In partially observable worlds with many agents, nested beliefs are formed when agents simultaneously reason about the unknown state of the world and the beliefs of the other agents. The multi-agent filtering problem is to efficiently represent and update these beliefs through time as the agents act in the world. In this paper, we formally define an infinite sequence of nested beliefs about the state of the world at the current time $t$ and present a filtering algorithm that maintains a finite representation which can be used to generate these beliefs. In some cases, this representation can be updated exactly in constant time; we also present a simple approximation scheme to compact beliefs if they become too complex. In experiments, we demonstrate efficient filtering in a range of multi-agent domains.
Some of our articles are applied and some of our articles are more theoretical. The following article is more theoretical, and requires fairly formal notation to even work through. However, it should be of interest as it touches on some of the fine points of cross-validation that are quite hard to perceive or discuss without the notational framework. We thought about including some "simplifying explanatory diagrams" but so many entities are being introduced and manipulated by the processes we are describing we found equation notation to be in fact cleaner than the diagrams we attempted and rejected.] In each case you are building a pipeline where "y-aware" (or outcome aware) choices and transformations made at each stage affect later stages.
Workflow verification is an important aspect of workflow modeling where the verification task is to ensure that the workflow describes feasible processes. It has been shown that verifying nested workflows with extra precedence, causal, and temporal synchronization constraints is an NP-complete problem and a verification method based on constraint satisfaction has been proposed. This paper theoretically justifies the task-collapsing component of this method and provides examples of easy-to-verify constraints.
We often talk about nested factors in mixed models -- students nested in classes, observations nested within subject. In this webinar, you'll learn the difference between crossed and nested factors. We'll walk through a number of examples of different designs from real studies to pull apart which factors are crossed, which are nested, and which are somewhere in between. Particular focus will be on how you can figure all this out in your own design and how it affects how you can and cannot analyze the data. Karen Grace-Martin helps statistics practitioners gain an intuitive understanding of how statistics is applied to real data in research studies.