objective(indPtr, colInds, indPtr, colInds, tempU, V, gp, gq)
                    
                    deltaU2[i,j] = (obj1-obj2)/(2*eps)
    
                #deltaU2[i,:] = deltaU2[i,:]/numpy.linalg.norm(deltaU2[i,:])
            
            #print(deltaU*100)
            #print(deltaU2*100)
            nptst.assert_almost_equal(deltaU, deltaU2, 3)
        
        #Try r != 0 and rho > 0
        for s in range(numRuns):
            U = numpy.random.randn(m, k)
            V = numpy.random.randn(n, k)
            learner.rho = 0.1
            
            deltaU = numpy.zeros(U.shape)
            for i in range(X.shape[0]): 
                deltaU[i, :] = learner.derivativeUi(indPtr, colInds, U, V, gp, gq, i)
            
            deltaU2 = numpy.zeros(U.shape) 
            eps = 10**-9        
            
            for i in range(m): 
                for j in range(k):
                    tempU = U.copy() 
                    tempU[i,j] += eps
                    obj1 = learner.objective(indPtr, colInds, indPtr, colInds, tempU, V, gp, gq)
                    
                    tempU = U.copy() 
                    tempU[i,j] -= eps
                    obj2 = learner.objective(indPtr, colInds, indPtr, colInds, tempU, V, gp, gq)
                    
                    deltaU2[i,j] = (obj1-obj2)/(2*eps)
                                
            nptst.assert_almost_equal(deltaU, deltaU2, 3)
        
        #Try lmbda > 0
        
        for s in range(numRuns):
            U = numpy.random.randn(m, k)
            V = numpy.random.randn(n, k)
            learner.lmbdaU = 0.5
            
            deltaU = numpy.zeros(U.shape)
            for i in range(X.shape[0]): 
                deltaU[i, :] = learner.derivativeUi(indPtr, colInds, U, V, gp, gq, i) 
            
            deltaU2 = numpy.zeros(U.shape) 
            eps = 10**-9        
            
            for i in range(m): 
                for j in range(k):
                    tempU = U.copy() 
                    tempU[i,j] += eps
                    obj1 = learner.objective(indPtr, colInds, indPtr, colInds, tempU, V, gp, gq)
                    
                    tempU = U.copy() 
                    tempU[i,j] -= eps
                    obj2 = learner.objective(indPtr, colInds, indPtr, colInds, tempU, V, gp, gq)
                    
                    deltaU2[i,j] = (obj1-obj2)/(2*eps)
                                
            nptst.assert_almost_equal(deltaU, deltaU2, 3)
Пример #12
0
    def testDerivativeUiApprox(self): 
        """
        We'll test the case in which we apprormate using a large number of samples 
        for the AUC and see if we get close to the exact derivative 
        """
        m = 20 
        n = 30 
        k = 3 
        X = SparseUtils.generateSparseBinaryMatrix((m, n), k, csarray=True)
        
        w = 0.1
        learner = MaxAUCTanh(k, w)
        learner.normalise = False
        learner.lmbdaU = 0
        learner.lmbdaV = 0
        learner.rho = 1.0
        learner.numAucSamples = 100

        U = numpy.random.rand(X.shape[0], k)
        V = numpy.random.rand(X.shape[1], k)

        gp = numpy.random.rand(n)
        gp /= gp.sum()        
        gq = numpy.random.rand(n)
        gq /= gq.sum()     

        
        numRuns = 200 
        numTests = 5
        
        indPtr, colInds = SparseUtils.getOmegaListPtr(X)
        permutedColInds = numpy.arange(n, dtype=numpy.uint32)

        #Test with small number of AUC samples, but normalise 
        learner.numAucSamples = n
        numRuns = 1000
        
        for i in numpy.random.permutation(m)[0:numTests]:  
            U = numpy.random.rand(X.shape[0], k)
            V = numpy.random.rand(X.shape[1], k)            
            
            du1 = numpy.zeros(k)
            for j in range(numRuns): 
                du1 += learner.derivativeUiApprox(indPtr, colInds, U, V, gp, gq, permutedColInds, i)
            du1 /= numRuns
            du2 = learner.derivativeUi(indPtr, colInds, U, V, gp, gq, i) 
            #print(du1, du2)
            print(du1/numpy.linalg.norm(du1), du2/numpy.linalg.norm(du2))
            #print(numpy.linalg.norm(du1 - du2)/numpy.linalg.norm(du1))
            self.assertTrue(numpy.linalg.norm(du1 - du2)/numpy.linalg.norm(du1) < 0.5)

        #Let's compare against using the exact derivative 
        for i in numpy.random.permutation(m)[0:numTests]:  
            U = numpy.random.rand(X.shape[0], k)
            V = numpy.random.rand(X.shape[1], k)            
            
            du1 = numpy.zeros(k)
            for j in range(numRuns): 
                du1 += learner.derivativeUiApprox(indPtr, colInds, U, V, gp, gq, permutedColInds, i)
            du1 /= numRuns
            du2 = learner.derivativeUi(indPtr, colInds, U, V, gp, gq, i)   
            
            print(du1/numpy.linalg.norm(du1), du2/numpy.linalg.norm(du2))
            nptst.assert_array_almost_equal(du1, du2, 2)
            
            
        learner.lmbdaV = 0.5 
        learner.rho = 0.5
        
        for i in numpy.random.permutation(m)[0:numTests]:  
            U = numpy.random.rand(X.shape[0], k)
            V = numpy.random.rand(X.shape[1], k)            
            
            du1 = numpy.zeros(k)
            for j in range(numRuns): 
                du1 += learner.derivativeUiApprox(indPtr, colInds, U, V, gp, gq, permutedColInds, i)
            du1 /= numRuns
            du2 = learner.derivativeUi(indPtr, colInds, U, V, gp, gq, i)   
            nptst.assert_array_almost_equal(du1, du2, 2)
            print(du1/numpy.linalg.norm(du1), du2/numpy.linalg.norm(du2))