In this work we address the problem of how to use time series data to choose from a finite set of candidate discrete state spaces, where these spaces are constructed by a domain expert. We formalize the notion of model selection consistency in the proposed setup. We then discuss the difference between our proposed framework and the classical Maximum Likelihood (ML) framework, and give an example where ML fails. Afterwards, we suggest alternative selection criteria and show them to be weakly consistent. Finally, we test the performance of the suggested criteria on both simulated and real world data.

Object manipulation in cluttered scenes is a difficult and important problem in robotics. To efficiently manipulate objects, it is crucial to understand their surroundings, especially in cases where multiple objects are stacked one on top of the other, preventing effective grasping. We here present DUQIM-Net, a decision-making approach for object manipulation in a setting of stacked objects. In DUQIM-Net, the hierarchical stacking relationship is assessed using Adj-Net, a model that leverages existing Transformer Encoder-Decoder object detectors by adding an adjacency head. The output of this head probabilistically infers the underlying hierarchical structure of the objects in the scene. We utilize the properties of the adjacency matrix in DUQIM-Net to perform decision making and assist with object-grasping tasks. Our experimental results show that Adj-Net surpasses the state-of-the-art in object-relationship inference on the Visual Manipulation Relationship Dataset (VMRD), and that DUQIM-Net outperforms comparable approaches in bin clearing tasks.