TASK DEFINITION: In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.
PROBLEM: We formalize synthesis of shared control protocols with correctness guarantees for temporal logic specifications. More specifically, we introduce a modeling formalism in which both a human and an autonomy protocol can issue commands to a robot towards performing a certain task. These commands are blended into a joint input to the robot. The autonomy protocol is synthesized using an abstraction of possible human commands accounting for randomness in decisions caused by factors such as fatigue or incomprehensibility of the problem at hand. The synthesis is designed to ensure that the resulting robot behavior satisfies given safety and performance specifications, e.g., in temporal logic. Our solution is based on nonlinear programming and we address the inherent scalability issue by presenting alternative methods. We assess the feasibility and the scalability of the approach by an experimental evaluation.

SOLUTION: Synthesis of Shared Control Protocols with Provable Safety and Performance Guarantees

PROBLEM: We start with an overview of a class of submodular functions called SCMMs (sums of concave composed with non-negative modular functions plus a final arbitrary modular). We then define a new class of submodular functions we call deep submodular functions or DSFs. We show that DSFs are a flexible parametric family of submodular functions that share many of the properties and advantages of deep neural networks (DNNs), including many-layered hierarchical topologies, representation learning, distributed representations, opportunities and strategies for training, and suitability to GPU-based matrix/vector computing. DSFs can be motivated by considering a hierarchy of descriptive concepts over ground elements and where one wishes to allow submodular interaction throughout this hierarchy. In machine learning and data science applications, where there is often either a natural or an automatically learnt hierarchy of concepts over data, DSFs therefore naturally apply. Results in this paper show that DSFs constitute a strictly larger class of submodular functions than SCMMs, thus justifying their mathematical and practical utility. Moreover, we show that, for any integer k > 0, there are k-layer DSFs that cannot be represented by a k-layer DSF for any k < k. This implies that, like DNNs, there is a utility to depth, but unlike DNNs (which can be universally approximated by shallow networks), the family of DSFs strictly increase with depth. Despite this property, however, we show that DSFs, even with arbitrarily large k, do not comprise all submodular functions. We show this using a technique that "backpropagates" certain requirements if it was the case that DSFs comprised all submodular functions. In offering the above results, we also define the notion of an antitone superdifferential of a concave function and show how this relates to submodular functions (in general), DSFs (in particular), negative second-order partial derivatives, continuous submodularity, and concave extensions. To further motivate our analysis, we provide various special case results from matroid theory, comparing DSFs with forms of matroid rank, in particular the laminar matroid. Lastly, we discuss strategies to learn DSFs, and define the classes of deep supermodular functions, deep difference of submodular functions, and deep multivariate submodular functions, and discuss where these can be useful in applications.

SOLUTION: Deep Submodular Functions

PROBLEM: In any knowledge discovery process the value of extracted knowledge is directly related to the quality of the data used. Big Data problems, generated by massive growth in the scale of data observed in recent years, also follow the same dictate. A common problem affecting data quality is the presence of noise, particularly in classification problems, where label noise refers to the incorrect labeling of training instances, and is known to be a very disruptive feature of data. However, in this Big Data era, the massive growth in the scale of the data poses a challenge to traditional proposals created to tackle noise, as they have difficulties coping with such a large amount of data. New algorithms need to be proposed to treat the noise in Big Data problems, providing high quality and clean data, also known as Smart Data. In this paper, two Big Data preprocessing approaches to remove noisy examples are proposed: an homogeneous ensemble and an heterogeneous ensemble filter, with special emphasis in their scalability and performance traits. The obtained results show that these proposals enable the practitioner to efficiently obtain a Smart Dataset from any Big Data classification problem.

SOLUTION:
Enabling Smart Data: Noise filtering in Big Data classification