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概要
公正インジケータの上に構築されたツールのスイートですTensorFlowモデル分析（TFMA）製品パイプラインにおける公平性メトリックの定期的な評価を可能にします。 TFMAは、TensorFlowと非TensorFlowの両方の機械学習モデルを評価するためのライブラリです。これにより、大量のデータでモデルを分散して評価し、さまざまなデータスライスでグラフ内およびその他のメトリックを計算し、ノートブックで視覚化することができます。
公正指標が同梱されてTensorFlowデータ検証（TFDV）とのwhat-ifツール。公平性指標を使用すると、次のことが可能になります。
- 定義されたユーザーグループ全体にスライスされたモデルのパフォーマンスを評価します
- 信頼区間と複数のしきい値での評価を使用して、結果について信頼を得る
- データセットの分布を評価する
- 個々のスライスを深く掘り下げて、根本的な原因と改善の機会を探ります
このノートブックでは、あなたが使用して訓練するモデルで、公平性の問題を修正するために公正インジケータを使用する市民がデータセットをコメント。この時計のビデオを実際のシナリオの詳細およびコンテキストのために、これはまた、公平性の指標を作成するための主要な動機の一つであるに基づいています。
データセット
このノートブックでは、あなたが動作する市民は、データセットをコメント約200万パブリックコメントは、公開により行われ、市民プラットフォームコメント進行中の研究のために2017年に。この取り組みは後援されたジグソーパズルだけでなく、意図しないモデルバイアスを最小限に抑えるよう毒性コメント分類する助けにKaggleに競技を主催しています、。
データセット内の個々のテキストコメントには毒性ラベルがあり、コメントが有毒である場合は1、無毒である場合は0のラベルが付いています。データ内で、コメントのサブセットは、性別、性的指向、宗教、人種または民族のカテゴリなど、さまざまなID属性でラベル付けされています。
設定
インストールfairness-indicatorsとwitwidget 。
pip install -q -U pip==20.2pip install -q fairness-indicatorspip install -q witwidget
インストール後、Colabランタイムを再起動する必要があります。コラボメニューからランタイム>再起動ランタイムを選択します。
最初にランタイムを再起動せずに、このチュートリアルの残りの部分に進まないでください。
他のすべての必要なライブラリをインポートします。
import os
import tempfile
import apache_beam as beam
import numpy as np
import pandas as pd
from datetime import datetime
import pprint
import tensorflow_hub as hub
import tensorflow as tf
import tensorflow_model_analysis as tfma
import tensorflow_data_validation as tfdv
from tensorflow_model_analysis.addons.fairness.post_export_metrics import fairness_indicators
from tensorflow_model_analysis.addons.fairness.view import widget_view
from fairness_indicators.tutorial_utils import util
from witwidget.notebook.visualization import WitConfigBuilder
from witwidget.notebook.visualization import WitWidget
データをダウンロードして分析する
デフォルトでは、このノートブックはこのデータセットの前処理済みバージョンをダウンロードしますが、元のデータセットを使用して、必要に応じて処理ステップを再実行できます。元のデータセットでは、各コメントには、コメントが特定のIDに対応すると信じている評価者の割合がラベル付けされています。たとえば、コメントには次のラベルが付けられます。{男性：0.3、女性：1.0、トランスジェンダー：0.0、異性愛者：0.8、同性愛者_gay_or_lesbian：1.0}処理ステップでは、IDをカテゴリ（性別、性的指向など）でグループ化し、削除します。スコアが0.5未満のID。したがって、上記の例は次のように変換されます。コメントが特定のアイデンティティに対応すると信じている評価者の場合。たとえば、コメントには次のラベルが付けられます：{性別：[女性]、性的指向：[異性愛者、同性愛者_ゲイ_またはレズビアン]}
download_original_data = False
if download_original_data:
train_tf_file = tf.keras.utils.get_file('train_tf.tfrecord',
'https://storage.googleapis.com/civil_comments_dataset/train_tf.tfrecord')
validate_tf_file = tf.keras.utils.get_file('validate_tf.tfrecord',
'https://storage.googleapis.com/civil_comments_dataset/validate_tf.tfrecord')
# The identity terms list will be grouped together by their categories
# (see 'IDENTITY_COLUMNS') on threshould 0.5. Only the identity term column,
# text column and label column will be kept after processing.
train_tf_file = util.convert_comments_data(train_tf_file)
validate_tf_file = util.convert_comments_data(validate_tf_file)
else:
train_tf_file = tf.keras.utils.get_file('train_tf_processed.tfrecord',
'https://storage.googleapis.com/civil_comments_dataset/train_tf_processed.tfrecord')
validate_tf_file = tf.keras.utils.get_file('validate_tf_processed.tfrecord',
'https://storage.googleapis.com/civil_comments_dataset/validate_tf_processed.tfrecord')
Downloading data from https://storage.googleapis.com/civil_comments_dataset/train_tf_processed.tfrecord 488161280/488153424 [==============================] - 6s 0us/step Downloading data from https://storage.googleapis.com/civil_comments_dataset/validate_tf_processed.tfrecord 324943872/324941336 [==============================] - 5s 0us/step
TFDVを使用してデータを分析し、欠測値やデータの不均衡など、公平性の不一致につながる可能性のある潜在的な問題を見つけます。
stats = tfdv.generate_statistics_from_tfrecord(data_location=train_tf_file)
tfdv.visualize_statistics(stats)
WARNING:apache_beam.runners.interactive.interactive_environment:Dependencies required for Interactive Beam PCollection visualization are not available, please use: `pip install apache-beam[interactive]` to install necessary dependencies to enable all data visualization features. WARNING:apache_beam.io.tfrecordio:Couldn't find python-snappy so the implementation of _TFRecordUtil._masked_crc32c is not as fast as it could be. WARNING:tensorflow:From /tmpfs/src/tf_docs_env/lib/python3.6/site-packages/tensorflow_data_validation/utils/stats_util.py:247: tf_record_iterator (from tensorflow.python.lib.io.tf_record) is deprecated and will be removed in a future version. Instructions for updating: Use eager execution and: `tf.data.TFRecordDataset(path)` WARNING:tensorflow:From /tmpfs/src/tf_docs_env/lib/python3.6/site-packages/tensorflow_data_validation/utils/stats_util.py:247: tf_record_iterator (from tensorflow.python.lib.io.tf_record) is deprecated and will be removed in a future version. Instructions for updating: Use eager execution and: `tf.data.TFRecordDataset(path)`
TFDVは、データにいくつかの重大な不均衡があり、モデルの結果に偏りが生じる可能性があることを示しています。
毒性ラベル（モデルによって予測された値）は不均衡です。トレーニングセットの例の8％のみが有毒です。つまり、分類器は、すべてのコメントが無毒であると予測することにより、92％の精度を得ることができます。
アイデンティティ用語に関連する分野では、108万人（0.61％）のトレーニング例のうち同性愛を扱っているのはわずか6.6kであり、バイセクシュアルに関連するものはさらにまれです。これは、トレーニングデータが不足しているために、これらのスライスのパフォーマンスが低下する可能性があることを示しています。
データを準備する
データを解析するためのフィーチャマップを定義します。それぞれの例は、ラベル、コメントテキストを持つことになり、そしてアイデンティティが特徴sexual orientation 、 gender 、 religion 、 race 、およびdisabilityテキストに関連しています。
BASE_DIR = tempfile.gettempdir()
TEXT_FEATURE = 'comment_text'
LABEL = 'toxicity'
FEATURE_MAP = {
# Label:
LABEL: tf.io.FixedLenFeature([], tf.float32),
# Text:
TEXT_FEATURE: tf.io.FixedLenFeature([], tf.string),
# Identities:
'sexual_orientation':tf.io.VarLenFeature(tf.string),
'gender':tf.io.VarLenFeature(tf.string),
'religion':tf.io.VarLenFeature(tf.string),
'race':tf.io.VarLenFeature(tf.string),
'disability':tf.io.VarLenFeature(tf.string),
}
次に、モデルにデータを供給するための入力関数を設定します。 TFDVによって識別されたクラスの不均衡を説明するために、各例に重み列を追加し、有毒な例を重み付けします。トレーニング中にコメントのみがモデルに入力されるため、評価フェーズではID機能のみを使用してください。
def train_input_fn():
def parse_function(serialized):
parsed_example = tf.io.parse_single_example(
serialized=serialized, features=FEATURE_MAP)
# Adds a weight column to deal with unbalanced classes.
parsed_example['weight'] = tf.add(parsed_example[LABEL], 0.1)
return (parsed_example,
parsed_example[LABEL])
train_dataset = tf.data.TFRecordDataset(
filenames=[train_tf_file]).map(parse_function).batch(512)
return train_dataset
モデルをトレーニングする
データに関する深層学習モデルを作成してトレーニングします。
model_dir = os.path.join(BASE_DIR, 'train', datetime.now().strftime(
"%Y%m%d-%H%M%S"))
embedded_text_feature_column = hub.text_embedding_column(
key=TEXT_FEATURE,
module_spec='https://tfhub.dev/google/nnlm-en-dim128/1')
classifier = tf.estimator.DNNClassifier(
hidden_units=[500, 100],
weight_column='weight',
feature_columns=[embedded_text_feature_column],
optimizer=tf.keras.optimizers.Adagrad(learning_rate=0.003),
loss_reduction=tf.losses.Reduction.SUM,
n_classes=2,
model_dir=model_dir)
classifier.train(input_fn=train_input_fn, steps=1000)
INFO:tensorflow:Using default config.
INFO:tensorflow:Using default config.
INFO:tensorflow:Using config: {'_model_dir': '/tmp/train/20210130-101939', '_tf_random_seed': None, '_save_summary_steps': 100, '_save_checkpoints_steps': None, '_save_checkpoints_secs': 600, '_session_config': allow_soft_placement: true
graph_options {
rewrite_options {
meta_optimizer_iterations: ONE
}
}
, '_keep_checkpoint_max': 5, '_keep_checkpoint_every_n_hours': 10000, '_log_step_count_steps': 100, '_train_distribute': None, '_device_fn': None, '_protocol': None, '_eval_distribute': None, '_experimental_distribute': None, '_experimental_max_worker_delay_secs': None, '_session_creation_timeout_secs': 7200, '_checkpoint_save_graph_def': True, '_service': None, '_cluster_spec': ClusterSpec({}), '_task_type': 'worker', '_task_id': 0, '_global_id_in_cluster': 0, '_master': '', '_evaluation_master': '', '_is_chief': True, '_num_ps_replicas': 0, '_num_worker_replicas': 1}
INFO:tensorflow:Using config: {'_model_dir': '/tmp/train/20210130-101939', '_tf_random_seed': None, '_save_summary_steps': 100, '_save_checkpoints_steps': None, '_save_checkpoints_secs': 600, '_session_config': allow_soft_placement: true
graph_options {
rewrite_options {
meta_optimizer_iterations: ONE
}
}
, '_keep_checkpoint_max': 5, '_keep_checkpoint_every_n_hours': 10000, '_log_step_count_steps': 100, '_train_distribute': None, '_device_fn': None, '_protocol': None, '_eval_distribute': None, '_experimental_distribute': None, '_experimental_max_worker_delay_secs': None, '_session_creation_timeout_secs': 7200, '_checkpoint_save_graph_def': True, '_service': None, '_cluster_spec': ClusterSpec({}), '_task_type': 'worker', '_task_id': 0, '_global_id_in_cluster': 0, '_master': '', '_evaluation_master': '', '_is_chief': True, '_num_ps_replicas': 0, '_num_worker_replicas': 1}
WARNING:tensorflow:From /tmpfs/src/tf_docs_env/lib/python3.6/site-packages/tensorflow/python/training/training_util.py:236: Variable.initialized_value (from tensorflow.python.ops.variables) is deprecated and will be removed in a future version.
Instructions for updating:
Use Variable.read_value. Variables in 2.X are initialized automatically both in eager and graph (inside tf.defun) contexts.
WARNING:tensorflow:From /tmpfs/src/tf_docs_env/lib/python3.6/site-packages/tensorflow/python/training/training_util.py:236: Variable.initialized_value (from tensorflow.python.ops.variables) is deprecated and will be removed in a future version.
Instructions for updating:
Use Variable.read_value. Variables in 2.X are initialized automatically both in eager and graph (inside tf.defun) contexts.
INFO:tensorflow:Calling model_fn.
INFO:tensorflow:Calling model_fn.
INFO:tensorflow:Saver not created because there are no variables in the graph to restore
INFO:tensorflow:Saver not created because there are no variables in the graph to restore
WARNING:tensorflow:From /tmpfs/src/tf_docs_env/lib/python3.6/site-packages/tensorflow_estimator/python/estimator/head/base_head.py:517: NumericColumn._get_dense_tensor (from tensorflow.python.feature_column.feature_column_v2) is deprecated and will be removed in a future version.
Instructions for updating:
The old _FeatureColumn APIs are being deprecated. Please use the new FeatureColumn APIs instead.
WARNING:tensorflow:From /tmpfs/src/tf_docs_env/lib/python3.6/site-packages/tensorflow_estimator/python/estimator/head/base_head.py:517: NumericColumn._get_dense_tensor (from tensorflow.python.feature_column.feature_column_v2) is deprecated and will be removed in a future version.
Instructions for updating:
The old _FeatureColumn APIs are being deprecated. Please use the new FeatureColumn APIs instead.
WARNING:tensorflow:From /tmpfs/src/tf_docs_env/lib/python3.6/site-packages/tensorflow/python/feature_column/feature_column.py:2192: NumericColumn._transform_feature (from tensorflow.python.feature_column.feature_column_v2) is deprecated and will be removed in a future version.
Instructions for updating:
The old _FeatureColumn APIs are being deprecated. Please use the new FeatureColumn APIs instead.
WARNING:tensorflow:From /tmpfs/src/tf_docs_env/lib/python3.6/site-packages/tensorflow/python/feature_column/feature_column.py:2192: NumericColumn._transform_feature (from tensorflow.python.feature_column.feature_column_v2) is deprecated and will be removed in a future version.
Instructions for updating:
The old _FeatureColumn APIs are being deprecated. Please use the new FeatureColumn APIs instead.
WARNING:tensorflow:From /tmpfs/src/tf_docs_env/lib/python3.6/site-packages/tensorflow/python/keras/optimizer_v2/adagrad.py:83: calling Constant.__init__ (from tensorflow.python.ops.init_ops) with dtype is deprecated and will be removed in a future version.
Instructions for updating:
Call initializer instance with the dtype argument instead of passing it to the constructor
WARNING:tensorflow:From /tmpfs/src/tf_docs_env/lib/python3.6/site-packages/tensorflow/python/keras/optimizer_v2/adagrad.py:83: calling Constant.__init__ (from tensorflow.python.ops.init_ops) with dtype is deprecated and will be removed in a future version.
Instructions for updating:
Call initializer instance with the dtype argument instead of passing it to the constructor
INFO:tensorflow:Done calling model_fn.
INFO:tensorflow:Done calling model_fn.
INFO:tensorflow:Create CheckpointSaverHook.
INFO:tensorflow:Create CheckpointSaverHook.
INFO:tensorflow:Graph was finalized.
INFO:tensorflow:Graph was finalized.
INFO:tensorflow:Running local_init_op.
INFO:tensorflow:Running local_init_op.
INFO:tensorflow:Done running local_init_op.
INFO:tensorflow:Done running local_init_op.
INFO:tensorflow:Calling checkpoint listeners before saving checkpoint 0...
INFO:tensorflow:Calling checkpoint listeners before saving checkpoint 0...
INFO:tensorflow:Saving checkpoints for 0 into /tmp/train/20210130-101939/model.ckpt.
INFO:tensorflow:Saving checkpoints for 0 into /tmp/train/20210130-101939/model.ckpt.
INFO:tensorflow:Calling checkpoint listeners after saving checkpoint 0...
INFO:tensorflow:Calling checkpoint listeners after saving checkpoint 0...
INFO:tensorflow:loss = 59.10357, step = 0
INFO:tensorflow:loss = 59.10357, step = 0
INFO:tensorflow:global_step/sec: 21.4277
INFO:tensorflow:global_step/sec: 21.4277
INFO:tensorflow:loss = 55.88044, step = 100 (4.669 sec)
INFO:tensorflow:loss = 55.88044, step = 100 (4.669 sec)
INFO:tensorflow:global_step/sec: 21.9772
INFO:tensorflow:global_step/sec: 21.9772
INFO:tensorflow:loss = 47.06628, step = 200 (4.550 sec)
INFO:tensorflow:loss = 47.06628, step = 200 (4.550 sec)
INFO:tensorflow:global_step/sec: 21.5857
INFO:tensorflow:global_step/sec: 21.5857
INFO:tensorflow:loss = 55.466003, step = 300 (4.633 sec)
INFO:tensorflow:loss = 55.466003, step = 300 (4.633 sec)
INFO:tensorflow:global_step/sec: 20.7493
INFO:tensorflow:global_step/sec: 20.7493
INFO:tensorflow:loss = 56.189507, step = 400 (4.820 sec)
INFO:tensorflow:loss = 56.189507, step = 400 (4.820 sec)
INFO:tensorflow:global_step/sec: 21.7353
INFO:tensorflow:global_step/sec: 21.7353
INFO:tensorflow:loss = 41.800144, step = 500 (4.600 sec)
INFO:tensorflow:loss = 41.800144, step = 500 (4.600 sec)
INFO:tensorflow:global_step/sec: 22.551
INFO:tensorflow:global_step/sec: 22.551
INFO:tensorflow:loss = 45.347168, step = 600 (4.434 sec)
INFO:tensorflow:loss = 45.347168, step = 600 (4.434 sec)
INFO:tensorflow:global_step/sec: 22.292
INFO:tensorflow:global_step/sec: 22.292
INFO:tensorflow:loss = 51.336346, step = 700 (4.486 sec)
INFO:tensorflow:loss = 51.336346, step = 700 (4.486 sec)
INFO:tensorflow:global_step/sec: 21.9374
INFO:tensorflow:global_step/sec: 21.9374
INFO:tensorflow:loss = 47.501987, step = 800 (4.559 sec)
INFO:tensorflow:loss = 47.501987, step = 800 (4.559 sec)
INFO:tensorflow:global_step/sec: 22.0593
INFO:tensorflow:global_step/sec: 22.0593
INFO:tensorflow:loss = 48.003296, step = 900 (4.533 sec)
INFO:tensorflow:loss = 48.003296, step = 900 (4.533 sec)
INFO:tensorflow:Calling checkpoint listeners before saving checkpoint 1000...
INFO:tensorflow:Calling checkpoint listeners before saving checkpoint 1000...
INFO:tensorflow:Saving checkpoints for 1000 into /tmp/train/20210130-101939/model.ckpt.
INFO:tensorflow:Saving checkpoints for 1000 into /tmp/train/20210130-101939/model.ckpt.
INFO:tensorflow:Calling checkpoint listeners after saving checkpoint 1000...
INFO:tensorflow:Calling checkpoint listeners after saving checkpoint 1000...
INFO:tensorflow:Loss for final step: 50.98375.
INFO:tensorflow:Loss for final step: 50.98375.
<tensorflow_estimator.python.estimator.canned.dnn.DNNClassifierV2 at 0x7f76540f3a20>
モデルを分析する
トレーニングされたモデルを取得したら、それを分析して、TFMAと公平性指標を使用して公平性メトリックを計算します。モデルをエクスポートすることから始めSavedModel 。
SavedModelをエクスポートします
def eval_input_receiver_fn():
serialized_tf_example = tf.compat.v1.placeholder(
dtype=tf.string, shape=[None], name='input_example_placeholder')
# This *must* be a dictionary containing a single key 'examples', which
# points to the input placeholder.
receiver_tensors = {'examples': serialized_tf_example}
features = tf.io.parse_example(serialized_tf_example, FEATURE_MAP)
features['weight'] = tf.ones_like(features[LABEL])
return tfma.export.EvalInputReceiver(
features=features,
receiver_tensors=receiver_tensors,
labels=features[LABEL])
tfma_export_dir = tfma.export.export_eval_savedmodel(
estimator=classifier,
export_dir_base=os.path.join(BASE_DIR, 'tfma_eval_model'),
eval_input_receiver_fn=eval_input_receiver_fn)
WARNING:tensorflow:From /tmpfs/src/tf_docs_env/lib/python3.6/site-packages/tensorflow_model_analysis/eval_saved_model/encoding.py:141: build_tensor_info (from tensorflow.python.saved_model.utils_impl) is deprecated and will be removed in a future version. Instructions for updating: This function will only be available through the v1 compatibility library as tf.compat.v1.saved_model.utils.build_tensor_info or tf.compat.v1.saved_model.build_tensor_info. WARNING:tensorflow:From /tmpfs/src/tf_docs_env/lib/python3.6/site-packages/tensorflow_model_analysis/eval_saved_model/encoding.py:141: build_tensor_info (from tensorflow.python.saved_model.utils_impl) is deprecated and will be removed in a future version. Instructions for updating: This function will only be available through the v1 compatibility library as tf.compat.v1.saved_model.utils.build_tensor_info or tf.compat.v1.saved_model.build_tensor_info. INFO:tensorflow:Calling model_fn. INFO:tensorflow:Calling model_fn. INFO:tensorflow:Saver not created because there are no variables in the graph to restore INFO:tensorflow:Saver not created because there are no variables in the graph to restore INFO:tensorflow:Done calling model_fn. INFO:tensorflow:Done calling model_fn. INFO:tensorflow:Signatures INCLUDED in export for Classify: None INFO:tensorflow:Signatures INCLUDED in export for Classify: None INFO:tensorflow:Signatures INCLUDED in export for Regress: None INFO:tensorflow:Signatures INCLUDED in export for Regress: None INFO:tensorflow:Signatures INCLUDED in export for Predict: None INFO:tensorflow:Signatures INCLUDED in export for Predict: None INFO:tensorflow:Signatures INCLUDED in export for Train: None INFO:tensorflow:Signatures INCLUDED in export for Train: None INFO:tensorflow:Signatures INCLUDED in export for Eval: ['eval'] INFO:tensorflow:Signatures INCLUDED in export for Eval: ['eval'] WARNING:tensorflow:Export includes no default signature! WARNING:tensorflow:Export includes no default signature! INFO:tensorflow:Restoring parameters from /tmp/train/20210130-101939/model.ckpt-1000 INFO:tensorflow:Restoring parameters from /tmp/train/20210130-101939/model.ckpt-1000 INFO:tensorflow:Assets added to graph. INFO:tensorflow:Assets added to graph. INFO:tensorflow:Assets written to: /tmp/tfma_eval_model/temp-1612002036/assets INFO:tensorflow:Assets written to: /tmp/tfma_eval_model/temp-1612002036/assets INFO:tensorflow:SavedModel written to: /tmp/tfma_eval_model/temp-1612002036/saved_model.pb INFO:tensorflow:SavedModel written to: /tmp/tfma_eval_model/temp-1612002036/saved_model.pb
公平性メトリクスを計算する
右側のパネルのドロップダウンを使用して、メトリックを計算するIDと、信頼区間で実行するかどうかを選択します。
公平性指標の計算オプション
tfma_eval_result_path = os.path.join(BASE_DIR, 'tfma_eval_result')
slice_selection = 'sexual_orientation'
print(f'Slice selection: {slice_selection}')
compute_confidence_intervals = False
print(f'Compute confidence intervals: {compute_confidence_intervals}')
# Define slices that you want the evaluation to run on.
slice_spec = [
tfma.slicer.SingleSliceSpec(), # Overall slice
tfma.slicer.SingleSliceSpec(columns=[slice_selection]),
]
# Add the fairness metrics.
add_metrics_callbacks = [
tfma.post_export_metrics.fairness_indicators(
thresholds=[0.1, 0.3, 0.5, 0.7, 0.9],
labels_key=LABEL
)
]
eval_shared_model = tfma.default_eval_shared_model(
eval_saved_model_path=tfma_export_dir,
add_metrics_callbacks=add_metrics_callbacks)
# Run the fairness evaluation.
with beam.Pipeline() as pipeline:
_ = (
pipeline
| 'ReadData' >> beam.io.ReadFromTFRecord(validate_tf_file)
| 'ExtractEvaluateAndWriteResults' >>
tfma.ExtractEvaluateAndWriteResults(
eval_shared_model=eval_shared_model,
slice_spec=slice_spec,
compute_confidence_intervals=compute_confidence_intervals,
output_path=tfma_eval_result_path)
)
eval_result = tfma.load_eval_result(output_path=tfma_eval_result_path)
Slice selection: sexual_orientation Compute confidence intervals: False WARNING:apache_beam.typehints.typehints:Ignoring send_type hint: <class 'NoneType'> WARNING:apache_beam.typehints.typehints:Ignoring return_type hint: <class 'NoneType'> WARNING:apache_beam.typehints.typehints:Ignoring send_type hint: <class 'NoneType'> WARNING:apache_beam.typehints.typehints:Ignoring return_type hint: <class 'NoneType'> WARNING:apache_beam.typehints.typehints:Ignoring send_type hint: <class 'NoneType'> WARNING:apache_beam.typehints.typehints:Ignoring return_type hint: <class 'NoneType'> WARNING:tensorflow:From /tmpfs/src/tf_docs_env/lib/python3.6/site-packages/tensorflow_model_analysis/eval_saved_model/load.py:169: load (from tensorflow.python.saved_model.loader_impl) is deprecated and will be removed in a future version. Instructions for updating: This function will only be available through the v1 compatibility library as tf.compat.v1.saved_model.loader.load or tf.compat.v1.saved_model.load. There will be a new function for importing SavedModels in Tensorflow 2.0. WARNING:tensorflow:From /tmpfs/src/tf_docs_env/lib/python3.6/site-packages/tensorflow_model_analysis/eval_saved_model/load.py:169: load (from tensorflow.python.saved_model.loader_impl) is deprecated and will be removed in a future version. Instructions for updating: This function will only be available through the v1 compatibility library as tf.compat.v1.saved_model.loader.load or tf.compat.v1.saved_model.load. There will be a new function for importing SavedModels in Tensorflow 2.0. INFO:tensorflow:Restoring parameters from /tmp/tfma_eval_model/1612002036/variables/variables INFO:tensorflow:Restoring parameters from /tmp/tfma_eval_model/1612002036/variables/variables WARNING:tensorflow:From /tmpfs/src/tf_docs_env/lib/python3.6/site-packages/tensorflow_model_analysis/eval_saved_model/graph_ref.py:189: get_tensor_from_tensor_info (from tensorflow.python.saved_model.utils_impl) is deprecated and will be removed in a future version. Instructions for updating: This function will only be available through the v1 compatibility library as tf.compat.v1.saved_model.utils.get_tensor_from_tensor_info or tf.compat.v1.saved_model.get_tensor_from_tensor_info. WARNING:tensorflow:From /tmpfs/src/tf_docs_env/lib/python3.6/site-packages/tensorflow_model_analysis/eval_saved_model/graph_ref.py:189: get_tensor_from_tensor_info (from tensorflow.python.saved_model.utils_impl) is deprecated and will be removed in a future version. Instructions for updating: This function will only be available through the v1 compatibility library as tf.compat.v1.saved_model.utils.get_tensor_from_tensor_info or tf.compat.v1.saved_model.get_tensor_from_tensor_info. WARNING:apache_beam.io.filebasedsink:Deleting 1 existing files in target path matching: WARNING:apache_beam.io.filebasedsink:Deleting 1 existing files in target path matching: WARNING:apache_beam.io.filebasedsink:Deleting 1 existing files in target path matching:
What-ifツールを使用してデータを視覚化する
このセクションでは、What-Ifツールのインタラクティブなビジュアルインターフェイスを使用して、マイクロレベルでデータを探索および操作します。
右側のパネルの散布図の各点は、ツールにロードされたサブセットの例の1つを表しています。ポイントの1つをクリックして、左側のパネルにこの特定の例の詳細を表示します。コメントテキスト、グラウンドトゥルース毒性、および該当するIDが表示されます。この左側のパネルの下部に、トレーニングしたばかりのモデルからの推論結果が表示されます。
例のテキストを変更して、変更内容が変更に認識される毒性予測を引き起こした方法を表示するファイル名を指定して実行推論ボタンをクリックしてください。
DEFAULT_MAX_EXAMPLES = 1000
# Load 100000 examples in memory. When first rendered,
# What-If Tool should only display 1000 of these due to browser constraints.
def wit_dataset(file, num_examples=100000):
dataset = tf.data.TFRecordDataset(
filenames=[file]).take(num_examples)
return [tf.train.Example.FromString(d.numpy()) for d in dataset]
wit_data = wit_dataset(train_tf_file)
config_builder = WitConfigBuilder(wit_data[:DEFAULT_MAX_EXAMPLES]).set_estimator_and_feature_spec(
classifier, FEATURE_MAP).set_label_vocab(['non-toxicity', LABEL]).set_target_feature(LABEL)
wit = WitWidget(config_builder)
公平性指標をレンダリングする
エクスポートされた評価結果を使用して、公平性インジケーターウィジェットをレンダリングします。
以下に、選択したメトリックのデータの各スライスのパフォーマンスを示す棒グラフを示します。ビジュアライゼーションの上部にあるドロップダウンメニューを使用して、ベースライン比較スライスと表示されるしきい値を調整できます。
Fairness Indicatorウィジェットは、上記でレンダリングされたWhat-Ifツールと統合されています。棒グラフでデータのスライスを1つ選択すると、What-Ifツールが更新され、選択したスライスの例が表示されます。上記のwhat-ifツールのデータのリロードは、毒性の色でを変更しようとします。これにより、スライスごとの例の毒性バランスを視覚的に理解できます。
event_handlers={'slice-selected':
wit.create_selection_callback(wit_data, DEFAULT_MAX_EXAMPLES)}
widget_view.render_fairness_indicator(eval_result=eval_result,
slicing_column=slice_selection,
event_handlers=event_handlers
)
FairnessIndicatorViewer(slicingMetrics=[{'sliceValue': 'Overall', 'slice': 'Overall', 'metrics': {'auc_precisi…
この特定のデータセットとタスクでは、特定のIDの誤検知率と誤検知率が体系的に高くなると、悪影響が生じる可能性があります。たとえば、コンテンツモデレーションシステムでは、特定のグループの誤検知率が全体よりも高いと、それらの音声が無音になる可能性があります。したがって、モデルを開発および改善する際には、これらのタイプの基準を定期的に評価し、公平性指標、TFDV、WITなどのツールを利用して潜在的な問題を明らかにすることが重要です。公平性の問題を特定したら、新しいデータソース、データバランシング、またはその他の手法を試して、パフォーマンスの低いグループのパフォーマンスを向上させることができます。
参照してくださいここに公正インジケータを使用する方法の詳細とご指導を。
公平性評価結果を使用する
eval_result中で上にレンダリングされたオブジェクト、 render_fairness_indicator()あなたはあなたのプログラムにTFMA結果を読み取るために活用できるという独自のAPIを持っています。
評価されたスライスとメトリックを取得する
使用get_slice_names()とget_metric_names()それぞれ、評価されたスライスとメトリックを取得します。
pp = pprint.PrettyPrinter()
print("Slices:")
pp.pprint(eval_result.get_slice_names())
print("\nMetrics:")
pp.pprint(eval_result.get_metric_names())
Slices:
[(),
(('sexual_orientation', 'homosexual_gay_or_lesbian'),),
(('sexual_orientation', 'heterosexual'),),
(('sexual_orientation', 'bisexual'),),
(('sexual_orientation', 'other_sexual_orientation'),)]
Metrics:
['post_export_metrics/true_positive_rate@0.90',
'post_export_metrics/false_omission_rate@0.50',
'post_export_metrics/negative_rate@0.70',
'post_export_metrics/negative_rate@0.90',
'post_export_metrics/false_positive_rate@0.70',
'post_export_metrics/false_omission_rate@0.70',
'post_export_metrics/false_discovery_rate@0.70',
'accuracy',
'prediction/mean',
'post_export_metrics/false_omission_rate@0.30',
'post_export_metrics/example_count',
'post_export_metrics/false_negative_rate@0.30',
'post_export_metrics/fairness/confusion_matrix_at_thresholds',
'average_loss',
'post_export_metrics/false_positive_rate@0.30',
'post_export_metrics/false_negative_rate@0.10',
'label/mean',
'post_export_metrics/positive_rate@0.70',
'auc',
'post_export_metrics/true_negative_rate@0.50',
'precision',
'post_export_metrics/false_positive_rate@0.90',
'post_export_metrics/positive_rate@0.10',
'post_export_metrics/false_omission_rate@0.90',
'post_export_metrics/false_discovery_rate@0.10',
'post_export_metrics/false_negative_rate@0.70',
'post_export_metrics/positive_rate@0.50',
'post_export_metrics/false_discovery_rate@0.30',
'post_export_metrics/positive_rate@0.30',
'post_export_metrics/negative_rate@0.30',
'post_export_metrics/negative_rate@0.50',
'post_export_metrics/false_discovery_rate@0.90',
'post_export_metrics/true_negative_rate@0.10',
'auc_precision_recall',
'post_export_metrics/true_positive_rate@0.50',
'accuracy_baseline',
'post_export_metrics/false_positive_rate@0.10',
'post_export_metrics/false_negative_rate@0.50',
'post_export_metrics/false_omission_rate@0.10',
'post_export_metrics/false_discovery_rate@0.50',
'post_export_metrics/false_negative_rate@0.90',
'post_export_metrics/true_positive_rate@0.70',
'post_export_metrics/true_positive_rate@0.10',
'post_export_metrics/true_negative_rate@0.30',
'post_export_metrics/true_positive_rate@0.30',
'post_export_metrics/false_positive_rate@0.50',
'post_export_metrics/true_negative_rate@0.90',
'post_export_metrics/positive_rate@0.90',
'post_export_metrics/true_negative_rate@0.70',
'post_export_metrics/negative_rate@0.10',
'recall']
使用get_metrics_for_slice()への辞書マッピングメトリック名として特定のスライスのメトリックを取得するためのメトリック値。
baseline_slice = ()
heterosexual_slice = (('sexual_orientation', 'heterosexual'),)
print("Baseline metric values:")
pp.pprint(eval_result.get_metrics_for_slice(baseline_slice))
print("\nHeterosexual metric values:")
pp.pprint(eval_result.get_metrics_for_slice(heterosexual_slice))
Baseline metric values:
{'accuracy': {'doubleValue': 0.7191107273101807},
'accuracy_baseline': {'doubleValue': 0.9198060631752014},
'auc': {'doubleValue': 0.7972093224525452},
'auc_precision_recall': {'doubleValue': 0.3029831349849701},
'average_loss': {'doubleValue': 0.5623680949211121},
'label/mean': {'doubleValue': 0.08019392192363739},
'post_export_metrics/example_count': {'doubleValue': 721950.0},
'post_export_metrics/fairness/confusion_matrix_at_thresholds': {'confusionMatrixAtThresholds': {'matrices': [{'boundedFalseNegatives': {'value': 340.0},
'boundedFalsePositives': {'value': 612773.0},
'boundedPrecision': {'value': 0.08586231619119644},
'boundedRecall': {'value': 0.9941273927688599},
'boundedTrueNegatives': {'value': 51281.0},
'boundedTruePositives': {'value': 57556.0},
'falseNegatives': 340.0,
'falsePositives': 612773.0,
'precision': 0.08586231619119644,
'recall': 0.9941273927688599,
'tDistributionFalseNegatives': {'unsampledValue': 340.0},
'tDistributionFalsePositives': {'unsampledValue': 612773.0},
'tDistributionPrecision': {'unsampledValue': 0.08586231619119644},
'tDistributionRecall': {'unsampledValue': 0.9941273927688599},
'tDistributionTrueNegatives': {'unsampledValue': 51281.0},
'tDistributionTruePositives': {'unsampledValue': 57556.0},
'threshold': 0.10000000149011612,
'trueNegatives': 51281.0,
'truePositives': 57556.0},
{'boundedFalseNegatives': {'value': 4971.0},
'boundedFalsePositives': {'value': 385684.0},
'boundedPrecision': {'value': 0.12066555768251419},
'boundedRecall': {'value': 0.9141391515731812},
'boundedTrueNegatives': {'value': 278370.0},
'boundedTruePositives': {'value': 52925.0},
'falseNegatives': 4971.0,
'falsePositives': 385684.0,
'precision': 0.12066555768251419,
'recall': 0.9141391515731812,
'tDistributionFalseNegatives': {'unsampledValue': 4971.0},
'tDistributionFalsePositives': {'unsampledValue': 385684.0},
'tDistributionPrecision': {'unsampledValue': 0.12066555768251419},
'tDistributionRecall': {'unsampledValue': 0.9141391515731812},
'tDistributionTrueNegatives': {'unsampledValue': 278370.0},
'tDistributionTruePositives': {'unsampledValue': 52925.0},
'threshold': 0.30000001192092896,
'trueNegatives': 278370.0,
'truePositives': 52925.0},
{'boundedFalseNegatives': {'value': 15684.0},
'boundedFalsePositives': {'value': 187104.0},
'boundedPrecision': {'value': 0.18407785892486572},
'boundedRecall': {'value': 0.7291004657745361},
'boundedTrueNegatives': {'value': 476950.0},
'boundedTruePositives': {'value': 42212.0},
'falseNegatives': 15684.0,
'falsePositives': 187104.0,
'precision': 0.18407785892486572,
'recall': 0.7291004657745361,
'tDistributionFalseNegatives': {'unsampledValue': 15684.0},
'tDistributionFalsePositives': {'unsampledValue': 187104.0},
'tDistributionPrecision': {'unsampledValue': 0.18407785892486572},
'tDistributionRecall': {'unsampledValue': 0.7291004657745361},
'tDistributionTrueNegatives': {'unsampledValue': 476950.0},
'tDistributionTruePositives': {'unsampledValue': 42212.0},
'threshold': 0.5,
'trueNegatives': 476950.0,
'truePositives': 42212.0},
{'boundedFalseNegatives': {'value': 31392.0},
'boundedFalsePositives': {'value': 64497.0},
'boundedPrecision': {'value': 0.291249543428421},
'boundedRecall': {'value': 0.4577863812446594},
'boundedTrueNegatives': {'value': 599557.0},
'boundedTruePositives': {'value': 26504.0},
'falseNegatives': 31392.0,
'falsePositives': 64497.0,
'precision': 0.291249543428421,
'recall': 0.4577863812446594,
'tDistributionFalseNegatives': {'unsampledValue': 31392.0},
'tDistributionFalsePositives': {'unsampledValue': 64497.0},
'tDistributionPrecision': {'unsampledValue': 0.291249543428421},
'tDistributionRecall': {'unsampledValue': 0.4577863812446594},
'tDistributionTrueNegatives': {'unsampledValue': 599557.0},
'tDistributionTruePositives': {'unsampledValue': 26504.0},
'threshold': 0.699999988079071,
'trueNegatives': 599557.0,
'truePositives': 26504.0},
{'boundedFalseNegatives': {'value': 51089.0},
'boundedFalsePositives': {'value': 6354.0},
'boundedPrecision': {'value': 0.5172099471092224},
'boundedRecall': {'value': 0.11757288873195648},
'boundedTrueNegatives': {'value': 657700.0},
'boundedTruePositives': {'value': 6807.0},
'falseNegatives': 51089.0,
'falsePositives': 6354.0,
'precision': 0.5172099471092224,
'recall': 0.11757288873195648,
'tDistributionFalseNegatives': {'unsampledValue': 51089.0},
'tDistributionFalsePositives': {'unsampledValue': 6354.0},
'tDistributionPrecision': {'unsampledValue': 0.5172099471092224},
'tDistributionRecall': {'unsampledValue': 0.11757288873195648},
'tDistributionTrueNegatives': {'unsampledValue': 657700.0},
'tDistributionTruePositives': {'unsampledValue': 6807.0},
'threshold': 0.8999999761581421,
'trueNegatives': 657700.0,
'truePositives': 6807.0}]} },
'post_export_metrics/false_discovery_rate@0.10': {'doubleValue': 0.9141376614570618},
'post_export_metrics/false_discovery_rate@0.30': {'doubleValue': 0.8793344497680664},
'post_export_metrics/false_discovery_rate@0.50': {'doubleValue': 0.8159221410751343},
'post_export_metrics/false_discovery_rate@0.70': {'doubleValue': 0.7087504267692566},
'post_export_metrics/false_discovery_rate@0.90': {'doubleValue': 0.4827900528907776},
'post_export_metrics/false_negative_rate@0.10': {'doubleValue': 0.0058725993148982525},
'post_export_metrics/false_negative_rate@0.30': {'doubleValue': 0.08586085587739944},
'post_export_metrics/false_negative_rate@0.50': {'doubleValue': 0.27089953422546387},
'post_export_metrics/false_negative_rate@0.70': {'doubleValue': 0.5422136187553406},
'post_export_metrics/false_negative_rate@0.90': {'doubleValue': 0.8824270963668823},
'post_export_metrics/false_omission_rate@0.10': {'doubleValue': 0.006586466915905476},
'post_export_metrics/false_omission_rate@0.30': {'doubleValue': 0.017544230446219444},
'post_export_metrics/false_omission_rate@0.50': {'doubleValue': 0.03183702379465103},
'post_export_metrics/false_omission_rate@0.70': {'doubleValue': 0.04975362494587898},
'post_export_metrics/false_omission_rate@0.90': {'doubleValue': 0.07207927852869034},
'post_export_metrics/false_positive_rate@0.10': {'doubleValue': 0.9227758646011353},
'post_export_metrics/false_positive_rate@0.30': {'doubleValue': 0.5808021426200867},
'post_export_metrics/false_positive_rate@0.50': {'doubleValue': 0.28176021575927734},
'post_export_metrics/false_positive_rate@0.70': {'doubleValue': 0.09712613373994827},
'post_export_metrics/false_positive_rate@0.90': {'doubleValue': 0.009568499401211739},
'post_export_metrics/negative_rate@0.10': {'doubleValue': 0.07150217890739441},
'post_export_metrics/negative_rate@0.30': {'doubleValue': 0.3924662470817566},
'post_export_metrics/negative_rate@0.50': {'doubleValue': 0.6823658347129822},
'post_export_metrics/negative_rate@0.70': {'doubleValue': 0.8739510774612427},
'post_export_metrics/negative_rate@0.90': {'doubleValue': 0.9817702174186707},
'post_export_metrics/positive_rate@0.10': {'doubleValue': 0.9284977912902832},
'post_export_metrics/positive_rate@0.30': {'doubleValue': 0.6075337529182434},
'post_export_metrics/positive_rate@0.50': {'doubleValue': 0.3176341950893402},
'post_export_metrics/positive_rate@0.70': {'doubleValue': 0.12604889273643494},
'post_export_metrics/positive_rate@0.90': {'doubleValue': 0.01822979375720024},
'post_export_metrics/true_negative_rate@0.10': {'doubleValue': 0.07722414284944534},
'post_export_metrics/true_negative_rate@0.30': {'doubleValue': 0.41919782757759094},
'post_export_metrics/true_negative_rate@0.50': {'doubleValue': 0.7182397842407227},
'post_export_metrics/true_negative_rate@0.70': {'doubleValue': 0.9028738737106323},
'post_export_metrics/true_negative_rate@0.90': {'doubleValue': 0.9904314875602722},
'post_export_metrics/true_positive_rate@0.10': {'doubleValue': 0.9941273927688599},
'post_export_metrics/true_positive_rate@0.30': {'doubleValue': 0.9141391515731812},
'post_export_metrics/true_positive_rate@0.50': {'doubleValue': 0.7291004657745361},
'post_export_metrics/true_positive_rate@0.70': {'doubleValue': 0.4577863812446594},
'post_export_metrics/true_positive_rate@0.90': {'doubleValue': 0.11757288873195648},
'precision': {'doubleValue': 0.18407785892486572},
'prediction/mean': {'doubleValue': 0.40011298656463623},
'recall': {'doubleValue': 0.7291004657745361} }
Heterosexual metric values:
{'accuracy': {'doubleValue': 0.5325203537940979},
'accuracy_baseline': {'doubleValue': 0.7601625919342041},
'auc': {'doubleValue': 0.6657300591468811},
'auc_precision_recall': {'doubleValue': 0.40228524804115295},
'average_loss': {'doubleValue': 0.8246824741363525},
'label/mean': {'doubleValue': 0.2398373931646347},
'post_export_metrics/example_count': {'doubleValue': 492.0},
'post_export_metrics/fairness/confusion_matrix_at_thresholds': {'confusionMatrixAtThresholds': {'matrices': [{'boundedFalseNegatives': {'value': 0.0},
'boundedFalsePositives': {'value': 362.0},
'boundedPrecision': {'value': 0.24583333730697632},
'boundedRecall': {'value': 1.0},
'boundedTrueNegatives': {'value': 12.0},
'boundedTruePositives': {'value': 118.0},
'falsePositives': 362.0,
'precision': 0.24583333730697632,
'recall': 1.0,
'tDistributionFalseNegatives': {'unsampledValue': 0.0},
'tDistributionFalsePositives': {'unsampledValue': 362.0},
'tDistributionPrecision': {'unsampledValue': 0.24583333730697632},
'tDistributionRecall': {'unsampledValue': 1.0},
'tDistributionTrueNegatives': {'unsampledValue': 12.0},
'tDistributionTruePositives': {'unsampledValue': 118.0},
'threshold': 0.10000000149011612,
'trueNegatives': 12.0,
'truePositives': 118.0},
{'boundedFalseNegatives': {'value': 10.0},
'boundedFalsePositives': {'value': 289.0},
'boundedPrecision': {'value': 0.27204030752182007},
'boundedRecall': {'value': 0.9152542352676392},
'boundedTrueNegatives': {'value': 85.0},
'boundedTruePositives': {'value': 108.0},
'falseNegatives': 10.0,
'falsePositives': 289.0,
'precision': 0.27204030752182007,
'recall': 0.9152542352676392,
'tDistributionFalseNegatives': {'unsampledValue': 10.0},
'tDistributionFalsePositives': {'unsampledValue': 289.0},
'tDistributionPrecision': {'unsampledValue': 0.27204030752182007},
'tDistributionRecall': {'unsampledValue': 0.9152542352676392},
'tDistributionTrueNegatives': {'unsampledValue': 85.0},
'tDistributionTruePositives': {'unsampledValue': 108.0},
'threshold': 0.30000001192092896,
'trueNegatives': 85.0,
'truePositives': 108.0},
{'boundedFalseNegatives': {'value': 31.0},
'boundedFalsePositives': {'value': 199.0},
'boundedPrecision': {'value': 0.3041957914829254},
'boundedRecall': {'value': 0.7372881174087524},
'boundedTrueNegatives': {'value': 175.0},
'boundedTruePositives': {'value': 87.0},
'falseNegatives': 31.0,
'falsePositives': 199.0,
'precision': 0.3041957914829254,
'recall': 0.7372881174087524,
'tDistributionFalseNegatives': {'unsampledValue': 31.0},
'tDistributionFalsePositives': {'unsampledValue': 199.0},
'tDistributionPrecision': {'unsampledValue': 0.3041957914829254},
'tDistributionRecall': {'unsampledValue': 0.7372881174087524},
'tDistributionTrueNegatives': {'unsampledValue': 175.0},
'tDistributionTruePositives': {'unsampledValue': 87.0},
'threshold': 0.5,
'trueNegatives': 175.0,
'truePositives': 87.0},
{'boundedFalseNegatives': {'value': 58.0},
'boundedFalsePositives': {'value': 111.0},
'boundedPrecision': {'value': 0.35087719559669495},
'boundedRecall': {'value': 0.508474588394165},
'boundedTrueNegatives': {'value': 263.0},
'boundedTruePositives': {'value': 60.0},
'falseNegatives': 58.0,
'falsePositives': 111.0,
'precision': 0.35087719559669495,
'recall': 0.508474588394165,
'tDistributionFalseNegatives': {'unsampledValue': 58.0},
'tDistributionFalsePositives': {'unsampledValue': 111.0},
'tDistributionPrecision': {'unsampledValue': 0.35087719559669495},
'tDistributionRecall': {'unsampledValue': 0.508474588394165},
'tDistributionTrueNegatives': {'unsampledValue': 263.0},
'tDistributionTruePositives': {'unsampledValue': 60.0},
'threshold': 0.699999988079071,
'trueNegatives': 263.0,
'truePositives': 60.0},
{'boundedFalseNegatives': {'value': 97.0},
'boundedFalsePositives': {'value': 16.0},
'boundedPrecision': {'value': 0.5675675868988037},
'boundedRecall': {'value': 0.17796610295772552},
'boundedTrueNegatives': {'value': 358.0},
'boundedTruePositives': {'value': 21.0},
'falseNegatives': 97.0,
'falsePositives': 16.0,
'precision': 0.5675675868988037,
'recall': 0.17796610295772552,
'tDistributionFalseNegatives': {'unsampledValue': 97.0},
'tDistributionFalsePositives': {'unsampledValue': 16.0},
'tDistributionPrecision': {'unsampledValue': 0.5675675868988037},
'tDistributionRecall': {'unsampledValue': 0.17796610295772552},
'tDistributionTrueNegatives': {'unsampledValue': 358.0},
'tDistributionTruePositives': {'unsampledValue': 21.0},
'threshold': 0.8999999761581421,
'trueNegatives': 358.0,
'truePositives': 21.0}]} },
'post_export_metrics/false_discovery_rate@0.10': {'doubleValue': 0.7541666626930237},
'post_export_metrics/false_discovery_rate@0.30': {'doubleValue': 0.7279596924781799},
'post_export_metrics/false_discovery_rate@0.50': {'doubleValue': 0.6958041787147522},
'post_export_metrics/false_discovery_rate@0.70': {'doubleValue': 0.6491228342056274},
'post_export_metrics/false_discovery_rate@0.90': {'doubleValue': 0.4324324429035187},
'post_export_metrics/false_negative_rate@0.10': {'doubleValue': 0.0},
'post_export_metrics/false_negative_rate@0.30': {'doubleValue': 0.08474576473236084},
'post_export_metrics/false_negative_rate@0.50': {'doubleValue': 0.26271185278892517},
'post_export_metrics/false_negative_rate@0.70': {'doubleValue': 0.49152541160583496},
'post_export_metrics/false_negative_rate@0.90': {'doubleValue': 0.8220338821411133},
'post_export_metrics/false_omission_rate@0.10': {'doubleValue': 0.0},
'post_export_metrics/false_omission_rate@0.30': {'doubleValue': 0.10526315867900848},
'post_export_metrics/false_omission_rate@0.50': {'doubleValue': 0.15048544108867645},
'post_export_metrics/false_omission_rate@0.70': {'doubleValue': 0.180685356259346},
'post_export_metrics/false_omission_rate@0.90': {'doubleValue': 0.2131868153810501},
'post_export_metrics/false_positive_rate@0.10': {'doubleValue': 0.9679144620895386},
'post_export_metrics/false_positive_rate@0.30': {'doubleValue': 0.7727272510528564},
'post_export_metrics/false_positive_rate@0.50': {'doubleValue': 0.5320855379104614},
'post_export_metrics/false_positive_rate@0.70': {'doubleValue': 0.2967914342880249},
'post_export_metrics/false_positive_rate@0.90': {'doubleValue': 0.04278074949979782},
'post_export_metrics/negative_rate@0.10': {'doubleValue': 0.024390242993831635},
'post_export_metrics/negative_rate@0.30': {'doubleValue': 0.19308942556381226},
'post_export_metrics/negative_rate@0.50': {'doubleValue': 0.4186991751194},
'post_export_metrics/negative_rate@0.70': {'doubleValue': 0.6524389982223511},
'post_export_metrics/negative_rate@0.90': {'doubleValue': 0.9247967600822449},
'post_export_metrics/positive_rate@0.10': {'doubleValue': 0.9756097793579102},
'post_export_metrics/positive_rate@0.30': {'doubleValue': 0.8069105744361877},
'post_export_metrics/positive_rate@0.50': {'doubleValue': 0.5813007950782776},
'post_export_metrics/positive_rate@0.70': {'doubleValue': 0.34756097197532654},
'post_export_metrics/positive_rate@0.90': {'doubleValue': 0.07520325481891632},
'post_export_metrics/true_negative_rate@0.10': {'doubleValue': 0.03208556026220322},
'post_export_metrics/true_negative_rate@0.30': {'doubleValue': 0.22727273404598236},
'post_export_metrics/true_negative_rate@0.50': {'doubleValue': 0.4679144322872162},
'post_export_metrics/true_negative_rate@0.70': {'doubleValue': 0.7032085657119751},
'post_export_metrics/true_negative_rate@0.90': {'doubleValue': 0.9572192430496216},
'post_export_metrics/true_positive_rate@0.10': {'doubleValue': 1.0},
'post_export_metrics/true_positive_rate@0.30': {'doubleValue': 0.9152542352676392},
'post_export_metrics/true_positive_rate@0.50': {'doubleValue': 0.7372881174087524},
'post_export_metrics/true_positive_rate@0.70': {'doubleValue': 0.508474588394165},
'post_export_metrics/true_positive_rate@0.90': {'doubleValue': 0.17796610295772552},
'precision': {'doubleValue': 0.3041957914829254},
'prediction/mean': {'doubleValue': 0.5550199747085571},
'recall': {'doubleValue': 0.7372881174087524} }
使用get_metrics_for_all_slices()あなたが実行しているから入手対応するメトリックに各スライスは、辞書マッピングなどのすべてのスライスのメトリックを取得するget_metrics_for_slice()それに。
pp.pprint(eval_result.get_metrics_for_all_slices())
{(): {'accuracy': {'doubleValue': 0.7191107273101807},
'accuracy_baseline': {'doubleValue': 0.9198060631752014},
'auc': {'doubleValue': 0.7972093224525452},
'auc_precision_recall': {'doubleValue': 0.3029831349849701},
'average_loss': {'doubleValue': 0.5623680949211121},
'label/mean': {'doubleValue': 0.08019392192363739},
'post_export_metrics/example_count': {'doubleValue': 721950.0},
'post_export_metrics/fairness/confusion_matrix_at_thresholds': {'confusionMatrixAtThresholds': {'matrices': [{'boundedFalseNegatives': {'value': 340.0},
'boundedFalsePositives': {'value': 612773.0},
'boundedPrecision': {'value': 0.08586231619119644},
'boundedRecall': {'value': 0.9941273927688599},
'boundedTrueNegatives': {'value': 51281.0},
'boundedTruePositives': {'value': 57556.0},
'falseNegatives': 340.0,
'falsePositives': 612773.0,
'precision': 0.08586231619119644,
'recall': 0.9941273927688599,
'tDistributionFalseNegatives': {'unsampledValue': 340.0},
'tDistributionFalsePositives': {'unsampledValue': 612773.0},
'tDistributionPrecision': {'unsampledValue': 0.08586231619119644},
'tDistributionRecall': {'unsampledValue': 0.9941273927688599},
'tDistributionTrueNegatives': {'unsampledValue': 51281.0},
'tDistributionTruePositives': {'unsampledValue': 57556.0},
'threshold': 0.10000000149011612,
'trueNegatives': 51281.0,
'truePositives': 57556.0},
{'boundedFalseNegatives': {'value': 4971.0},
'boundedFalsePositives': {'value': 385684.0},
'boundedPrecision': {'value': 0.12066555768251419},
'boundedRecall': {'value': 0.9141391515731812},
'boundedTrueNegatives': {'value': 278370.0},
'boundedTruePositives': {'value': 52925.0},
'falseNegatives': 4971.0,
'falsePositives': 385684.0,
'precision': 0.12066555768251419,
'recall': 0.9141391515731812,
'tDistributionFalseNegatives': {'unsampledValue': 4971.0},
'tDistributionFalsePositives': {'unsampledValue': 385684.0},
'tDistributionPrecision': {'unsampledValue': 0.12066555768251419},
'tDistributionRecall': {'unsampledValue': 0.9141391515731812},
'tDistributionTrueNegatives': {'unsampledValue': 278370.0},
'tDistributionTruePositives': {'unsampledValue': 52925.0},
'threshold': 0.30000001192092896,
'trueNegatives': 278370.0,
'truePositives': 52925.0},
{'boundedFalseNegatives': {'value': 15684.0},
'boundedFalsePositives': {'value': 187104.0},
'boundedPrecision': {'value': 0.18407785892486572},
'boundedRecall': {'value': 0.7291004657745361},
'boundedTrueNegatives': {'value': 476950.0},
'boundedTruePositives': {'value': 42212.0},
'falseNegatives': 15684.0,
'falsePositives': 187104.0,
'precision': 0.18407785892486572,
'recall': 0.7291004657745361,
'tDistributionFalseNegatives': {'unsampledValue': 15684.0},
'tDistributionFalsePositives': {'unsampledValue': 187104.0},
'tDistributionPrecision': {'unsampledValue': 0.18407785892486572},
'tDistributionRecall': {'unsampledValue': 0.7291004657745361},
'tDistributionTrueNegatives': {'unsampledValue': 476950.0},
'tDistributionTruePositives': {'unsampledValue': 42212.0},
'threshold': 0.5,
'trueNegatives': 476950.0,
'truePositives': 42212.0},
{'boundedFalseNegatives': {'value': 31392.0},
'boundedFalsePositives': {'value': 64497.0},
'boundedPrecision': {'value': 0.291249543428421},
'boundedRecall': {'value': 0.4577863812446594},
'boundedTrueNegatives': {'value': 599557.0},
'boundedTruePositives': {'value': 26504.0},
'falseNegatives': 31392.0,
'falsePositives': 64497.0,
'precision': 0.291249543428421,
'recall': 0.4577863812446594,
'tDistributionFalseNegatives': {'unsampledValue': 31392.0},
'tDistributionFalsePositives': {'unsampledValue': 64497.0},
'tDistributionPrecision': {'unsampledValue': 0.291249543428421},
'tDistributionRecall': {'unsampledValue': 0.4577863812446594},
'tDistributionTrueNegatives': {'unsampledValue': 599557.0},
'tDistributionTruePositives': {'unsampledValue': 26504.0},
'threshold': 0.699999988079071,
'trueNegatives': 599557.0,
'truePositives': 26504.0},
{'boundedFalseNegatives': {'value': 51089.0},
'boundedFalsePositives': {'value': 6354.0},
'boundedPrecision': {'value': 0.5172099471092224},
'boundedRecall': {'value': 0.11757288873195648},
'boundedTrueNegatives': {'value': 657700.0},
'boundedTruePositives': {'value': 6807.0},
'falseNegatives': 51089.0,
'falsePositives': 6354.0,
'precision': 0.5172099471092224,
'recall': 0.11757288873195648,
'tDistributionFalseNegatives': {'unsampledValue': 51089.0},
'tDistributionFalsePositives': {'unsampledValue': 6354.0},
'tDistributionPrecision': {'unsampledValue': 0.5172099471092224},
'tDistributionRecall': {'unsampledValue': 0.11757288873195648},
'tDistributionTrueNegatives': {'unsampledValue': 657700.0},
'tDistributionTruePositives': {'unsampledValue': 6807.0},
'threshold': 0.8999999761581421,
'trueNegatives': 657700.0,
'truePositives': 6807.0}]} },
'post_export_metrics/false_discovery_rate@0.10': {'doubleValue': 0.9141376614570618},
'post_export_metrics/false_discovery_rate@0.30': {'doubleValue': 0.8793344497680664},
'post_export_metrics/false_discovery_rate@0.50': {'doubleValue': 0.8159221410751343},
'post_export_metrics/false_discovery_rate@0.70': {'doubleValue': 0.7087504267692566},
'post_export_metrics/false_discovery_rate@0.90': {'doubleValue': 0.4827900528907776},
'post_export_metrics/false_negative_rate@0.10': {'doubleValue': 0.0058725993148982525},
'post_export_metrics/false_negative_rate@0.30': {'doubleValue': 0.08586085587739944},
'post_export_metrics/false_negative_rate@0.50': {'doubleValue': 0.27089953422546387},
'post_export_metrics/false_negative_rate@0.70': {'doubleValue': 0.5422136187553406},
'post_export_metrics/false_negative_rate@0.90': {'doubleValue': 0.8824270963668823},
'post_export_metrics/false_omission_rate@0.10': {'doubleValue': 0.006586466915905476},
'post_export_metrics/false_omission_rate@0.30': {'doubleValue': 0.017544230446219444},
'post_export_metrics/false_omission_rate@0.50': {'doubleValue': 0.03183702379465103},
'post_export_metrics/false_omission_rate@0.70': {'doubleValue': 0.04975362494587898},
'post_export_metrics/false_omission_rate@0.90': {'doubleValue': 0.07207927852869034},
'post_export_metrics/false_positive_rate@0.10': {'doubleValue': 0.9227758646011353},
'post_export_metrics/false_positive_rate@0.30': {'doubleValue': 0.5808021426200867},
'post_export_metrics/false_positive_rate@0.50': {'doubleValue': 0.28176021575927734},
'post_export_metrics/false_positive_rate@0.70': {'doubleValue': 0.09712613373994827},
'post_export_metrics/false_positive_rate@0.90': {'doubleValue': 0.009568499401211739},
'post_export_metrics/negative_rate@0.10': {'doubleValue': 0.07150217890739441},
'post_export_metrics/negative_rate@0.30': {'doubleValue': 0.3924662470817566},
'post_export_metrics/negative_rate@0.50': {'doubleValue': 0.6823658347129822},
'post_export_metrics/negative_rate@0.70': {'doubleValue': 0.8739510774612427},
'post_export_metrics/negative_rate@0.90': {'doubleValue': 0.9817702174186707},
'post_export_metrics/positive_rate@0.10': {'doubleValue': 0.9284977912902832},
'post_export_metrics/positive_rate@0.30': {'doubleValue': 0.6075337529182434},
'post_export_metrics/positive_rate@0.50': {'doubleValue': 0.3176341950893402},
'post_export_metrics/positive_rate@0.70': {'doubleValue': 0.12604889273643494},
'post_export_metrics/positive_rate@0.90': {'doubleValue': 0.01822979375720024},
'post_export_metrics/true_negative_rate@0.10': {'doubleValue': 0.07722414284944534},
'post_export_metrics/true_negative_rate@0.30': {'doubleValue': 0.41919782757759094},
'post_export_metrics/true_negative_rate@0.50': {'doubleValue': 0.7182397842407227},
'post_export_metrics/true_negative_rate@0.70': {'doubleValue': 0.9028738737106323},
'post_export_metrics/true_negative_rate@0.90': {'doubleValue': 0.9904314875602722},
'post_export_metrics/true_positive_rate@0.10': {'doubleValue': 0.9941273927688599},
'post_export_metrics/true_positive_rate@0.30': {'doubleValue': 0.9141391515731812},
'post_export_metrics/true_positive_rate@0.50': {'doubleValue': 0.7291004657745361},
'post_export_metrics/true_positive_rate@0.70': {'doubleValue': 0.4577863812446594},
'post_export_metrics/true_positive_rate@0.90': {'doubleValue': 0.11757288873195648},
'precision': {'doubleValue': 0.18407785892486572},
'prediction/mean': {'doubleValue': 0.40011298656463623},
'recall': {'doubleValue': 0.7291004657745361} },
(('sexual_orientation', 'bisexual'),): {'accuracy': {'doubleValue': 0.5431034564971924},
'accuracy_baseline': {'doubleValue': 0.8017241358757019},
'auc': {'doubleValue': 0.6259934902191162},
'auc_precision_recall': {'doubleValue': 0.3277454376220703},
'average_loss': {'doubleValue': 0.7425483465194702},
'label/mean': {'doubleValue': 0.1982758641242981},
'post_export_metrics/example_count': {'doubleValue': 116.0},
'post_export_metrics/fairness/confusion_matrix_at_thresholds': {'confusionMatrixAtThresholds': {'matrices': [{'boundedFalseNegatives': {'value': 0.0},
'boundedFalsePositives': {'value': 84.0},
'boundedPrecision': {'value': 0.21495327353477478},
'boundedRecall': {'value': 1.0},
'boundedTrueNegatives': {'value': 9.0},
'boundedTruePositives': {'value': 23.0},
'falsePositives': 84.0,
'precision': 0.21495327353477478,
'recall': 1.0,
'tDistributionFalseNegatives': {'unsampledValue': 0.0},
'tDistributionFalsePositives': {'unsampledValue': 84.0},
'tDistributionPrecision': {'unsampledValue': 0.21495327353477478},
'tDistributionRecall': {'unsampledValue': 1.0},
'tDistributionTrueNegatives': {'unsampledValue': 9.0},
'tDistributionTruePositives': {'unsampledValue': 23.0},
'threshold': 0.10000000149011612,
'trueNegatives': 9.0,
'truePositives': 23.0},
{'boundedFalseNegatives': {'value': 4.0},
'boundedFalsePositives': {'value': 67.0},
'boundedPrecision': {'value': 0.22093023359775543},
'boundedRecall': {'value': 0.8260869383811951},
'boundedTrueNegatives': {'value': 26.0},
'boundedTruePositives': {'value': 19.0},
'falseNegatives': 4.0,
'falsePositives': 67.0,
'precision': 0.22093023359775543,
'recall': 0.8260869383811951,
'tDistributionFalseNegatives': {'unsampledValue': 4.0},
'tDistributionFalsePositives': {'unsampledValue': 67.0},
'tDistributionPrecision': {'unsampledValue': 0.22093023359775543},
'tDistributionRecall': {'unsampledValue': 0.8260869383811951},
'tDistributionTrueNegatives': {'unsampledValue': 26.0},
'tDistributionTruePositives': {'unsampledValue': 19.0},
'threshold': 0.30000001192092896,
'trueNegatives': 26.0,
'truePositives': 19.0},
{'boundedFalseNegatives': {'value': 9.0},
'boundedFalsePositives': {'value': 44.0},
'boundedPrecision': {'value': 0.24137930572032928},
'boundedRecall': {'value': 0.6086956262588501},
'boundedTrueNegatives': {'value': 49.0},
'boundedTruePositives': {'value': 14.0},
'falseNegatives': 9.0,
'falsePositives': 44.0,
'precision': 0.24137930572032928,
'recall': 0.6086956262588501,
'tDistributionFalseNegatives': {'unsampledValue': 9.0},
'tDistributionFalsePositives': {'unsampledValue': 44.0},
'tDistributionPrecision': {'unsampledValue': 0.24137930572032928},
'tDistributionRecall': {'unsampledValue': 0.6086956262588501},
'tDistributionTrueNegatives': {'unsampledValue': 49.0},
'tDistributionTruePositives': {'unsampledValue': 14.0},
'threshold': 0.5,
'trueNegatives': 49.0,
'truePositives': 14.0},
{'boundedFalseNegatives': {'value': 16.0},
'boundedFalsePositives': {'value': 20.0},
'boundedPrecision': {'value': 0.25925925374031067},
'boundedRecall': {'value': 0.30434781312942505},
'boundedTrueNegatives': {'value': 73.0},
'boundedTruePositives': {'value': 7.0},
'falseNegatives': 16.0,
'falsePositives': 20.0,
'precision': 0.25925925374031067,
'recall': 0.30434781312942505,
'tDistributionFalseNegatives': {'unsampledValue': 16.0},
'tDistributionFalsePositives': {'unsampledValue': 20.0},
'tDistributionPrecision': {'unsampledValue': 0.25925925374031067},
'tDistributionRecall': {'unsampledValue': 0.30434781312942505},
'tDistributionTrueNegatives': {'unsampledValue': 73.0},
'tDistributionTruePositives': {'unsampledValue': 7.0},
'threshold': 0.699999988079071,
'trueNegatives': 73.0,
'truePositives': 7.0},
{'boundedFalseNegatives': {'value': 22.0},
'boundedFalsePositives': {'value': 0.0},
'boundedPrecision': {'value': 1.0},
'boundedRecall': {'value': 0.043478261679410934},
'boundedTrueNegatives': {'value': 93.0},
'boundedTruePositives': {'value': 1.0},
'falseNegatives': 22.0,
'precision': 1.0,
'recall': 0.043478261679410934,
'tDistributionFalseNegatives': {'unsampledValue': 22.0},
'tDistributionFalsePositives': {'unsampledValue': 0.0},
'tDistributionPrecision': {'unsampledValue': 1.0},
'tDistributionRecall': {'unsampledValue': 0.043478261679410934},
'tDistributionTrueNegatives': {'unsampledValue': 93.0},
'tDistributionTruePositives': {'unsampledValue': 1.0},
'threshold': 0.8999999761581421,
'trueNegatives': 93.0,
'truePositives': 1.0}]} },
'post_export_metrics/false_discovery_rate@0.10': {'doubleValue': 0.7850467562675476},
'post_export_metrics/false_discovery_rate@0.30': {'doubleValue': 0.7790697813034058},
'post_export_metrics/false_discovery_rate@0.50': {'doubleValue': 0.7586206793785095},
'post_export_metrics/false_discovery_rate@0.70': {'doubleValue': 0.7407407164573669},
'post_export_metrics/false_discovery_rate@0.90': {'doubleValue': 0.0},
'post_export_metrics/false_negative_rate@0.10': {'doubleValue': 0.0},
'post_export_metrics/false_negative_rate@0.30': {'doubleValue': 0.17391304671764374},
'post_export_metrics/false_negative_rate@0.50': {'doubleValue': 0.3913043439388275},
'post_export_metrics/false_negative_rate@0.70': {'doubleValue': 0.695652186870575},
'post_export_metrics/false_negative_rate@0.90': {'doubleValue': 0.95652174949646},
'post_export_metrics/false_omission_rate@0.10': {'doubleValue': 0.0},
'post_export_metrics/false_omission_rate@0.30': {'doubleValue': 0.13333334028720856},
'post_export_metrics/false_omission_rate@0.50': {'doubleValue': 0.1551724076271057},
'post_export_metrics/false_omission_rate@0.70': {'doubleValue': 0.17977528274059296},
'post_export_metrics/false_omission_rate@0.90': {'doubleValue': 0.19130434095859528},
'post_export_metrics/false_positive_rate@0.10': {'doubleValue': 0.9032257795333862},
'post_export_metrics/false_positive_rate@0.30': {'doubleValue': 0.7204301357269287},
'post_export_metrics/false_positive_rate@0.50': {'doubleValue': 0.47311827540397644},
'post_export_metrics/false_positive_rate@0.70': {'doubleValue': 0.2150537669658661},
'post_export_metrics/false_positive_rate@0.90': {'doubleValue': 0.0},
'post_export_metrics/negative_rate@0.10': {'doubleValue': 0.07758620381355286},
'post_export_metrics/negative_rate@0.30': {'doubleValue': 0.2586206793785095},
'post_export_metrics/negative_rate@0.50': {'doubleValue': 0.5},
'post_export_metrics/negative_rate@0.70': {'doubleValue': 0.767241358757019},
'post_export_metrics/negative_rate@0.90': {'doubleValue': 0.9913793206214905},
'post_export_metrics/positive_rate@0.10': {'doubleValue': 0.9224137663841248},
'post_export_metrics/positive_rate@0.30': {'doubleValue': 0.7413793206214905},
'post_export_metrics/positive_rate@0.50': {'doubleValue': 0.5},
'post_export_metrics/positive_rate@0.70': {'doubleValue': 0.23275862634181976},
'post_export_metrics/positive_rate@0.90': {'doubleValue': 0.008620689623057842},
'post_export_metrics/true_negative_rate@0.10': {'doubleValue': 0.09677419066429138},
'post_export_metrics/true_negative_rate@0.30': {'doubleValue': 0.2795698940753937},
'post_export_metrics/true_negative_rate@0.50': {'doubleValue': 0.5268816947937012},
'post_export_metrics/true_negative_rate@0.70': {'doubleValue': 0.7849462628364563},
'post_export_metrics/true_negative_rate@0.90': {'doubleValue': 1.0},
'post_export_metrics/true_positive_rate@0.10': {'doubleValue': 1.0},
'post_export_metrics/true_positive_rate@0.30': {'doubleValue': 0.8260869383811951},
'post_export_metrics/true_positive_rate@0.50': {'doubleValue': 0.6086956262588501},
'post_export_metrics/true_positive_rate@0.70': {'doubleValue': 0.30434781312942505},
'post_export_metrics/true_positive_rate@0.90': {'doubleValue': 0.043478261679410934},
'precision': {'doubleValue': 0.24137930572032928},
'prediction/mean': {'doubleValue': 0.4882037043571472},
'recall': {'doubleValue': 0.6086956262588501} },
(('sexual_orientation', 'heterosexual'),): {'accuracy': {'doubleValue': 0.5325203537940979},
'accuracy_baseline': {'doubleValue': 0.7601625919342041},
'auc': {'doubleValue': 0.6657300591468811},
'auc_precision_recall': {'doubleValue': 0.40228524804115295},
'average_loss': {'doubleValue': 0.8246824741363525},
'label/mean': {'doubleValue': 0.2398373931646347},
'post_export_metrics/example_count': {'doubleValue': 492.0},
'post_export_metrics/fairness/confusion_matrix_at_thresholds': {'confusionMatrixAtThresholds': {'matrices': [{'boundedFalseNegatives': {'value': 0.0},
'boundedFalsePositives': {'value': 362.0},
'boundedPrecision': {'value': 0.24583333730697632},
'boundedRecall': {'value': 1.0},
'boundedTrueNegatives': {'value': 12.0},
'boundedTruePositives': {'value': 118.0},
'falsePositives': 362.0,
'precision': 0.24583333730697632,
'recall': 1.0,
'tDistributionFalseNegatives': {'unsampledValue': 0.0},
'tDistributionFalsePositives': {'unsampledValue': 362.0},
'tDistributionPrecision': {'unsampledValue': 0.24583333730697632},
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'post_export_metrics/true_negative_rate@0.90': {'doubleValue': 1.0},
'post_export_metrics/true_positive_rate@0.10': {'doubleValue': 1.0},
'post_export_metrics/true_positive_rate@0.30': {'doubleValue': 1.0},
'post_export_metrics/true_positive_rate@0.50': {'doubleValue': 1.0},
'post_export_metrics/true_positive_rate@0.70': {'doubleValue': 1.0},
'post_export_metrics/true_positive_rate@0.90': {'doubleValue': 0.0},
'precision': {'doubleValue': 0.3333333432674408},
'prediction/mean': {'doubleValue': 0.5955214500427246},
'recall': {'doubleValue': 1.0} } }