Forecasting Uncertainty Ranges in Any Linear Regression Analysis
In the realm of machine learning, it's essential to handle situations where assumptions are violated. One such assumption is exchangeability, and when it's not met, methods like Conformal Prediction (CP) can help.
CP is a user-friendly paradigm for creating statistically rigorous uncertainty sets or intervals for the predictions of models. In Julia, it's possible to leverage CP for supervised regression tasks using the packages Flux and MLJ.
The process typically involves training a regression model using Flux or MLJ, followed by the application of CP techniques to calibrate and transform point predictions into valid confidence/prediction intervals around the predicted output. This method, being distribution-free and model-agnostic, complements MLJ and Flux models by providing uncertainty estimates.
For regression tasks, CP takes model residuals on a calibration set to define a nonparametric quantile threshold, which determines the size of the prediction interval for new inputs. This ensures the intervals cover the true response value with a controlled error rate.
The procedure usually involves training a regression model, using a held-out calibration dataset to compute residuals between predictions and true values, computing quantile thresholds from residuals to form conformal prediction intervals, and using these intervals on test predictions to produce reliable predictive sets.
Popular open-source Julia packages like ConformalPrediction.jl and MLJ.jl are used to implement CP for regression by leveraging the residual-based quantile calibration step after model fitting. Flux handles model training, MLJ for workflow and prediction, and CP code modules perform the uncertainty quantification.
By default, CP creates an Inductive Conformal Regressor when called on a model. The marginal coverage guarantee holds under the assumption that training and test data are exchangeable. However, increasing the domain of the input can violate this assumption, causing the marginal coverage property not to hold.
Despite not providing a direct Julia code implementation combining CP with Flux and MLJ, search results confirm that CP in supervised regression delivers finite sample coverage for any ML predictors, including neural networks (Flux) and classical ML models available via MLJ.
In summary, CP offers a principled way to augment supervised regression models trained with Flux or MLJ in Julia by providing calibrated prediction intervals with statistical guarantees, enhancing interpretability and reliability of model outputs without distributional assumptions.
For more information on Conformal Prediction, resources include a Gentle Introduction to Conformal Prediction, a comprehensive Python library for conformal prediction, and a repository of resources on Conformal Prediction. The post, available as a fully interactive notebook, serves as a starting point for learning about CP in Julia for supervised learning tasks, including regression problems.
Technology in data-and-cloud-computing, such as Conformal Prediction (CP), plays a crucial role in handling uncertainty in machine learning, especially when assumptions like exchangeability are violated. CP, when implemented with packages like Flux and MLJ in Julia, offers a user-friendly way to create statistically rigorous prediction intervals for models, providing an enhancement to their interpretability and reliability in supervised regression tasks.
