Machine Learning & Deep Learning

1. Statistical Foundations: Regression Done Properly

Regression is still the fastest way to understand a system. A well-built regression model tells you which inputs matter, in which direction, by how much and with what confidence. That is exactly what engineers, analysts and executives need before trusting a more opaque model.

• Linear and multivariate regression as a transparent, defensible baseline.
• Regularized regression (ridge, lasso, elastic net) to handle many correlated inputs and keep models stable.
• Generalized linear models for counts, rates and pass/fail outcomes such as yield or defect occurrence.

2. Establishing the Parameter Set

Most of the value is in choosing the right inputs. We work with your domain experts to define a parameter set that is complete enough to explain the outcome and lean enough to stay stable:

• Input and output classification: separating controllable process inputs from measured outputs (for example KPIV/KPOV in manufacturing) so the model answers the question you can act on.
• Collinearity checks (correlation analysis, variance inflation factors) so overlapping signals do not distort each other.
• Feature selection by regularization, stepwise testing and cross-validation, with every dropped variable documented.
• Designed experiments where historical data cannot separate the effects you care about.

3. Measuring Influence

Once the parameter set is fixed, we quantify how much each input moves the result, and which individual records are pulling the model:

4. Non-Linear Approaches

When residuals show curvature, thresholds or interactions that a linear model cannot capture, we move to non-linear methods and keep the regression baseline as the benchmark they must beat:

• Tree ensembles (random forest, gradient boosting) for interactions and thresholds, with SHAP values to keep each prediction explainable.
• Generalized additive models that capture smooth non-linear effects while staying interpretable input by input.
• Kernel methods such as support vector regression for smaller, high-dimensional datasets.
• Graph features from knowledge graphs (embeddings, centrality, community membership) that add relationship context no flat table contains.

5. Deep Learning

Deep learning earns its place when the signal lives in raw, high-dimensional data:

• Sequence models (1-D convolutional networks, recurrent networks, transformers) for sensor time series and process traces.
• Convolutional networks for images, inspection maps and engineering drawings.
• Language models and embeddings for unstructured text, from clinical notes to news events.
• Graph neural networks for problems where the relationships themselves are the signal.

6. Validation & Deployment

Every model ships with honest validation (hold-out and time-based splits, error analysis against the baseline) and a path to production: versioned, point-in-time training datasets, batch or real-time scoring, drift monitoring and scheduled retraining.