1 /* Copyright 2016 The TensorFlow Authors. All Rights Reserved. 2 3 Licensed under the Apache License, Version 2.0 (the "License"); 4 you may not use this file except in compliance with the License. 5 You may obtain a copy of the License at 6 7 http://www.apache.org/licenses/LICENSE-2.0 8 9 Unless required by applicable law or agreed to in writing, software 10 distributed under the License is distributed on an "AS IS" BASIS, 11 WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 12 See the License for the specific language governing permissions and 13 limitations under the License. 14 ==============================================================================*/ 15 16 #ifndef TENSORFLOW_CORE_KERNELS_POISSON_LOSS_H_ 17 #define TENSORFLOW_CORE_KERNELS_POISSON_LOSS_H_ 18 19 #include <cmath> 20 21 #include "tensorflow/core/kernels/loss.h" 22 #include "tensorflow/core/lib/core/errors.h" 23 24 namespace tensorflow { 25 26 class PoissonLossUpdater : public DualLossUpdater { 27 public: 28 // Update is found by a Newton algorithm (see readme.md). ComputeUpdatedDual(const int num_loss_partitions,const double label,const double example_weight,const double current_dual,const double wx,const double weighted_example_norm)29 double ComputeUpdatedDual(const int num_loss_partitions, const double label, 30 const double example_weight, 31 const double current_dual, const double wx, 32 const double weighted_example_norm) const final { 33 // Newton algorithm converges quadratically so 10 steps will be largely 34 // enough to achieve a very good precision 35 static const int newton_total_steps = 10; 36 // Initialize the Newton optimization at x such that 37 // exp(x) = label - current_dual 38 const double y_minus_a = label - current_dual; 39 double x = (y_minus_a > 0) ? log(y_minus_a) : 0; 40 for (int i = 0; i < newton_total_steps; ++i) { 41 x = NewtonStep(x, num_loss_partitions, label, wx, example_weight, 42 weighted_example_norm, current_dual); 43 } 44 return label - exp(x); 45 } 46 47 // Dual of poisson loss function. 48 // https://en.wikipedia.org/wiki/Convex_conjugate ComputeDualLoss(const double current_dual,const double example_label,const double example_weight)49 double ComputeDualLoss(const double current_dual, const double example_label, 50 const double example_weight) const final { 51 // Dual of the poisson loss function is 52 // (y-a)*(log(y-a)-1), where a is the dual variable. 53 // It is defined only for a<y. 54 const double y_minus_a = example_label - current_dual; 55 if (y_minus_a == 0.0) { 56 // (y-a)*(log(y-a)-1) approaches 0 as y-a approaches 0. 57 return 0.0; 58 } 59 if (y_minus_a < 0.0) { 60 return std::numeric_limits<double>::max(); 61 } 62 return y_minus_a * (log(y_minus_a) - 1) * example_weight; 63 } 64 ComputePrimalLoss(const double wx,const double example_label,const double example_weight)65 double ComputePrimalLoss(const double wx, const double example_label, 66 const double example_weight) const final { 67 return (exp(wx) - wx * example_label) * example_weight; 68 } 69 PrimalLossDerivative(const double wx,const double label,const double example_weight)70 double PrimalLossDerivative(const double wx, const double label, 71 const double example_weight) const final { 72 return (exp(wx) - label) * example_weight; 73 } 74 75 // TODO(chapelle): We need to introduce a maximum_prediction parameter, 76 // expose that parameter to the user and have this method return 77 // 1.0/maximum_prediction. 78 // Setting this at 1 for now, it only impacts the adaptive sampling. SmoothnessConstant()79 double SmoothnessConstant() const final { return 1; } 80 ConvertLabel(float * const example_label)81 Status ConvertLabel(float* const example_label) const final { 82 if (*example_label < 0.0) { 83 return errors::InvalidArgument( 84 "Only non-negative labels can be used with the Poisson log loss. " 85 "Found example with label: ", *example_label); 86 } 87 return Status::OK(); 88 } 89 90 private: 91 // One Newton step (see readme.md). NewtonStep(const double x,const int num_loss_partitions,const double label,const double wx,const double example_weight,const double weighted_example_norm,const double current_dual)92 double NewtonStep(const double x, const int num_loss_partitions, 93 const double label, const double wx, 94 const double example_weight, 95 const double weighted_example_norm, 96 const double current_dual) const { 97 const double expx = exp(x); 98 const double numerator = 99 x - wx - num_loss_partitions * weighted_example_norm * 100 example_weight * (label - current_dual - expx); 101 const double denominator = 102 1 + num_loss_partitions * weighted_example_norm * example_weight * expx; 103 return x - numerator / denominator; 104 } 105 }; 106 107 } // namespace tensorflow 108 109 #endif // TENSORFLOW_CORE_KERNELS_LOGISTIC_LOSS_H_ 110