Multivariate Bayesian Inversion for Classification and Regression
Soch, J.; Allefeld, C.
Show abstract
We propose the statistical modelling approach to supervised learning (i.e. predicting labels from features) as an alternative to algorithmic machine learning (ML). The approach is demonstrated by employing a multivariate general linear model (MGLM) describing the effects of labels on features, possibly accounting for covariates of no interest, in combination with prior distributions on the model parameters. ML "training" is translated into estimating the MGLM parameters via Bayesian inference and ML "testing" or application is translated into Bayesian model comparison - a reciprocal relationship we refer to as multivariate Bayesian inversion (MBI). We devise MBI algorithms for the standard cases of supervised learning, discrete classification and continuous regression, derive novel classification rules and regression predictions, and use practical examples (simulated and real data) to illustrate the benefits of the statistical modelling approach: interpretability, incorporation of prior knowledge, and probabilistic predictions. We close by discussing further advantages, disadvantages and the future potential of MBI.
Matching journals
The top 6 journals account for 50% of the predicted probability mass.
Similar papers in this journal
- Parsimonious EBM: generalising the event-based model of disease progression for simultaneous events 95%
- Post-hoc modification of linear models: combining machine learning with domain information to make solid inferences from noisy data 95%
- Valid and powerful group statistics for decoding accuracy: Information Prevalence Inference using the i-th order statistic (i-test) 95%
Similar papers in this journal
- The winner's curse under dependence: repairing empirical Bayes using convoluted densities 97%
- Tree-informed Bayesian multi-source domain adaptation: cross-population probabilistic cause-of-death assignment using verbal autopsy 97%
- Survival Analysis on Rare Events Using Group-Regularized Multi-Response Cox Regression 95%
Similar papers in this journal
Similar papers in this journal
"Similar papers" are the closest papers from that journal in the model's embedding space. They show what the match is built on, but the ranking comes mostly from a classifier over the whole training set, not from these examples alone.