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Register a new userA Time and Space Efficient Junction Tree Architecture
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Stephen Pasteris
Publication date
2013
fields
Informatics Engineering
and research's language is
English
Authors
Stephen Pasteris
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The junction tree algorithm is a way of computing marginals of boolean multivariate probability distributions that factorise over sets of random variables. The junction tree algorithm first constructs a tree called a junction tree whos vertices are sets of random variables. The algorithm then performs a generalised version of belief propagation on the junction tree. The Shafer-Shenoy and Hugin architectures are two ways to perform this belief propagation that tradeoff time and space complexities in different ways: Hugin propagation is at least as fast as Shafer-Shenoy propagation and in the cases that we have large vertices of high degree is significantly faster. However, this speed increase comes at the cost of an increased space complexity. This paper first introduces a simple novel architecture, ARCH-1, which has the best of both worlds: the speed of Hugin propagation and the low space requirements of Shafer-Shenoy propagation. A more complicated novel architecture, ARCH-2, is then introduced which has, up to a factor only linear in the maximum cardinality of any vertex, time and space complexities at least as good as ARCH-1 and in the cases that we have large vertices of high degree is significantly faster than ARCH-1.
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Using logical clauses to represent patterns, Tsetlin Machines (TMs) have recently obtained competitive performance in terms of accuracy, memory footprint, energy, and learning speed on several benchmarks. Each TM clause votes for or against a particular class, with classification resolved using a majority vote. While the evaluation of clauses is fast, being based on binary operators, the voting makes it necessary to synchronize the clause evaluation, impeding parallelization. In this paper, we propose a novel scheme for desynchronizing the evaluation of clauses, eliminating the voting bottleneck. In brief, every clause runs in its own thread for massive native parallelism. For each training example, we keep track of the class votes obtained from the clauses in local voting tallies. The local voting tallies allow us to detach the processing of each clause from the rest of the clauses, supporting decentralized learning. This means that the TM most of the time will operate on outdated voting tallies. We evaluated the proposed parallelization across diverse learning tasks and it turns out that our decentralized TM learning algorithm copes well with working on outdated data, resulting in no significant loss in learning accuracy. Furthermore, we show that the proposed approach provides up to 50 times faster learning. Finally, learning time is almost constant for reasonable clause amounts (employing from 20 to 7,000 clauses on a Tesla V100 GPU). For sufficiently large clause numbers, computation time increases approximately proportionally. Our parallel and asynchronous architecture thus allows processing of massive datasets and operating with more clauses for higher accuracy.
We propose a method to incrementally learn an embedding space over the domain of network architectures, to enable the careful selection of architectures for evaluation during compressed architecture search. Given a teacher network, we search for a compressed network architecture by using Bayesian Optimization (BO) with a kernel function defined over our proposed embedding space to select architectures for evaluation. We demonstrate that our search algorithm can significantly outperform various baseline methods, such as random search and reinforcement learning (Ashok et al., 2018). The compressed architectures found by our method are also better than the state-of-the-art manually-designed compact architecture ShuffleNet (Zhang et al., 2018). We also demonstrate that the learned embedding space can be transferred to new settings for architecture search, such as a larger teacher network or a teacher network in a different architecture family, without any training. Code is publicly available here: https://github.com/Friedrich1006/ESNAC .
Scheduling in the presence of uncertainty is an area of interest in artificial intelligence due to the large number of applications. We study the problem of dynamic controllability (DC) of disjunctive temporal networks with uncertainty (DTNU), which seeks a strategy to satisfy all constraints in response to uncontrollable action durations. We introduce a more restricted, stronger form of controllability than DC for DTNUs, time-based dynamic controllability (TDC), and present a tree search approach to determine whether or not a DTNU is TDC. Moreover, we leverage the learning capability of a message passing neural network (MPNN) as a heuristic for tree search guidance. Finally, we conduct experiments for which the tree search shows superior results to state-of-the-art timed-game automata (TGA) based approaches. We observe that using an MPNN for tree search guidance leads to a significant increase in solving performance and scalability to harder DTNU problems.
Cutting-plane methods have enabled remarkable successes in integer programming over the last few decades. State-of-the-art solvers integrate a myriad of cutting-plane techniques to speed up the underlying tree-search algorithm used to find optimal solutions. In this paper we prove the first guarantees for learning high-performing cut-selection policies tailored to the instance distribution at hand using samples. We first bound the sample complexity of learning cutting planes from the canonical family of Chvatal-Gomory cuts. Our bounds handle any number of waves of any number of cuts and are fine tuned to the magnitudes of the constraint coefficients. Next, we prove sample complexity bounds for more sophisticated cut selection policies that use a combination of scoring rules to choose from a family of cuts. Finally, beyond the realm of cutting planes for integer programming, we develop a general abstraction of tree search that captures key components such as node selection and variable selection. For this abstraction, we bound the sample complexity of learning a good policy for building the search tree.
The Wasserstein barycenter has been widely studied in various fields, including natural language processing, and computer vision. However, it requires a high computational cost to solve the Wasserstein barycenter problem because the computation of the Wasserstein distance requires a quadratic time with respect to the number of supports. By contrast, the Wasserstein distance on a tree, called the tree-Wasserstein distance, can be computed in linear time and allows for the fast comparison of a large number of distributions. In this study, we propose a barycenter under the tree-Wasserstein distance, called the fixed support tree-Wasserstein barycenter (FS-TWB) and its extension, called the fixed support tree-sliced Wasserstein barycenter (FS-TSWB). More specifically, we first show that the FS-TWB and FS-TSWB problems are convex optimization problems and can be solved by using the projected subgradient descent. Moreover, we propose a more efficient algorithm to compute the subgradient and objective function value by using the properties of tree-Wasserstein barycenter problems. Through real-world experiments, we show that, by using the proposed algorithm, the FS-TWB and FS-TSWB can be solved two orders of magnitude faster than the original Wasserstein barycenter.
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