A/B Test Winner Selection Using Histogram-Based Bayesian Inference
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Solution Overview
Problem
Existing A/B testing systems limit the number of metrics that can be used to determine a winning variation, often relying on manually characterized subsets or user input, which can lead to suboptimal message optimization and difficulty in modeling non-binary metrics like revenue, especially when probabilistic modeling is required.
Innovation Solution
A computer-implemented method using historical data to create a histogram-based Dirichlet distribution, updating it with new data via conjugate prior formulae, and inferring central tendencies to determine a winning arm of A/B testing without user intervention, allowing for arbitrary numerical metrics.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of operation
If A/B testing systems limit the number of metrics to manually characterized subsets or require user input, then the system complexity is reduced and ease of operation is improved, but the ability to optimize messages for important metrics is limited and measurement precision deteriorates
Solution Approach 1:
The system performs self-service by automatically inferring metric distributions and determining winning arms without requiring user input or manual characterization. The Bayesian inference engine autonomously processes historical data, creates distributions, and identifies winners based on arbitrary numerical metrics, eliminating the need for users to provide cognitive load-intensive inputs while maintaining high measurement precision.
Solution Approach 2:
The system changes parameters by transforming arbitrary numerical metrics into standardized probability distributions through Bayesian inference. By converting any metric into a distribution that can be sampled and compared, the system maintains measurement precision across diverse metrics without requiring manual characterization or user input for each metric type.
2Adaptability or versatility
If A/B testing systems require user input for expected conversion rates and minimum detectable sample size, then the system can be configured for specific needs, but users carry large cognitive load and must answer questions they may not be able to answer
Solution Approach 1:
The system eliminates cognitive load by performing self-service inference. It automatically determines the necessary parameters for testing by analyzing historical data and inferring metric distributions, rather than requiring users to provide expected conversion rates or sample size calculations. The system adapts to any metric type autonomously through Bayesian inference.
Solution Approach 2:
The system performs preliminary action by pre-processing historical data to create distributions and infer metrics before the actual A/B testing begins. This preliminary inference of metric characteristics and required sample sizes eliminates the need for users to answer complex setup questions, as the system has already characterized the testing parameters based on historical patterns.
3Device complexity
If A/B testing systems use traditional probabilistic modeling for single metrics, then the model can be simplified, but non-binary metrics like revenue are especially difficult to model and handling any metric requires complex flexible models
Solution Approach 1:
The system achieves universality by creating a single Bayesian inference framework that handles any arbitrary numerical metric uniformly. Through histogram-based distribution creation and sampling, the same mechanism works for binary metrics like conversion rates and non-binary metrics like revenue, eliminating the need for different models for different metric types while maintaining simplicity.
Solution Approach 2:
The system transforms any arbitrary numerical metric into a probability distribution with specific parameters (mean, variance, skewness) that can be sampled. By changing the representation of metrics from raw values to distribution parameters, the system simplifies the modeling process while maintaining versatility across metric types, as all metrics are treated through the same distribution-based framework.
4Productivity
If A/B testing systems use histogram-based Bayesian inference with fast operations, then computational speed and accuracy are improved, but the system requires sophisticated algorithms and historical data processing
Solution Approach 1:
The system performs preliminary computation by pre-processing historical data into histograms with bins and weights before the actual A/B testing. This pre-computation creates ready-to-use distributions that can be quickly updated during testing, significantly improving computational speed during the experiment while the complexity is contained in the offline historical data processing rather than online operations.
Solution Approach 2:
The system segments the complex algorithm into distinct modular components: historical data processing into histograms, distribution creation from histogram weights, Bayesian updating with new data, and sampling for inference. This segmentation allows each component to be optimized independently and improves overall computational efficiency by avoiding the need to recompute everything from scratch during each testing iteration.
Data Source
AI summary
Apparatuses, methods, and systems for determining winning arms of electronic testing. One method includes obtaining historical data related to the testing, creating a histogram based on the historical data, the histogram including bins and weights, creating a distribution by computing parameters of the distribution from the weights of the histogram, executing the testing, receiving new data collected based on the execution of the test, allocating the new data into same bins as the bins of the histogram of the historical data yielding a new data bin count, computing a posterior distribution comprising updating the distribution using the same bins and the new data bin counts and the parameters of the distribution, inferring corresponding statistics of samplings of a metric distribution, constructing an overall distribution for each arms of the test, and determining a winning arm of the testing.