Date Engineering, Statistics, AI/ML, Operations Research, Visualization
the far side of the Moon This report presents a structured taxonomy of machine learning methodologies specialized for Within-Wafer (WIW) variation prediction in semiconductor manufacturing. General-purpose ML approaches often fail to exploit the unique spatial structure of wafer data: circular geometry, process-induced radial symmetry, and strong inter-site correlations. The seven categories below organize WIW-specific methods…
The Core Principle of PIML: Loss Function $$ { \mathcal{L}_{total} = \mathcal{L}_{data} + \lambda \cdot \mathcal{L}_{phys} } $$ Experience(Observations) + Reason(First Principles) Numeric data-driven AI/ML models are powerful when abundant training data is available, but they suffer from fundamental limitations: poor performance with scarce data, physically implausible predictions, and rapid degradation outside the training distribution…
A trained regressor that performs well on historical data often drifts in production for two distinct reasons: Retraining is the principled fix for both, but it is expensive and sometimes impossible (no fresh labels, frozen model in a regulated pipeline). A cheap, production-friendly alternative is a two-term post-hoc correction: 1. Long-term bias (residual_bias) Definition, computed…
1. What is One-Hot Encoding? One-hot encoding is the most fundamental technique for converting categorical variables into numerical vectors that machine learning models can process. Given N unique categories, each category is represented as an N-dimensional vector with a 1 at the position corresponding to that category and 0 elsewhere. Example: [‘Seoul’, ‘Busan’, ‘Daegu’] →…
Aerial view of the Great Blue Hole in Belize In the model training process, the responsiveness (sensitivity) of $Y$ to variations in $X$ is a core factor that determines the balance between generalization performance and explainability ($R^2$). $$R^2 = 1 – \frac{SS{res}}{SS_{tot}} = 1- \frac{\sum_{i=1}^{n}{(y_{i} – \hat{y}_{i})^2}}{\sum_{i=1}^{n}{(y_{i} – \bar{y})^2}}$$ Where: 1. Root Causes of Sensitivity…
1. Analysis of Small Positive Ranges (0 to 0.2) While a target range of 0 to 0.2 is mathematically valid, it presents several practical challenges in model training and optimization. 1.1 Training Speed and Convergence Issues 1.2 Loss Function Sensitivity 1.3 Compatibility with Activation Functions 2. Analysis of Negative Ranges (-1 to 0) Targeting a…
Delicate dandelion seed heads Random Seed Sensitivity in Feature Selection 1. Problem Statement Feature selection results can vary significantly depending on the random seed used during model training, data splitting, or stochastic optimization. This instability undermines reproducibility and trustworthiness, particularly in high-stakes domains such as healthcare and genomics where consistent feature identification is critical for…
Introduction to Center Alignment Index (CAI) as a Regression Metric 1. Mathematical Definition and Components The Center Alignment Index (CAI) is a bounded metric designed to quantify how closely the central tendency of paired observations aligns with the 1:1 identity line (y = x). In many scientific and engineering domains, comparing two measurement systems or…
Introduction to Lin’s Concordance Correlation Coefficient (CCC) In the fields of Artificial Intelligence (AI) and Machine Learning (ML), evaluating model performance typically revolves around accuracy, precision, or error metrics. However, when the goal is to assess agreement between two continuous variables—specifically, how well a model’s predicted values ($Y$) match the gold-standard observed values ($X$)—standard correlation…
1. Executive Summary The Coefficient of Determination, denoted as $R^2$, is one of the most widely used metrics for assessing the goodness-of-fit in linear regression models. However, its interpretation is often fraught with misunderstanding, particularly regarding how it fluctuates not just with the “correctness” of a model, but with the underlying distribution of the data….
1. Executive Summary In advanced engineering domains—such as semiconductor manufacturing, virtual metrology, and multi-sensor time-series analysis—the validation of predictive models requires more than a single performance score. We must distinguish between how well a model tracks a trend (Precision) versus how close the prediction is to the physical truth (Accuracy). This report establishes a rigorous…
Categorical Inference Bias in AI/ML: Stage-by-Stage Cause, Countermeasure, and Recommendation When an AI/ML model yields systematically different inference results for certain categories—for example, a facial recognition system that misidentifies people with darker skin tones at a higher rate, or a hiring algorithm that consistently deprioritizes female applicants—the root cause almost never originates from a single…
