# Keras Auc Metric

Performance of such models is commonly evaluated using the. the proportion of outliers in the data set. For example you could pick accuracy or logarithmic loss. 4 is based on open-source CRAN R 3. First we define the custom metric, as shown here. Neither the precision nor recall take into account the number of true negatives, thus the PR AUC metric is less prone to inflation by the class imbalance than the ROC AUC metric is. Linear regression models. Using Keras and scikit-learn to evaluate regression and classification neural networks. I've tried this comparison out on a larger, real-world multi-label classification problem from Kaggle (the toxic comments competition) and am seeing the same issue. Release Notes for Version 1. Model() function. Always test against the metric you are being tested on. Computes the approximate AUC (Area under the curve) via a Riemann sum. It's probably the second most popular one, after accuracy. In this tutorial, we will see how Snorkel can be used for Information Extraction. a classification task. You have to use Keras backend functions. 75) and I'd like to try optimizing the AUROC directly instead of using binary cross-entropy loss. ROC, AUC for a categorical classifier. 在keras中自带的性能评估有准确性以及loss，当需要以auc作为评价验证集的好坏时，就得自己写个评价函数了： [python] view plain. The classification accuracy metric works better if there is an equal number of samples in each class. This release brings the API in sync with the tf. 0 is the first release of multi-backend Keras that supports TensorFlow 2. I've seen a few examples of using the same model within multiple threads, but in this particular case, I run into various errors regarding conflicting graphs, etc. For estimation of the metric over a stream of data, the function creates an update_op operation that updates these variables and returns the auc. the required inteface seems to be the same, but calling: model. optimizers import RMSprop from keras. Briefed on the confusion matrix, we can now move forward and calculate the ROC AUC metric itself, using a toy-sized example. AUC, or Area Under Curve, is a metric for binary classification. GridSearchCV and model_selection. 3 when the BN layer was frozen (trainable = False) it kept updating its batch statistics, something that caused epic headaches to its users. metrics import. In this lab, you'll directly ingest a BigQuery dataset and train a fraud detection model with TensorFlow Enterprise on Google Cloud AI Platform. metrics import log_loss, roc_auc_score, matthews_corrcoef import keras. Aprendizaje Automático con Tensorflow y R Edgar Ruiz edgararuiz theotheredgar edgararuiz. What is a Random Forest? Random forest is an ensemble tool which takes a subset of observations and a subset of variables to build a decision trees. Note that if you specify more than one evaluation metric the last one in param['eval_metric'] is used for early stopping. conf data = higgs. Finally the xgboost model exhibits a ridiculously high auc on the training subset, but slightly lower auc on the testing subset to the Keras classifier above. It works on standard, generic hardware. Hyper-parameter tuning with grid search allows us to test different combinations of hyper-parameters and find one with improved accuracy. a classification task. Also ROC AUC is not a metric that be accumulated in mini-batches, it has to be computed for all the data at once. Purchase Order Number SELECT PORDNMBR [Order ID], * FROM PM10000 WITH(nolock) WHERE DEX_ROW_TS > '2019-05-01';. The calculation is run after every epoch. Nice! An AUC of 0. We expect the AUC to be slightly over 0. 2 Bag-of-words Our baseline model is "bag-of-words" using a standard 3-layer neural network, with 300-d sum/mean word as inputs. Neither the precision nor recall take into account the number of true negatives, thus the PR AUC metric is less prone to inflation by the class imbalance than the ROC AUC metric is. However note that it does not support most TensorFlow 2. We simplified the problem by doing a binary classification and only using two classes: our normal and our ceiling effects plots. In this lab, you'll directly ingest a BigQuery dataset and train a fraud detection model with TensorFlow Enterprise on Google Cloud AI Platform. Deep Metric Learning Deep metric learning uses deep neural networks to directly learn a similarity metric, rather than creating it as a byproduct of solving e. Release Notes for Version 1. I am SUPER EXCITED about two recent packages available in R for Deep Learning that everyone is preaching about: keras for Neural Network(NN) API & lime for LIME(Local Interpretable Model-agnostic Explanations) to explain the behind the scene of NN. AUC The top performing models based on the average AUC are the boosted trees models (GBDT and Random Forest), as well as the Deep Learning and k-NN models, with scores hovering around 0. print_evaluation ([period, show_stdv]): Create a callback that prints the evaluation results. We can later load this model in the Flask app to serve model predictions. contamination ( float in ( 0. In the meantime, a digital "rough cut" of the entire book became available in Safari Books (which offers free 10-day trials) this week. Feature Selection and Learning using the Group LASSO on Deep CNN Features for Object Detection. To calculate and plot these metrics, we can use the ROCR package. Code for case study - Customer Churn with Keras/TensorFlow and H2O Dr. It's probably the second most popular one, after accuracy. 我试图从scikit-learn导入ROC,AUC功能 from sklearn. ROC curve extends to problems with three or more classes with what is known as the one-vs-all approach. We can later load this model in the Flask app to serve model predictions. #Predict: y_pred = regressor. Regression examples · Baseball batting averages · Beer sales vs. If you have less than 400-300, you are kind of doomed!. For example, if there is 90% class A samples and 10% of class B, and trained a model, the model would have a 90% training accuracy just by predicting every sample as class A. Being able to go from idea to result with the least possible delay is key to doing good research. The code snippet defines a custom metric function, which is used to train the model to optimize for the ROC AUC metric. metrics import roc_auc_score model = keras. ) and to maximize (MAP, NDCG, AUC). It is always better to train the model to directly optimize for the metric it will be evaluated on. The entire code accompanying the workshop can be found below the video. 05 or 5%) for the number of consecutive rounds defined by stopping rounds. Their behavior will depend on the value this metric. A model whose predictions are 100% wrong has an AUC of 0. Metric functions are to be supplied in the metrics parameter of the compile. Both loss functions and explicitly defined Keras metrics can be used as training metrics. Another example of metric for evaluation of machine learning algorithms is precision recall or NDCG, which can be used for sorting algorithms primarily used by search engines. Average precision. First Load in the required packages. This can actually mean one of several things. The AUC score is in a two class classification class equal to the probability that our classifier will detect a fraudulent transaction given one fraudulent and genuine transaction to choice from. Big Data Deep Learning Framework using Keras: A Case Study of Pneumonia Prediction rate is also an important metric to consider network trained on different subjects can lead to an AUC. If you have less than 400-300, you are kind of doomed!. Log Loss uses negative log to provide an easy metric for comparison. Hyper-parameter Tuning with Grid Search for Deep Learning. First we define the custom metric, as shown here. 825 AUC score (remember that an AUC ranges between 0. The auc on the test set is 0. The following are code examples for showing how to use keras. metrics import. auc]) results with the error: Using TensorFlow backend. Adam) as we did in the CNN TensorFlow tutorial. Esben Jannik Bjerrum / January 15, 2017 / Blog, Cheminformatics, Machine Learning, Neural Network, RDkit / 9 comments. View Iurii Chervonyi’s profile on LinkedIn, the world's largest professional community. #Predict: y_pred = regressor. mae, metrics. Let’s say, as shown in Table 11. In this case the ROC curve is independent of the probability threshold so we have to use something else. The two-dimensional graphs in the first bullet above are always more informative than a single number, but if you need a single-number metric, one of these is preferable to accuracy: The Area Under the ROC curve (AUC) is a good general statistic. AUC The top performing models based on the average AUC are the boosted trees models (GBDT and Random Forest), as well as the Deep Learning and k-NN models, with scores hovering around 0. プログラミングに関係のない質問 やってほしいことだけを記載した丸投げの質問 問題・課題が含まれていない質問 意図的に内容が抹消された質問 広告と受け取られるような投稿. For macro average you pass in the per label count and then sum, for micro average you average the counts first, then apply your metric function. I have a missing AUC and ROC in my model analysis. Data format description. A medical school’s first-time pass rate on USMLE Step 1 is therefore an important metric to look at when evaluating a medical school. Keras used to implement the f1 score in its metrics; however, the developers decided to remove it in Keras 2. 02 and is pretty low: our yummly mushroom model works well! Advanced features ¶ Most of the features below have been implemented to help you to improve your model by offering a better understanding of its content. For estimation of the metric over a stream of data, the function creates an update_op operation that updates these variables and returns the auc. The classification accuracy metric works better if there is an equal number of samples in each class. Many thanks to Addison-Wesley Professional for providing the permissions to excerpt "Natural Language Processing" from the book, Deep Learning Illustrated by Krohn, Beyleveld, and Bassens. I'm trying to use a tensorflow metric function in keras. Oracle Principal Data Scientist Taylor Foust tackles the common issue of label bias in positive and unlabeled learning, and shares some techniques that may be useful in identifying and mitigating these problems. AUC represents the probability that a random positive (green) example is positioned to the right of a random negative (red) example. Keras used to implement the f1 score in its metrics; however, the developers decided to remove it in Keras 2. For example, if there is 90% class A samples and 10% of class B, and trained a model, the model would have a 90% training accuracy just by predicting every sample as class A. I found some interesting toxicology datasets from the Tox21 challenge, and wanted to see if it was possible to build a toxicology predictor using a deep neural network. Predicting Fraud with Autoencoders and Keras. AUC ranges in value from 0 to 1. The relevant methods of the callbacks will then be called at each stage of the training. If your metric cares about exact probabilities, like logarithmic loss does, you can calibrate the classifier, that is post-process the predictions to get better estimates. The K-nearest neighbors (KNN) algorithm is a type of supervised machine learning algorithms. • Exploratory data analysis projected with data visualization tools benchmarked the model. Watch Queue Queue. metrics import auc # Get metrics to graph auc_keras = auc(fpr_keras, tpr_keras) y I need to choose a metric that. Hi, I'm working on a personal project for fun and was going to test out different models for this Kaggle competition: Credit Card Fraud Detection. Basic evaluation measures from the confusion matrix. 🚀 This release brings the API in sync with the tf. Introduction¶. Keras also provides a way to specify a loss function during model training. They are extracted from open source Python projects. The AUC score is in a two class classification class equal to the probability that our classifier will detect a fraudulent transaction given one fraudulent and genuine transaction to choice from. Code for case study - Customer Churn with Keras/TensorFlow and H2O Dr. Have a look under the hood and see what it includes, as well as what. As accuracy is not very informative in this case, the AUC (Aera under the curve) a better metric to assess the model quality. First Load in the required packages. Detecting spouse mentions in sentences. The K-nearest neighbors (KNN) algorithm is a type of supervised machine learning algorithms. Model() function. This is performed using the likelihood ratio test, which compares the likelihood of the data under the full model against the likelihood of the data under a model with fewer predictors. metrics import roc_auc_score model = keras. concluded his talk by demonstrating several ways to deploy a keras or tensorflow model, including publishing to RStudio Connect. The two-dimensional graphs in the first bullet above are always more informative than a single number, but if you need a single-number metric, one of these is preferable to accuracy: The Area Under the ROC curve (AUC) is a good general statistic. Neste modelo, quero adicionar métricas adicionais, como ROC e AUC, mas, até onde sei, as keras não possuem funções métricas internas de ROC e AUC. # Visualize the ROC curve from sklearn. Calculating AUC and GINI Model Metrics for Logistic Classification In this code-heavy tutorial, learn how to build a logistic classification model in H2O using the prostate dataset to calculate. As you can see, given the AUC metric, Keras classifier outperforms the other classifier. the proportion of outliers in the data set. If weights is None, weights default to 1. Unfortunately, there is only limited literature on the comparison of different base learners for boosting (see for example Joshi et al. Mostraremos cómo es posible interactuar con Tensorflow desde R, y en qué escenarios puede ser útil aprovechar esta integración. #2 best model for Click-Through Rate Prediction on Bing News (AUC metric) #2 best model for Click-Through Rate Prediction on Bing News (AUC metric) xxxmin/ctr_Keras. keras will be used to fit a model with 5 hidden units and uses a 10% dropout rate to regularize the model. 75) and I'd like to try optimizing the AUROC directly instead of using binary cross-entropy loss. For macro average you pass in the per label count and then sum, for micro average you average the counts first, then apply your metric function. 0 is the first release of multi-backend Keras that supports TensorFlow 2. The code snippet defines a custom metric function, which is used to train the model to optimize for the ROC AUC metric. the required inteface seems to be the same, but calling: model. Detecting spouse mentions in sentences. It is written in Python, but there is an R package called 'keras' from RStudio, which is basically a R interface for Keras. class Accuracy: Calculates how often predictions matches labels. A model whose predictions are 100% wrong has an AUC of 0. 1 ) ) – The amount of contamination of the data set, i. Average precision. 5 represents a model that is as good as random. , aimed at fast experimentation. I'm trying to use a tensorflow metric function in keras. An area of 1. 4, we provide four inputs to a binary-classification model. They are extracted from open source Python projects. I was making binary classifier (0 or 1) Multi-Layer Perceptron Model using Keras for “Kaggle Quora competition”. Model type and size of dataset. keras API as of TensorFlow 2. Model Evaluation - Classification: Confusion Matrix: A confusion matrix shows the number of correct and incorrect predictions made by the classification model compared to the actual outcomes (target value) in the data. We can later load this model in the Flask app to serve model predictions. metrics import roc_auc_score model = keras. 05 or 5%) for the number of consecutive rounds defined by stopping rounds. keras will be used to fit a model with 5 hidden units and uses a 10% dropout rate to regularize the model. Normally we might look at the area under the ROC curve as a metric to choose our final values. The framework we're gonna use is the Embed, Encode, Attend and Predict framework this was introduced by Matthew Honnibal. Therefore, we see that different metrics are required to measure the efficiency of different algorithms, also depending upon the dataset at hand. Up until this point, we've been using AUC to give us a single-number summary of classifier performance. Please, take all these outputs with several grains of salt. 2 Bag-of-words Our baseline model is "bag-of-words" using a standard 3-layer neural network, with 300-d sum/mean word as inputs. この曲線の下側の面積(AUC)をAverage Precisionというらしいです. A deep Tox21 neural network with RDKit and Keras. Posted on Aug 30, 2013 • lo ** What is the Class Imbalance Problem? It is the problem in machine learning where the total number of a class of data (positive) is far less than the total number of another class of data (negative). 5 represents a model that is as good as random. In our experiments, we restrict our attention to character recognition, although the basic approach can be replicated for almost any modality (Figure 2). An alternative to AUC is to use the precision-recall curve or the sensitivity (recall)-specificity curve. Classification experiment using AUC weighted as the primary metric with a max time of 12,000 seconds per iteration, with the experiment to end after 50 iterations and 2 cross-validation folds. keras API as of TensorFlow 2. # not needed in Kaggle, but required in Jupyter. # alternative metric to optimize over grid parameters: AUC # other scoring parameters include 'recall' or 'precision' grid_clf Auto Keras uses neural network for. How to define and use your own custom metric in Keras with a worked example. Filippo Valsorda talks about the challenges in maintaining and keeping the cryptographic libraries written in Go secure, safe, useful and modern. You can pass a list of callbacks (as the keyword argument callbacks) to the. eval_metric = "rmse", booster = "gbtree") One can choose between decision trees ( gbtree and dart ) and linear models ( gblinear ). First, I am training the unsupervised neural network model using deep learning autoencoders. Keras also supplies many optimisers - as can be seen here. We then compute the AUC based on these predictions for this user, do this for all users, and average all the AUC values. Keras doesn't have any inbuilt function to measure AUC metric. inverse_transform(y_pred) #Assess Success of Prediction: ROC AUC TP/TN F1 Confusion Matrix #Tweak Parameters to Optimise Metrics: #Select A new Model #Repeat the process. We use cookies for various purposes including analytics. This should be the accepted solution. Both stored procedure use functions from sklearn to calculate an accuracy metric, AUC (area under curve). 以下のソースコードは長くなっていますが、基本的にはprecision_recall_curve関数に正解ラベルと推定したラベルの確率(あるいは決定境界からの距離)を与えて、その結果をグラフにすればいいだけです. keras recall metric (5) I am building a multi-class classifier with Keras 2. contamination ( float in ( 0. 579686209744. Pre-trained models and datasets built by Google and the community. It's just a way of encapsulating some of the most common techniques in natural language into usable blocks, blocks they play well with each other. In this case the ROC curve is independent of the probability threshold so we have to use something else. Model type and size of dataset. As you can see, given the AUC metric, Keras classifier outperforms the other classifier. Exploratory notebooks, model training runs, code, hyperparameters, metrics, data versions, results exploration visualizations and more. 5 is random and 1 is perfect). This is a large release for yardstick, with more metrics, grouped data frame integration, multiclass metric support, and a few breaking changes. In the end, your neural network will be easy to use and will serve as a powerful tool going forward in your career as a Data Scientist. Data format description. Simple guide to confusion matrix terminology. metrics import auc. These include AUC, ommission rates, sensitivity, specificity, proportion correctly identified and Kappa. I was making binary classifier (0 or 1) Multi-Layer Perceptron Model using Keras for "Kaggle Quora competition". backend as K from keras. A medical school’s first-time pass rate on USMLE Step 1 is therefore an important metric to look at when evaluating a medical school. auc (x, y, reorder=’deprecated’) [source] ¶ Compute Area Under the Curve (AUC) using the trapezoidal rule This is a general function, given points on a curve. 13, as well as Theano and CNTK. Unfortunately, there is only limited literature on the comparison of different base learners for boosting (see for example Joshi et al. GridSearchCV and model_selection. In the end, your neural network will be easy to use and will serve as a powerful tool going forward in your career as a Data Scientist. Area under ROC curve (AUC-ROC) is one of the most common evaluation metric for binary classification problems. KNN is extremely easy to implement in its most basic form, and yet performs quite complex classification tasks. We can later load this model in the Flask app to serve model predictions. For best results, predictions should be distributed approximately uniformly in the range [0, 1] and not peaked around 0 or 1. Scikit-plot tries to stay out of your way as much as possible. We were able to get fantastic validation accuracy, but never checked accuracy on a test set, and never considered alternate metrics of evaluating model performance ("accuracy" is not always the most informative metric). We use a standard neural network of 2 hidden layers using keras: LINEAR —¥ RELU —+ LINEAR —¥ RELU -+ LINEAR —¥ SIGMOID. import keras as keras import numpy as np from keras. The following figure shows the AUROC graphically: In this figure, the blue area corresponds to the Area Under the curve of the Receiver Operating Characteristic (AUROC). The relevant methods of the callbacks will then be called at each stage of the training. concluded his talk by demonstrating several ways to deploy a keras or tensorflow model, including publishing to RStudio Connect. keras API as of TensorFlow 2. # not needed in Kaggle, but required in Jupyter. from sklearn. Using Keras and scikit-learn to evaluate regression and classification neural networks. In our case we select categorical_crossentropy, which is another term for multi-class log loss. In our experiments, we restrict our attention to character recognition, although the basic approach can be replicated for almost any modality (Figure 2). Note that if you specify more than one evaluation metric the last one in param['eval_metric'] is used for early stopping. metric_params (dict, optional (default = None)) - Additional keyword arguments for the metric function. Has anyone successfully implemented AUROC as a loss function for Theano/Lasagne/Keras? I have a binary classification problem where we expect very low AUROC values (in the range of 0. If it is RMSE, then RMSE and so on. この曲線の下側の面積(AUC)をAverage Precisionというらしいです. Integrate any user defined function in Keras metrics like function to get F1 score on training and validation data. Mathematics of simple regression. この曲線の下側の面積(AUC)をAverage Precisionというらしいです. metrics import roc_curve, auc from keras. 0] I decided to look into Keras callbacks. Neste modelo, quero adicionar métricas adicionais, como ROC e AUC, mas, até onde sei, as keras não possuem funções métricas internas de ROC e AUC. The relevant methods of the callbacks will then be called at each stage of the training. Customer Analytics: Using Deep Learning With Keras To Predict Customer Churn Written by Matt Dancho on November 28, 2017 Customer churn is a problem that all companies need to monitor, especially those that depend on subscription-based revenue streams. It is more difficult to overfit with 500,000 rows versus with 10,000 rows. the required inteface seems to be the same, but calling: model. 5 is random and 1 is perfect). class Accuracy: Calculates how often predictions matches labels. 0; one whose predictions are 100% correct has an AUC of 1. It is a lazy learning algorithm since it doesn't have a specialized training phase. Combine precision and recall into a single metric called the F1 score, in particular, if you need a simple way to compare classifiers. augmented reality. We simplified the problem by doing a binary classification and only using two classes: our normal and our ceiling effects plots. AUC (Area under the ROC Curve) An evaluation metric that considers all possible classification thresholds. AUC represents the probability that a random positive (green) example is positioned to the right of a random negative (red) example. Class Imbalance Problem. #Predict: y_pred = regressor. libraries for deep learning, Keras stands out for it's simplicity in modeling. conf data = higgs. It maintains compatibility with TensorFlow 1. Like K-means clustering, hierarchical clustering also groups together the data points with similar characteristics. Hyper-parameter tuning with grid search allows us to test different combinations of hyper-parameters and find one with improved accuracy. Measure the metric for the first class (which is then a binary task) and so on. Watch Queue Queue. Mostraremos cómo es posible interactuar con Tensorflow desde R, y en qué escenarios puede ser útil aprovechar esta integración. Feature Selection and Learning using the Group LASSO on Deep CNN Features for Object Detection. If weights is None, weights default to 1. Keep in mind though, that hyper-parameter tuning can only improve the model so much without overfitting. 13, as well as Theano and CNTK. 在keras中自带的性能评估有准确性以及loss，当需要以auc作为评价验证集的好坏时，就得自己写个评价函数了： [python] view plain. You have to use Keras backend functions. It might be a good idea to use ROC AUC score as a tuning metric when training, to make sure our model do not discriminate the minor group (in our case the fraudulent transactions). Calculating the ROC AUC Metric. You can use callbacks to get a view on internal states and statistics of the model during training. The above approach we should try for the skewed data also and then build the final model with the whole training dataset and predict the classes in the test. Accuracy metrics such as AUC can only be generated if you also provide the target label (the tipped column). Wrapper function that allows to fit distinct data mining (14 classification and 15 regression) methods under the same coherent function structure. Costume callback for AUC in keras. For example, if model A has an AUC higher than model B, but the 95% confidence interval around each AUC value overlaps, then the models may not be. Keras can separate a portion of your training data into a validation dataset and evaluate the performance of your model on that validation dataset each epoch. But for certain metrics, this may be very difficult or impossible. I hope it will be helpful for optimizing number of epochs. However, there is an issue with AUC ROC, it only takes into account the order of probabilities and hence it does not take into account the model’s capability to predict higher probability for samples more likely to be positive. MinMax Rule. 6, which isn't bad when predicting the stock market and an accuracy of 57%, so a tad better than the natural balance of the data of 0. A project to classify songs into 10 different genres based on 264 feature values, which correspond to three main aspects of a music signal: timbre, pitch, and rhythm. I am a student using the free version. 选择 Keras 作为编程框架，是因为 Keras 强调简单、快速地设计模型，而不去纠缠底层代码，使得内容相当易于理解，使用者可以在 CNTK、 TensorFlow 和 Theano 的后台之间随意切换，非常灵活。 **实录提要：** - 在推荐系统那部分，Keras 中能直接以 auc 指标计算 loss 吗？. We actually did a much deeper analysis on a larger and more diverse dataset and observed 90% detection with a 1/10,000 false positive rate, and this can be combined with other approaches outside the scope of this post to improve detection even further. The above approach we should try for the skewed data also and then build the final model with the whole training dataset and predict the classes in the test. We were able to get fantastic validation accuracy, but never checked accuracy on a test set, and never considered alternate metrics of evaluating model performance ("accuracy" is not always the most informative metric). 8 Using TensorFlow with keras (instead of kerasR) There are two packages available for the front end of TensorFlow. GridSearchCV and model_selection. These changes were made with the intention of standardizing both the API and the output of each metric. Keras does this automatically if you use accuracy or log_loss as a metric. 600883159876 Accuracy on all data: 0. An area of 1. Normally we might look at the area under the ROC curve as a metric to choose our final values. import numpy as np from sklearn. Custom Metrics You can provide an arbitrary R function as a custom metric. To discretize the AUC curve, a linearly spaced set of thresholds is used to compute pairs of recall and precision values. Let's say, as shown in Table 11. Download Open Datasets on 1000s of Projects + Share Projects on One Platform. For instance, if we have three classes, we will create three ROC curves,. Model Evaluation - Classification: Confusion Matrix: A confusion matrix shows the number of correct and incorrect predictions made by the classification model compared to the actual outcomes (target value) in the data. Iurii has 5 jobs listed on their profile. Model type and size of dataset. The models developed for pneumonia and COPD are slighlty better (<3%) than the current models developed by us. 13, as well as Theano and CNTK. model_selection import train_test_split. AUC ROC considers the predicted probabilities for determining our model's performance. It’s probably the second most popular one, after accuracy. You can do this in a callback. Keras doesn't have any inbuilt function to measure AUC metric. in your AUC metric. the proportion of outliers in the data set. For detailed session information including R version, operating system and package versions, see the sessionInfo() output at the end of this document. 0 represents a model that made all predictions perfectly.