More Like this

1. Multiscale Gaussian Process Level Set Estimation

   Shekhar, Subhanshu; Javidi, Tara (April 2019, Proceedings of Machine Learning Research)

   In this paper, the problem of estimating the level set of a black-box function from noisy and expensive evaluation queries is considered. A new algorithm for this problem in the Bayesian framework with a Gaussian Process (GP) prior is proposed. The proposed algorithm employs a hierarchical sequence of partitions to explore different regions of the search space at varying levels of detail depending upon their proximity to the level set boundary. It is shown that this approach results in the algorithm having a low complexity implementation whose computational cost is significantly smaller than the existing algorithms for higher dimensional search space \X. Furthermore, high probability bounds on a measure of discrepancy between the estimated level set and the true level set for the the proposed algorithm are obtained, which are shown to be strictly better than the existing guarantees for a large class of GPs.In the process, a tighter characterization of the information gain of the proposed algorithm is obtained which takes into account the structured nature of the evaluation points. This approach improves upon the existing technique of bounding the information gain with maximum information gain. 

   more » « less
2. Using Deep Learning to Bootstrap Abstractions for Robot Planning

   Shah, Naman; Srivastava, Siddharth (May 2022, Proceedings of the International Conference on Autonomous Agents)

   This paper addresses the problem of learning abstractions that boost robot planning performance while providing strong guarantees of reliability. Although state-of-the-art hierarchical robot planning algorithms allow robots to efficiently compute long-horizon motion plans for achieving user desired tasks, these methods typically rely upon environment-dependent state and action abstractions that need to be hand-designed by experts. We present a new approach for bootstrapping the entire hierarchical planning process. This allows us to compute abstract states and actions for new environments automatically using the critical regions predicted by a deep neural network with an auto-generated robot-specific architecture. We show that the learned abstractions can be used with a novel multi-source bi-directional hierarchical robot planning algorithm that is sound and probabilistically complete. An extensive empirical evaluation on twenty different settings using holonomic and non-holonomic robots shows that (a) our learned abstractions provide the information necessary for efficient multi-source hierarchical planning; and that (b) this approach of learning, abstractions, and planning outperforms state-of-the-art baselines by nearly a factor of ten in terms of planning time on test environments not seen during training. 

   more » « less
3. Using Deep Learning to Bootstrap Abstractions for Hierarchical Robot Planning

   Shah, Naman; Srivastava, Siddharth (May 2022, International Conference on Autonomous Agents and Multiagent Systems)

   Pelachaud, Catherine; Taylor, Matthew E.; Mascardi, Viviana (Ed.)

   This paper addresses the problem of learning abstractions that boost robot planning performance while providing strong guarantees of reliability. Although state-of-the-art hierarchical robot planning algorithms allow robots to efficiently compute long-horizon motion plans for achieving user desired tasks, these methods typically rely upon environment-dependent state and action abstractions that need to be hand-designed by experts. We present a new approach for bootstrapping the entire hierarchical planning process. This allows us to compute abstract states and actions for new environments automatically using the critical regions predicted by a deep neural network with an auto-generated robot-specific architecture. We show that the learned abstractions can be used with a novel multi-source bi-directional hierarchical robot planning algorithm that is sound and probabilistically complete. An extensive empirical evaluation on twenty different settings using holonomic and non-holonomic robots shows that (a) our learned abstractions provide the information necessary for efficient multi-source hierarchical planning; and that (b) this approach of learning, abstractions, and planning outperforms state-of-the-art baselines by nearly a factor of ten in terms of planning time on test environments not seen during training. 

   more » « less
4. The Optimal Sample Complexity of Matrix Completion with Hierarchical Similarity Graphs

   https://doi.org/10.1109/ISIT50566.2022.9834449  

   Elmahdy, Adel; Ahn, Junhyung; Mohajer, Soheil; Suh, Changho (January 2022, 2022 IEEE International Symposium on Information Theory (ISIT))

   We study a matrix completion problem that lever-ages a hierarchical structure of social similarity graphs as side information in the context of recommender systems. We assume that users are categorized into clusters, each of which comprises sub-clusters (or what we call “groups”). We consider a low-rank matrix model for the rating matrix, and a hierarchical stochastic block model that well respects practically-relevant social graphs.Under this setting, we characterize the information-theoretic limit on the number of observed matrix entries (i.e., optimal sample complexity) as a function of the quality of graph side information (to be detailed) by proving sharp upper and lower bounds on the sample complexity. Furthermore, we develop a matrix completion algorithm and empirically demonstrate via extensive experiments that the proposed algorithm achieves the optimal sample complexity. 

   more » « less
5. HERO: A Hierarchical Set Partitioning and Join Framework for Speeding up the Set Intersection Over Graphs

   Yang, B; Zheng, W; Lian, X; Cai, Y; Wang, Sean X (March 2024, Association for Computing Machinery)

   As one of the most primitive operators in graph algorithms, such as the triangle counting, maximal clique enumeration, and subgraph listing, a set intersection operator returns common vertices between any two given sets of vertices in data graphs. It is therefore very important to accelerate the set intersection, which will benefit a bunch of tasks that take it as a built-in block. Existing works on the set intersection usually followed the merge intersection or galloping-search framework, and most optimization research focused on how to leverage the SIMD hardware instructions. In this paper, we propose a novel multi-level set intersection framework, namely hierarchical set partitioning and join (HERO), by using our well-designed set intersection bitmap tree (SIB-tree) index, which is independent of SIMD instructions and completely orthogonal to the merge intersection framework. We recursively decompose the set intersection task into small-sized subtasks and solve each subtask using bitmap and boolean AND operations. To sufficiently achieve the acceleration brought by our proposed intersection approach, we formulate a graph reordering problem, prove its NP-hardness, and then develop a heuristic algorithm to tackle this problem. Extensive experiments on real-world graphs have been conducted to confirm the efficiency and effectiveness of our HERO approach. The speedup over classic merge intersection achieves up to 188x and 176x for triangle counting and maximal clique enumeration, respectively. 

   more » « less