Correcting Predictions for Approximate Bayesian Inference

arXiv.org Machine Learning

Bayesian models quantify uncertainty and facilitate optimal decision-making in downstream applications. For most models, however, practitioners are forced to use approximate inference techniques that lead to sub-optimal decisions due to incorrect posterior predictive distributions. We present a novel approach that corrects for inaccuracies in posterior inference by altering the decision-making process. We train a separate model to make optimal decisions under the approximate posterior, combining interpretable Bayesian modeling with optimization of direct predictive accuracy in a principled fashion. The solution is generally applicable as a plug-in module for predictive decision-making for arbitrary probabilistic programs, irrespective of the posterior inference strategy. We demonstrate the approach empirically in several problems, confirming its potential.


An Overview of Some Recent Developments in Bayesian Problem-Solving Techniques

AI Magazine

The last few years have seen a surge in interest in the use of techniques from Bayesian decision theory to address problems in AI. Decision theory provides a normative framework for representing and reasoning about decision problems under uncertainty. Within the context of this framework, researchers in uncertainty in the AI community have been developing computational techniques for building rational agents and representations suited to engineering their knowledge bases. The articles cover the topics of inference in Bayesian networks, decision-theoretic planning, and qualitative decision theory. Here, I provide a brief introduction to Bayesian networks and then cover applications of Bayesian problem-solving techniques, knowledge-based model construction and structured representations, and the learning of graphic probability models.


An Overview of Some Recent Developments in Bayesian Problem-Solving Techniques

AI Magazine

The last few years have seen a surge in interest in the use of techniques from Bayesian decision theory to address problems in AI. Decision theory provides a normative framework for representing and reasoning about decision problems under uncertainty. Within the context of this framework, researchers in uncertainty in the AI community have been developing computational techniques for building rational agents and representations suited to engineering their knowledge bases. This special issue reviews recent research in Bayesian problem-solving techniques. The articles cover the topics of inference in Bayesian networks, decision-theoretic planning, and qualitative decision theory. Here, I provide a brief introduction to Bayesian networks and then cover applications of Bayesian problem-solving techniques, knowledge-based model construction and structured representations, and the learning of graphic probability models.


Playing against Nature: causal discovery for decision making under uncertainty

arXiv.org Artificial Intelligence

We consider decision problems under uncertainty where the options available to a decision maker and the resulting outcome are related through a causal mechanism which is unknown to the decision maker. We ask how a decision maker can learn about this causal mechanism through sequential decision making as well as using current causal knowledge inside each round in order to make better choices had she not considered causal knowledge and propose a decision making procedure in which an agent holds \textit{beliefs} about her environment which are used to make a choice and are updated using the observed outcome. As proof of concept, we present an implementation of this causal decision making model and apply it in a simple scenario. We show that the model achieves a performance similar to the classic Q-learning while it also acquires a causal model of the environment.


von Neumann-Morgenstern and Savage Theorems for Causal Decision Making

arXiv.org Artificial Intelligence

Decision making under uncertain conditions has been well studied when uncertainty can only be considered at the associative level of information. The classical Theorems of von Neumann-Morgenstern and Savage provide a formal criterion for rationally making choices using associative information. We provide here a previous result from Pearl and show that it can be considered as a causal version of the von Neumann-Morgenstern Theorem; furthermore, we consider the case when the true causal mechanism that controls the environment is unknown to the decision maker and propose a causal version of the Savage Theorem. As applications, we argue how previous optimal action learning methods for causal environments fit within the Causal Savage Theorem we present thus showing the utility of our result in the justification and design of learning algorithms; furthermore, we define a Causal Nash Equilibria for a strategic game in a causal environment in terms of the preferences induced by our Causal Decision Making Theorem.