Down the Rabbit Hole of Event Prediction: A Guide to Time-Related Event Analysis and Beyond
Understanding churn, purchase, time series, failure, and survival analysis
In data science, event prediction refers to the task of forecasting the likelihood of a specific event occurring in the future. There are many different types of events that can be predicted, such as churn (customer loss), purchase, time series, and failure. Survival analysis is a statistical method used to analyze data on the time it takes for an event of interest to occur. In this article, we will go down the rabbit hole and explore these different types of event prediction, understanding how they are similar and how they are used in practice.
We will cover the following:
· Comparing Classic Machine Learning to Time-Related Data
· Types of Event Prediction
· Time series
· Churn Prediction
∘ More Resources
· Purchase Prediction
∘ More Resources
· Survival Analysis
∘ Important Concepts in Survival Analysis
∘ Survival Analysis Techniques
∘ More Resources
· Similarities Between Types of Event Prediction
· Summary
Comparing Classic Machine Learning to Time-Related Data
In classical supervised machine learning, you will usually have a feature matrix and a target vector, in other words- labeled data.
When dealing with event prediction, the data is time-related, and, if placed on a physical timeline (t), will look something like that:
Types of Event Prediction
Time series
Time series prediction involves predicting future values in a time-dependent series. This can be useful for forecasting demand for a product or service or predicting financial market trends. This video and this complete guide are good places to cover the basics of time-series analysis.
Purchase Prediction
Purchase prediction involves predicting whether a customer will make a purchase in the future. This can be useful for businesses in order to target marketing campaigns or to understand customer behavior.
More Purchase Prediction Resources
- This a good article for leading thoughts about conversion as a result of promotions.
- This great article dealing with purchase prediction addresses the history of the customer as features for the predicting model as well as presenting feature importance analysis for this prediction.
- Predicting Next Purchase Day
Churn Prediction
Churn prediction predicts whether a customer will stop doing business with a company. This is a common problem in industries such as telecommunications, where customers may switch to a different service provider.
In the WTTE-RNN article, the importance of defining the problem in order to find an effective solution is discussed. The Weibull Time to the Next Event Recurrent Neural Network (WTTE-RNN) is introduced as a tool for predicting the time to the next event, which could be something like churn, an engine failure, a click, or a purchase.
The author discusses the concept of “censored data,” which refers to data in which some events end in the future. In these cases, it is necessary to assume that the endpoint of these future events is the last day of the observed past.
Censored data refers to data that is only partially observed or reported. In survival analysis, censored data is often encountered when the event of interest has not yet occurred for some subjects or when the subjects had dropped out of the study before the event occurred. There are different types of censorship in survival analysis, including right-censorship, left-censorship, and interval-censorship. Censored data can present challenges for survival analysis, as it can be difficult to make inferences about the underlying population based on incomplete data. However, some statistical methods and techniques can be used to analyze censored data in survival analysis.
The author presents several models for solving this problem, but notes that they are not sufficient. One of these models is the sliding box model, which has the advantage of simplicity and flexibility, but can produce uninformative predictions and has difficulty excluding events that have not yet finished.
Another approach mentioned is learning to rank, or machine-learned ranking (MLR), which involves predicting who is more likely to churn or make a purchase. The author emphasizes the importance of minimizing the probability of resurrection (the return of a churned customer), maximizing the probability of detection, and maximizing the interpretability of the churn definition.
The author suggests using a recurrent neural network (RNN) as the machine learning algorithm, as it can handle recurrent events, time-varying covariates, temporal patterns, sequences of varying lengths, and censored data. The Weibull distribution is also mentioned as a flexible and versatile choice for the objective function. The article concludes by noting that deep learning can eliminate the need for feature engineering as long as the data is organized according to timestamps of events and grouped by the desired prediction (such as cycles of events).
More Churn Prediction Resources
- This WTTE-RNN article which, without a doubt, a gem.
Based on the author’s thesis.
The code is available here.
Other implementations are available here.
And here. - Sparkify (MIT) churn prediction, or the power of time-series data
- Exploration mini-dataset Sparkify
Survival Analysis
Survival analysis is a statistical method used to analyze data on the time it takes for an event of interest to occur. This event could be something like death, disease, or bankruptcy. Survival analysis is commonly used in fields such as medicine, engineering, and economics. This video and this guide are good places to cover the basics of Survival Analysis.
Failure prediction involves predicting when a system or component is likely to fail. This is important for maintenance and repair planning, as well as for ensuring the reliability and safety of systems. Survival analysis can be used as a tool for failure prediction by analyzing data on the time it takes for a failure event to occur. By understanding the factors that influence the likelihood and timing of failures, organizations can take proactive steps to prevent or mitigate them.
Important Concepts in Survival Analysis
In survival analysis, we often use the following four functions to describe the data:
- Survival function: This function represents the probability that an event has not occurred by a certain time.
- Hazard function: This function represents the probability of an event occurring at a given time, given that it has not occurred yet.
- Cumulative hazard function: This function represents the total risk of an event occurring by a certain time.
- Hazard ratio: This ratio compares the hazard function of one group to another. A hazard ratio of 1 indicates that the two groups have the same hazard, while a ratio greater than 1 indicates that the first group has a higher hazard. A ratio less than 1 indicates that the first group has a lower hazard.
Survival Analysis Techniques
One of the most common tools in survival analysis is the Kaplan-Meier curve, which is a graphical representation of the probability of an event occurring over time. The curve is created by plotting the number of failures (on the y-axis) against the number of units at risk (on the x-axis).
We can use the log-rank test to compare survival curves between different groups. This test determines whether the survival curves are significantly different from each other based on the data.
Another popular method in survival analysis is Cox regression, which is a type of regression model that allows us to estimate the effect of multiple variables on the hazard rate (discussed above).
We can also use parametric survival models, such as the Weibull and exponential models, to fit a curve to the data and make predictions about the likelihood of an event occurring.
More Survival Analysis Resources
- This video and this guide are good places to cover the basics of Survival Analysis.
- Fast Training of Support Vector Machines for Survival Analysis
- pycox is a python package for survival analysis and time-to-event prediction with PyTorch (BSD-2)
- Deep Learning for Survival Analysis using pycox
- How to Implement Deep Neural Networks for Time-to-Event Analyses. Comparing DeepHit and DeepSurv models. Using pycox
Similarities Between Types of Event Prediction
One way in which these types of event prediction are similar is that they all involve forecasting the likelihood of an event occurring in the future. In each case, the goal is to use data and statistical models to make informed predictions about the event of interest.
Another way in which these types of event prediction are similar is that they all involve analyzing data over time. Churn prediction involves looking at customer behavior over time to predict whether a customer is likely to stop doing business with a company. Purchase prediction involves analyzing customer behavior over time to predict whether a customer is likely to make a purchase. Time series prediction involves forecasting future values in a time-dependent series, such as demand for a product or financial market trends. Survival analysis involves analyzing the time it takes for an event of interest to occur.
Summary
Event prediction is a crucial task in data science, with applications in various industries such as telecommunications, retail, and healthcare. Techniques such as Kaplan-Meier curves and log-rank tests allow us to visualize and compare the likelihood of events occurring over time, while Cox regression and parametric models enable us to understand the impact of different variables on the hazard rate. This article provided a comprehensive guide for data scientists seeking to understand and effectively use event prediction in their work, helping them to make informed predictions and assist organizations in making better decisions.
