CSAIL Digital Archive
http://hdl.handle.net/1721.1/29806
2017-03-11T03:22:26ZThe Tensor Algebra Compiler
http://hdl.handle.net/1721.1/107013
The Tensor Algebra Compiler
Kjolstad, Fredrik; Kamil, Shoaib; Chou, Stephen; Lugato, David; Amarasinghe, Saman
Tensor and linear algebra is pervasive in data analytics and the physical sciences. Often the tensors, matrices or even vectors are sparse. Computing expressions involving a mix of sparse and dense tensors, matrices and vectors requires writing kernels for every operation and combination of formats of interest. The number of possibilities is infinite, which makes it impossible to write library code for all. This problem cries out for a compiler approach. This paper presents a new technique that compiles compound tensor algebra expressions combined with descriptions of tensor formats into efficient loops. The technique is evaluated in a prototype compiler called taco, demonstrating competitive performance to best-in-class hand-written codes for tensor and matrix operations.
2017-02-17T00:00:00ZCollaborative Diagnosis of Over-Subscribed Temporal Plans
http://hdl.handle.net/1721.1/106886
Collaborative Diagnosis of Over-Subscribed Temporal Plans
Yu, Peng
Over-subscription, that is, being assigned too many tasks or requirements that are too demanding, is commonly encountered in temporal planning problems. As human beings, we often want to do more than we can, ask for things that may not be available, while underestimating how long it takes to perform each task. It is often difficult for us to detect the causes of failure in such situations and then find resolutions that are effective. We can greatly benefit from tools that assist us by looking out for these plan failures, by identifying their root causes, and by proposing preferred resolutions to these failures that lead to feasible plans. In recent literature, several approaches have been developed to resolve such over-subscribed problems, which are often framed as over-constrained scheduling, configuration design or optimal planning problems. Most of them take an all-or-nothing approach, in which over-subscription is resolved through suspending constraints or dropping goals. While helpful, in real-world scenarios, we often want to preserve our plan goals as much possible. As human beings, we know that slightly weakening the requirements of a travel plan, or replacing one of its destinations with an alternative one is often sufficient to resolve an over-subscription problem, no matter if the requirement being weakened is the duration of a deep-sea survey being planned for, or the restaurant cuisine for a dinner date. The goal of this thesis is to develop domain independent relaxation algorithms that perform this type of slight weakening of constraints, which we will formalize as continuous relaxation, and to embody them in a computational aid, Uhura, that performs tasks akin to an experienced travel agent or ocean scientists. In over-subscribed situations, Uhura helps us diagnose the causes of failure, suggests alternative plans, and collaborates with us in order to resolve conflicting requirements in the most preferred way. Most importantly, the algorithms underlying Uhura supports the weakening, instead of suspending, of constraints and variable domains in a temporally flexible plan. The contribution of this thesis is two-fold. First, we developed an algorithmic framework, called Best-first Conflict-Directed Relaxation (BCDR), for performing plan relaxation. Second, we use the BCDR framework to perform relaxation for several different families of plan representations involving different types of constraints. These include temporal constraints, chance constraints and variable domain constraints, and we incorporate several specialized conflict detection and resolution algorithms in support of the continuous weakening of them. The key idea behind BCDR's approach to continuous relaxation is to generalize the concepts of discrete conflicts and relaxations, first introduced by the model-based diagnosis community, to hybrid conflicts and relaxations, which denote minimal inconsistencies and minimal relaxations to both discrete and continuous relaxable constraints.
PhD thesis
2016-10-14T00:00:00ZSE-Sync: A Certifiably Correct Algorithm for Synchronization over the Special Euclidean Group
http://hdl.handle.net/1721.1/106885
SE-Sync: A Certifiably Correct Algorithm for Synchronization over the Special Euclidean Group
Rosen, David M.; Carlone, Luca; Bandeira, Afonso S.; Leonard, John J.
Many important geometric estimation problems naturally take the form of synchronization over the special Euclidean group: estimate the values of a set of unknown poses given noisy measurements of a subset of their pairwise relative transforms. Examples of this class include the foundational problems of pose-graph simultaneous localization and mapping (SLAM) (in robotics), camera motion estimation (in computer vision), and sensor network localization (in distributed sensing), among others. This inference problem is typically formulated as a nonconvex maximum-likelihood estimation that is computationally hard to solve in general. Nevertheless, in this paper we present an algorithm that is able to efficiently recover certifiably globally optimal solutions of the special Euclidean synchronization problem in a non-adversarial noise regime. The crux of our approach is the development of a semidefinite relaxation of the maximum-likelihood estimation whose minimizer provides an exact MLE so long as the magnitude of the noise corrupting the available measurements falls below a certain critical threshold; furthermore, whenever exactness obtains, it is possible to verify this fact a posteriori, thereby certifying the optimality of the recovered estimate. We develop a specialized optimization scheme for solving large-scale instances of this semidefinite relaxation by exploiting its low-rank, geometric, and graph-theoretic structure to reduce it to an equivalent optimization problem defined on a low-dimensional Riemannian manifold, and then design a Riemannian truncated-Newton trust-region method to solve this reduction efficiently. Finally, we combine this fast optimization approach with a simple rounding procedure to produce our algorithm, SE-Sync. Experimental evaluation on a variety of simulated and real-world pose-graph SLAM datasets shows that SE-Sync is capable of recovering certifiably globally optimal solutions when the available measurements are corrupted by noise up to an order of magnitude greater than that typically encountered in robotics and computer vision applications, and does so more than an order of magnitude faster than the Gauss-Newton-based approach that forms the basis of current state-of-the-art techniques.
2017-02-05T00:00:00ZPropositional and Activity Monitoring Using Qualitative Spatial Reasoning
http://hdl.handle.net/1721.1/105848
Propositional and Activity Monitoring Using Qualitative Spatial Reasoning
Lane, Spencer Dale
Communication is the key to effective teamwork regardless of whether the team members are humans or machines. Much of the communication that makes human teams so effective is non-verbal; they are able to recognize the actions that the other team members are performing and take their own actions in order to assist. A robotic team member should be able to make the same inferences, observing the state of the environment and inferring what actions are being taken. In this thesis I introduce a novel approach to the combined problem of activity recognition and propositional monitoring. This approach breaks down the problem into smaller sub-tasks. First, the raw sensor input is parsed into simple, easy to understand primitive semantic relationships known as qualitative spatial relations (QSRs). These primitives are then combined to estimate the state of the world in the same language used by most planners, planning domain definition language (PDDL) propositions. Both the primitives and propositions are combined to infer the status of the actions that the human is taking. I describe an algorithm for solving each of these smaller problems and describe the modeling process for a variety of tasks from an abstracted electronic component assembly (ECA) scenario. I implemented this scenario on a robotic testbed and collected data of a human performing the example actions.
SM thesis
2016-12-14T00:00:00Z