How would you validate-test a predictive model?
Why evaluate/test model at all?
Evaluating the performance of a model is one of the most important stages in predictive modeling, it indicates how successful model has been for the dataset. It enables to tune parameters and in the end test the tuned model against a fresh cut of data.
Below we will look at few most common validation metrics used for predictive modeling. The choice of metrics influences how you weight the importance of different characteristics in the results and your ultimate choice of which machine learning algorithm to choose. Before we move on to a variety of metrics lets get basics right.
Golden rules for validating-testing a model.
Never use same data for training and testing!!!
Look at Rule #1
What it means is, always leave cut of data that are not included in training to test your model against after fitting/tuning is finished.
There is a very simple way to set data aside, using Scikit-Learn:
from sklearn import datasets from sklearn.cross_validation import train_test_split data = datasets.load_iris() X = data['data'] y = data['target'] X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.3, random_state=0) print('Full dataset, features:',len(X)) print('Full dataset, labels:',len(y)) print('Train dataset, features:',len(X_train)) print('Test dataset, features:',len(X_test)) print('Train dataset, labels:',len(y_train)) print('Test dataset, features:',len(y_test))
In some cases, it may seem like ‘losing’ part of the training set, especially when data sample is not large enough.There are ways around it as well, one of most popular is ‘Cross Validation’.
It is simple ‘trick’ that splits data into n equal parts. Then successively hold out each part and fit the model using the rest. This gives n estimates of model performance that can be combined into an overall measure. Although very ‘heavy’ from computing point of view, very efficient and widely used method to avoid overfitting and improve ‘out of sample’ performance of the model.
Here is an example of Cross Validation using Scikit-Learn:
from sklearn import cross_validation from sklearn.linear_model import LogisticRegression from sklearn import datasets from sklearn.cross_validation import train_test_split data = datasets.load_iris() X = data['data'] y = data['target'] X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.3, random_state=0) num_instances = len(X_train) kfold = cross_validation.KFold(len(X_train),n_folds=10, random_state=1) model = LogisticRegression() preds = cross_validation.cross_val_score(model, X_train, y_train, cv=kfold) print(preds.mean(), preds.std())
Two main types of predictive models.
Talking about a predictive modeling, there are two main types of problems to be solved:
- Regression problems are those where you are trying to predict or explain one thing (dependent variable) using other things (independent variables) with continuous output eg exact price of a stock next day.
- Classification problems try to determine group membership by deriving probabilities eg. will the stock price go up/down or will not change next day. Algorithms like SVM and KNN create a class output. Algorithms like Logistic Regression, Random Forest, Gradient Boosting, Adaboost etc. give probability outputs. Converting probability outputs to class output is just a matter of creating a threshold probability.
In regression problems, we do not have such inconsistencies in output. The output is always continuous in nature and requires no further treatment.
Techniques/metrics for model validation.
Having the dataset divided, and model fitted there is a question, what kind of quantifiable validation metrics to use. There are few very basic quick and dirty methods to check performance. One of them is value range – if model outputs are far outside of the response variable range, that would immediately indicate poor estimation or model inaccuracy.
Most often there is a need to use something more sophisticated and ‘scientific’.
Accuracy is a classification metric, it the number of correct predictions made as a ratio of all predictions. Probably it is the most common evaluation metric for classification problems.
Below is an example of calculating classification accuracy using Scikit-Learn.
from sklearn.linear_model import LogisticRegression from sklearn import datasets from sklearn.cross_validation import train_test_split from sklearn.metrics import accuracy_score data = datasets.load_iris() X = data['data'] y = data['target'] X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.3, random_state=0) model = LogisticRegression() model.fit(X_train,y_train) preds = model.predict(X_test) print(accuracy_score(preds,y_test))
Precision is the ratio of correctly predicted positive observations to the total predicted positive observations. The question that this metric answer is of all passengers that labeled as survived, how many actually survived? High precision relates to the low false positive rate.
from sklearn.linear_model import LogisticRegression from sklearn import datasets from sklearn.cross_validation import train_test_split from sklearn.metrics import precision_score data = datasets.load_iris() X = data['data'] y = data['target'] X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.3, random_state=0) model = LogisticRegression() model.fit(X_train,y_train) preds = model.predict(X_test) print(precision_score(preds,y_test, average=None))
Sensitivity or Recall
Recall (Sensitivity) – is the ratio of correctly predicted positive observations to all observations in actual class.
from sklearn.linear_model import LogisticRegression from sklearn import datasets from sklearn.cross_validation import train_test_split from sklearn.metrics import recall_score data = datasets.load_iris() X = data['data'] y = data['target'] X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.3, random_state=0) model = LogisticRegression() model.fit(X_train,y_train) preds = model.predict(X_test) print(recall_score(preds,y_test, average=None))
F1 Score is the weighted average of Precision and Recall. Therefore, this score takes both false positives and false negatives into account. Intuitively it is not as easy to understand as accuracy, but F1 is usually more useful than accuracy, especially if you have an uneven class distribution.
from sklearn.linear_model import LogisticRegression from sklearn import datasets from sklearn.cross_validation import train_test_split from sklearn.metrics import f1_score data = datasets.load_iris() X = data['data'] y = data['target'] X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.3, random_state=0) model = LogisticRegression() model.fit(X_train,y_train) preds = model.predict(X_test) print(f1_score(preds,y_test, average=None))
It is a matrix of dimension N x N, where N is the number of classes being predicted. The confusion matrix is a presentation of the accuracy of a model with two or more classes. The table presents predictions on the x-axis and accuracy outcomes on the y-axis.
There are four possible options:
- True positives (TP), which are the instances that are positives and are classified as positives.
- False positives (FP), which are the instances that are negatives and are classified as positives.
- False negatives (FN), which are the instances that are positives and are classified as negatives.
- True negatives (TN), which are the instances that are negatives and are classified as negatives.
Below is an example code to compute confusion matrix, using ScikitLearn.
from sklearn.linear_model import LogisticRegression from sklearn import datasets from sklearn.cross_validation import train_test_split from sklearn.metrics import confusion_matrix data = datasets.load_iris() X = data['data'] y = data['target'] X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.3, random_state=0) model = LogisticRegression() model.fit(X_train,y_train) preds = model.predict(X_test) print(confusion_matrix(preds,y_test))
Gain and Lift Chart.
Many times the measure of the overall effectiveness of the model is not enough. It may be important to know if the model does increasingly better with more data. Is there any marginal improvement in the model’s predictive ability if for example, we consider 70% of the data versus only 50%?
The lift charts represent the actual lift for each percentage of the population, which is defined as the ratio between the percentage of positive instances found by using the model and without using it.
These types of charts are common in business analytics of Direct Marketing where the problem is to identify if a particular prospect was worth calling.
This non-parametric statistical test is used to compare two distributions, to assess how close they are to each other. In this context, one of the distributions is the theoretical distribution that the observations are supposed to follow (usually a continuous distribution with one or two parameters, such as Gaussian), while the other distribution is the actual, empirical, parameter-free, discrete distribution computed on the observations.
KS is maximum difference between % cumulative Goods and Bads distribution across score/probability bands. The gains table typically has % cumulative Goods (or Event) and % Cumulative Bads (Or Non-event) across 10/20 score bands. Using gains table, we can find the KS for the model which has been used for creating gains table.
KS is point estimate, meaning it is only one value and indicate the score/probability band where separate between Goods (or Event) and Bads (or Non-event) is maximum.
Area Under the ROC curve (AUC – ROC)
The ROC curve is almost independent of the response rate. The Receiver Operating Characteristic (ROC), or ROC curve, is a graphical plot that illustrates the performance of a binary classifier. The curve is created by plotting the true positive rate (TP) against the false positive rate (FP) at various threshold settings. This is one of the popular metrics used in the industry. The biggest advantage of using ROC curve is that it is independent of the change in
The biggest advantage of ROC curve is that it is independent of the change in the proportion of responders.
An area under ROC Curve (or AUC) is a performance metric for binary classification problems. The AUC represents a model’s ability to discriminate between positive and negative classes. An area of 1.0 represents a model that made all predictions perfectly. An area of 0.5 represents a model as good as random.
The example below provides a demonstration of calculating AUC.
import numpy as np from sklearn.metrics import roc_auc_score y_true = np.array([0, 0, 1, 1]) y_scores = np.array([0.1, 0.4, 0.35, 0.8]) roc_auc_score(y_true, y_scores)
Gini coefficient is used in classification problems. It can be derived from the AUC ROC number.
from sklearn.linear_model import LogisticRegression from sklearn import datasets from sklearn.cross_validation import train_test_split def gini(list_of_values): sorted_list = sorted(list(list_of_values)) height, area = 0, 0 for value in sorted_list: height += value area += height - value / 2. fair_area = height * len(list_of_values) / 2 return (fair_area - area) / fair_area def normalized_gini(y_pred, y): normalized_gini = gini(y_pred)/gini(y) return normalized_gini data = datasets.load_iris() X = data['data'] y = data['target'] X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.3, random_state=0) model = LogisticRegression() model.fit(X_train,y_train) preds = model.predict(X_test) print(normalized_gini(preds,y_test))
Log Loss quantifies the accuracy of a classifier by penalizing false classifications. Minimizing the Log Loss is basically equivalent to maximizing the accuracy of the classifier.
In order to calculate Log Loss, the classifier must assign a probability to each class rather than simply give the most likely class. A perfect classifier would have a Log Loss of precisely zero. Less ideal classifiers have progressively larger values of Log Loss.
Mean Absolute Error
The mean absolute error (MAE) is a quantity used to measure how close forecasts or predictions are to the eventual outcomes.
The Mean Absolute Error (or MAE) is the sum of the absolute differences between predictions and actual values. The measure gives an idea of the magnitude of the error, but no idea of the direction.
The example below demonstrates simple example:
from sklearn.metrics import mean_absolute_error y_true = [3, -0.5, 2, 7] y_pred = [2.5, 0.0, 2, 8] print(mean_absolute_error(y_true, y_pred))
Mean Squared Error
One of the most common measures used to quantify the performance of the model. It is an average of the squares of the difference between the actual observations and those predicted. The squaring of the errors tends to heavily weight statistical outliers, affecting the accuracy of the results.
Below a basic example of calculation using ScikitLearn.
from sklearn.metrics import mean_squared_error y_true = [3, -0.5, 2, 7] y_pred = [2.5, 0.0, 2, 8] print(mean_squared_error(y_true, y_pred))
Root Mean Squared Error (RMSE)
RMSE is the most popular evaluation metric used in regression problems. It follows an assumption that error is unbiased and follow a normal distribution.
RMSE metric is given by:
where N is Total Number of Observations.
The R^2 (or R Squared) metric provides an indication of the goodness of fit of a set of predictions to the actual values. In statistical literature, this measure is called the coefficient of determination. This is a value between 0 and 1 for no-fit and perfect fit respectively.
Below a basic example of calculation using ScikitLearn.
from sklearn.metrics import r2_score y_true = [3, -0.5, 2, 7] y_pred = [2.5, 0.0, 2, 8] print(r2_score(y_true, y_pred))
Was the above useful? Please share with others on social media.
Recommended reading list:
|Hands-On Machine Learning with Scikit-Learn and TensorFlow: Concepts, Tools, and Techniques to Build Intelligent Systems
Through a series of recent breakthroughs, deep learning has boosted the entire field of machine learning. Now, even programmers who know close to nothing about this technology can use simple, efficient tools to implement programs capable of learning from data. This practical book shows you how.
By using concrete examples, minimal theory, and two production-ready Python frameworks—scikit-learn and TensorFlow—author Aurélien Géron helps you gain an intuitive understanding of the concepts and tools for building intelligent systems. You’ll learn a range of techniques, starting with simple linear regression and progressing to deep neural networks. With exercises in each chapter to help you apply what you’ve learned, all you need is programming experience to get started.
Explore the machine learning landscape, particularly neural nets
Use scikit-learn to track an example machine-learning project end-to-end
Explore several training models, including support vector machines, decision trees, random forests, and ensemble methods
Use the TensorFlow library to build and train neural nets
Dive into neural net architectures, including convolutional nets, recurrent nets, and deep reinforcement learning
Learn techniques for training and scaling deep neural nets
Apply practical code examples without acquiring excessive machine learning theory or algorithm details
|Data Science from Scratch: First Principles with Python
Data science libraries, frameworks, modules, and toolkits are great for doing data science, but they’re also a good way to dive into the discipline without actually understanding data science. In this book, you’ll learn how many of the most fundamental data science tools and algorithms work by implementing them from scratch.
If you have an aptitude for mathematics and some programming skills, author Joel Grus will help you get comfortable with the math and statistics at the core of data science, and with hacking skills you need to get started as a data scientist. Today’s messy glut of data holds answers to questions no one’s even thought to ask. This book provides you with the know-how to dig those answers out.
Get a crash course in Python
Learn the basics of linear algebra, statistics, and probability—and understand how and when they're used in data science
Collect, explore, clean, munge, and manipulate data
Dive into the fundamentals of machine learning
Implement models such as k-nearest Neighbors, Naive Bayes, linear and logistic regression, decision trees, neural networks, and clustering
Explore recommender systems, natural language processing, network analysis, MapReduce, and databases
|Practical Statistics for Data Scientists: 50 Essential Concepts
Statistical methods are a key part of of data science, yet very few data scientists have any formal statistics training. Courses and books on basic statistics rarely cover the topic from a data science perspective. This practical guide explains how to apply various statistical methods to data science, tells you how to avoid their misuse, and gives you advice on what's important and what's not.
Many data science resources incorporate statistical methods but lack a deeper statistical perspective. If you’re familiar with the R programming language, and have some exposure to statistics, this quick reference bridges the gap in an accessible, readable format.
With this book, you’ll learn:
Why exploratory data analysis is a key preliminary step in data science
How random sampling can reduce bias and yield a higher quality dataset, even with big data
How the principles of experimental design yield definitive answers to questions
How to use regression to estimate outcomes and detect anomalies
Key classification techniques for predicting which categories a record belongs to
Statistical machine learning methods that “learn” from data
Unsupervised learning methods for extracting meaning from unlabeled data
|Doing Data Science: Straight Talk from the Frontline
Now that people are aware that data can make the difference in an election or a business model, data science as an occupation is gaining ground. But how can you get started working in a wide-ranging, interdisciplinary field that’s so clouded in hype? This insightful book, based on Columbia University’s Introduction to Data Science class, tells you what you need to know.
In many of these chapter-long lectures, data scientists from companies such as Google, Microsoft, and eBay share new algorithms, methods, and models by presenting case studies and the code they use. If you’re familiar with linear algebra, probability, and statistics, and have programming experience, this book is an ideal introduction to data science.
Statistical inference, exploratory data analysis, and the data science process
Spam filters, Naive Bayes, and data wrangling
Recommendation engines and causality
Social networks and data journalism
Data engineering, MapReduce, Pregel, and Hadoop
|The Data Science Handbook: Advice and Insights from 25 Amazing Data Scientists
The Data Science Handbook contains interviews with 25 of the world s best data scientists. We sat down with them, had in-depth conversations about their careers, personal stories, perspectives on data science and life advice. In The Data Science Handbook, you will find war stories from DJ Patil, US Chief Data Officer and one of the founders of the field. You ll learn industry veterans such as Kevin Novak and Riley Newman, who head the data science teams at Uber and Airbnb respectively. You ll also read about rising data scientists such as Clare Corthell, who crafted her own open source data science masters program. This book is perfect for aspiring or current data scientists to learn from the best. It s a reference book packed full of strategies, suggestions and recipes to launch and grow your own data science career.
|Introduction to Machine Learning with Python: A Guide for Data Scientists
Machine learning has become an integral part of many commercial applications and research projects, but this field is not exclusive to large companies with extensive research teams. If you use Python, even as a beginner, this book will teach you practical ways to build your own machine learning solutions. With all the data available today, machine learning applications are limited only by your imagination.
You’ll learn the steps necessary to create a successful machine-learning application with Python and the scikit-learn library. Authors Andreas Müller and Sarah Guido focus on the practical aspects of using machine learning algorithms, rather than the math behind them. Familiarity with the NumPy and matplotlib libraries will help you get even more from this book.
With this book, you’ll learn:
Fundamental concepts and applications of machine learning
Advantages and shortcomings of widely used machine learning algorithms
How to represent data processed by machine learning, including which data aspects to focus on
Advanced methods for model evaluation and parameter tuning
The concept of pipelines for chaining models and encapsulating your workflow
Methods for working with text data, including text-specific processing techniques
Suggestions for improving your machine learning and data science skills