Decision-Sufficient Posterior Approximation

Key points

• A target posterior $P$ and loss determine a regret geometry on actions, a baseline approximation $Q0$ determines the forward-Kullback-Leibler information required to induce action changes, and a restricted approximation family $\mathcal{Q}$ determines which such changes are available.1
• Contracting KL divergence over Bayes-action fibers gives exact distances to decision adequacy and decision failure together with the least-informative posterior deformations that reach either side of the decision boundary.1
• In regular finite-dimensional problems, the target and baseline constructions have quadratic local limits: a target regret Hessian $G$ and a baseline information metric $JI$ .1
• Their generalized eigenproblem $Gv = γJIv$ orders local decision directions by regret consequence per unit information cost and induces a tolerance-dependent effective dimension.1

Sources (1)

• [1]Decision-Sufficient Posterior Approximation
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 8, 12:43 AM

  We investigate the consequences of requiring a posterior approximation to preserve a specified downstream decision problem.

  A target posterior $P$ and loss determine a regret geometry on actions, a baseline approximation $Q_0$ determines the forward-Kullback-Leibler information required to induce action changes, and a restricted approximation family $\mathcal{Q}$ determines which such changes are available.

Extractive summary: sentences quoted from the sources.