"Generating Synthetic Data: A Practical Guide Using Bayesian Sampling and Univariate Distributions"

Introduction to Synthetic Data In recent years, the importance of high-quality data has become evident, driving more accurate conclusions and better-informed decisions. However, real-world data can often be sensitive, expensive, imbalanced, or difficult to collect, especially for rare or edge-case scenarios. This is where synthetic data shines, as it can be generated to mimic the statistical properties of real observations. This article explores two primary techniques for generating synthetic data: Bayesian Sampling and Univariate Distribution Sampling. The Python libraries bnlearn and distfit are used to illustrate practical examples. Key Concepts and Techniques 1. Univariate Distribution Sampling This method involves fitting a model to each individual continuous variable and generating synthetic values based on the fitted distribution, assuming the variables are independent. Example: Torque Measurements Using the predictive maintenance dataset, which includes 10,000 sensor data points, we start by analyzing the Torque measurements. These measurements typically range between 20 and 50 Nm, with high values indicating potential mechanical strain. The distfit library is used to find the best-suited distribution for the Torque data, resulting in a Loggamma distribution. We then generate 200 synthetic Torque measurements, which are validated against the real data's distribution. Step-by-Step Process: Data Inspection: Visualize the real data to understand its range and characteristics. Distribution Fitting: Use distfit to scan and fit various distributions to the data. Parameter Estimation: Identify the best fit and its parameters. Data Generation: Generate synthetic data using the estimated parameters. 2. Synthesizing Data from Expert Knowledge When no dataset exists, experts' knowledge can be translated into a statistical model using Probability Density Functions (PDFs). Example: Operational Activities Intensity Experts describe the intensity of machinery operations, noting that: - Peak intensity is around 10 AM. - Some operations occur early in the morning. - A small peak happens around 1-2 PM, followed by a gradual decline until 6 PM. To model this, we use a mixture of distributions: - Morning: Normal distribution with a mean of 10 AM and a standard deviation of 1. - Afternoon: Generalized Gamma distribution, tuned to match the described afternoon pattern. The synthetic data is generated by combining these distributions, ensuring the samples are shuffled to avoid bias. Categorical Data Generation 1. Mimicking an Existing Categorical Dataset For categorical data, the approach involves learning the structure and parameters from an existing dataset using Bayesian methods. Example: Predictive Maintenance Dataset We use the same dataset to focus on categorical variables related to machine failures. The steps are: 1. Data Cleaning: Select relevant variables and remove unique identifiers. 2. Structure Learning: Use bnlearn to learn the causal relationships between variables. 3. Parameter Learning: Estimate conditional probabilities for each variable. 4. Data Generation: Generate synthetic categorical data using the modeled Bayesian Network. The resulting Directed Acyclic Graph (DAG) shows complex dependencies, such as the influence of power failure (PWF) and overstrain failure (OSF) on machine failure. 2. Generating Data from Expert Knowledge When no dataset is available, experts' knowledge can be used to define the DAG and Conditional Probability Distributions (CPDs). Example: Predictive Maintenance System Experts provide insights on how machine failures occur: - High process temperature or high torque increases the risk of failures. - High torque or tool wear leads to overstrain failures (OSF). - Process temperature is influenced by air temperature. - Tool wear and air temperature are independent. The steps involve: 1. Defining Relationships: Manually create a DAG based on expert insights. 2. Setting CPDs: Define the CPDs for each node, reflecting the expert's knowledge. 3. Connecting DAG and CPDs: Update the DAG with the CPDs. 4. Data Generation: Use the bn.sampling() function to generate synthetic data. Importance and Limitations of Synthetic Data Synthetic data is crucial in various fields, including healthcare, finance, cybersecurity, and autonomous systems, especially when real data is limited. However, it has limitations: - Complexity: Real-world phenomena can be highly complex, and synthetic data might not capture all nuances. - Biases: Poor assumptions, overly simplified models, or incorrectly estimated parameters can introduce biases. - Validation: Rigorous validation is necessary to ensure generated data aligns with domain expectations. Industry Insights and Company Profiles bnlearn: This Python library is designed to address challenges in Bayesian network analysis, offering efficient structure and parameter learning. It is particularly useful for modeling dependencies between variables. distfit: This library automates the process of fitting theoretical distributions to empirical data, ranking them based on goodness-of-fit metrics. It is invaluable for estimating the best distribution without manual trial-and-error. Both libraries significantly enhance the ability to generate high-quality synthetic data, making them indispensable tools in data-driven research and development. Conclusion Synthetic data offers a robust solution when real data is limited or sensitive. By leveraging probabilistic models, we can generate synthetic data that closely mimics real-world observations. Univariate distribution sampling is effective for independent continuous variables, while Bayesian sampling is ideal for dependent categorical variables. Despite its advantages, synthetic data generation must be approached with caution to avoid introducing biases and to ensure alignment with domain knowledge. The use of libraries like bnlearn and distfit streamlines the process and enhances the accuracy of synthetic data, opening new avenues for testing, modeling, and decision-making. Stay informed and innovative with synthetic data. Cheers!