1/* Copyright 2016 The TensorFlow Authors. All Rights Reserved.
2
3Licensed under the Apache License, Version 2.0 (the "License");
4you may not use this file except in compliance with the License.
5You may obtain a copy of the License at
6
7 http://www.apache.org/licenses/LICENSE-2.0
8
9Unless required by applicable law or agreed to in writing, software
10distributed under the License is distributed on an "AS IS" BASIS,
11WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
12See the License for the specific language governing permissions and
13limitations 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
24namespace tensorflow {
25
26class PoissonLossUpdater : public DualLossUpdater {
27 public:
28 // Update is found by a Newton algorithm (see readme.md).
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
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
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
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.
79 double SmoothnessConstant() const final { return 1; }
80
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 OkStatus();
88 }
89
90 private:
91 // One Newton step (see readme.md).
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