Sum-product networks: A survey <s> B. Robotics <s> Flying autonomous micro aerial vehicles (MAVs) in indoor environments is still a challenging task, as MAVs are not capable of carrying heavy sensors as Lidar or RGD-B, and GPS signals are not reliable indoors. We investigate a strategy where image classification is used to guide a MAV, one of the main requirements then is to have a classifier that can produce results quickly during operation. The goal here is to explore the performance of Sum-Product Networks and Arithmetic Circuits as image classifiers, because these formalisms lead to deep probabilistic models that are tractable during operation. We have trained and tested our classifiers using the Libra toolkit and real images. We describe our approach and report the result of our experiments in the paper. <s> BIB001 </s> Sum-product networks: A survey <s> B. Robotics <s> We introduce Graph-Structured Sum-Product Networks (GraphSPNs), a probabilistic approach to structured prediction for problems where dependencies between latent variables are expressed in terms of arbitrary, dynamic graphs. While many approaches to structured prediction place strict constraints on the interactions between inferred variables, many real-world problems can be only characterized using complex graph structures of varying size, often contaminated with noise when obtained from real data. Here, we focus on one such problem in the domain of robotics. We demonstrate how GraphSPNs can be used to bolster inference about semantic, conceptual place descriptions using noisy topological relations discovered by a robot exploring large-scale office spaces. Through experiments, we show that GraphSPNs consistently outperform the traditional approach based on undirected graphical models, successfully disambiguating information in global semantic maps built from uncertain, noisy local evidence. We further exploit the probabilistic nature of the model to infer marginal distributions over semantic descriptions of as yet unexplored places and detect spatial environment configurations that are novel and incongruent with the known evidence. <s> BIB002 </s> Sum-product networks: A survey <s> B. Robotics <s> We introduce TopoNets, end-to-end probabilistic deep networks for modeling semantic maps with structure reflecting the topology of large-scale environments. TopoNets build a unified deep network spanning multiple levels of abstraction and spatial scales, from pixels representing geometry of local places to high-level descriptions of semantics of buildings. To this end, TopoNets leverage complex spatial relations expressed in terms of arbitrary, dynamic graphs. We demonstrate how TopoNets can be used to perform end-to-end semantic mapping from partial sensory observations and noisy topological relations discovered by a robot exploring large-scale office spaces. Thanks to their probabilistic nature and generative properties, TopoNets extend the problem of semantic mapping beyond classification. We show that TopoNets successfully perform uncertain reasoning about yet unexplored space and detect novel and incongruent environment configurations unknown to the robot. Our implementation of TopoNets achieves real-time, tractable and exact inference, which makes these new deep models a promising, practical solution to mobile robot spatial understanding at scale. <s> BIB003
Sguerra and Cozman BIB001 used SPNs for aerial robots navigation. Micro aerial vehicles need a set of sensors that must comply with two criteria: light weight and realtime response. Optical recognition with cameras satisfies the former while fast inference with SPNs ensures the latter, as they were able to classify-in real time-what the camera sees into pilot commands, such as "turn right", and obtaining 75% of accuracy with just 66 images. Pronobis et al.  designed a probabilistic representation of spatial knowledge called "deep spatial affordance hierarchy" (DASH), which encodes several levels of abstractions using a deep model of spatial concepts. It models knowledge gaps and affordances by a deep generative spatial model (DGSM) which uses SPNs for inference across different levels of abstractions. SPNs fit naturally with DGSM because latent variables of the former are internal descriptors in the latter. The authors tested it in a robot equipped with a laser-range sensor. Zheng et al. BIB002 designed graph-structured SPNs (GraphSPNs) for structured prediction. Their algorithm learns template SPNs and makes a mixture over them (a template distribution), which can be applied to graphs of varying size re-using the same templates. The authors applied them to model large-scale global semantic maps of office environments with a exploring robot, obtaining better results than with the classical approach based on undirected graphical models (Markov networks). The authors joined both models into an end-to-end deep model for semantic mapping in large-scale environments with multiple levels of abstraction, called TopoNets BIB003 . These can perform inference about unknown spatial information, are useful for novelty detection, and achieve real-time performance.