74 lines
3.0 KiB
C++
74 lines
3.0 KiB
C++
/* Copyright 2016 The TensorFlow Authors. All Rights Reserved.
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Licensed under the Apache License, Version 2.0 (the "License");
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you may not use this file except in compliance with the License.
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You may obtain a copy of the License at
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http://www.apache.org/licenses/LICENSE-2.0
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Unless required by applicable law or agreed to in writing, software
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distributed under the License is distributed on an "AS IS" BASIS,
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WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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See the License for the specific language governing permissions and
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limitations under the License.
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==============================================================================*/
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#ifndef TENSORFLOW_CORE_KERNELS_SQUARED_LOSS_H_
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#define TENSORFLOW_CORE_KERNELS_SQUARED_LOSS_H_
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#include "tensorflow/core/kernels/loss.h"
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namespace tensorflow {
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class SquaredLossUpdater : public DualLossUpdater {
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public:
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// Closed form solution that decreases the dual squared loss.
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// See page 23 of http://arxiv.org/pdf/1309.2375v2.pdf for the derivation of
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// the update rule when the example weights are equal to 1.0.
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// Note: There is a typo in the formula in the paper: the denominator should
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// be 1 + ||x_i||^2/(\lambda n) (without the 2 multiplier).
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//
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// The CoCoA+ modification is detailed in readme.md.
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double ComputeUpdatedDual(const int num_loss_partitions, const double label,
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const double example_weight,
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const double current_dual, const double wx,
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const double weighted_example_norm) const final {
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const double delta_numerator = label - current_dual - wx;
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const double delta_denominator =
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1 + num_loss_partitions * weighted_example_norm * example_weight;
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return current_dual + delta_numerator / delta_denominator;
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}
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// Dual of squared loss function.
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// https://en.wikipedia.org/wiki/Convex_conjugate
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double ComputeDualLoss(const double current_dual, const double example_label,
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const double example_weight) const final {
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// Dual of the squared loss function = b * (y + b/2), where b is the
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// dual variable and y is the label. This is Dual(-b).
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return current_dual * (0.5 * current_dual - example_label) * example_weight;
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}
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// Squared loss for linear regression.
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double ComputePrimalLoss(const double wx, const double example_label,
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const double example_weight) const final {
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const double error = wx - example_label;
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return error * error * example_weight * 0.5;
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}
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inline double PrimalLossDerivative(const double wx, const double label,
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const double example_weight) const final {
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return (wx - label) * example_weight;
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}
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inline double SmoothnessConstant() const final { return 1.0; }
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// Labels don't require conversion for linear regression.
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Status ConvertLabel(float* const example_label) const final {
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return Status::OK();
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}
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};
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} // namespace tensorflow
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#endif // TENSORFLOW_CORE_KERNELS_SQUARED_LOSS_H_
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