Knowledge Compilation meets Uniform Sampling

Sharma, Shubham; Gupta, Rahul; Roy, Subhajit; Meel, Kuldeep S.

doi:10.29007/h4p9

Cited by 23 publications

(48 citation statements)

References 24 publications

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“…Recently, another representation called as Sentential Decision Diagram (SDD) [16] was proposed which maintains canonicity and polytime support for boolean combinations and bridged the gap of succinctness between OBDDs and d-DNNFs. In our recent work [49], we were able to tackle the problem of uniform sampling by exploiting the properties of d-DNNF. Specifically, we were able to take advantage of recent advancements made in the field of knowledge compilation and use the compiled structure to generate uniform samples while competing with the state-of-the-art tools for uniform sampling.…”

Section: Related Workmentioning

confidence: 99%

“…Algorithm Sampler takes the annotated d-DNNF dag and the required number of samples s and returns SampleList, a list of s samples conforming to the distribution of their weights as governed by weight function W given to WAnnotate. The subroutine Sampler is very similar to the sampling procedure in our previous work [49] except that we take the annotated weight of the node instead of the annotated count in the previous work as the probability for Bernoulli trials. We refer the readers to Appendix for a detailed discussion.…”

Section: Samplingmentioning

confidence: 99%

“…A significant advantage of our framework is its simplicity: we show that our previously proposed framework in the context of uniform sampling, KUS [49], can be lifted to handle literal-weighted, projection and conditioned sampling. We demonstrate that unlike hashing-based techniques, the runtime performance of WAPS is not dependent on the underlying weight distribution.…”

Section: Introductionmentioning

confidence: 99%

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$$\mathsf {WAPS}$$ : Weighted and Projected Sampling

Gupta

Sharma

Roy

et al. 2019

Lecture Notes in Computer Science

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Given a set of constraints F and a user-defined weight function W on the assignment space, the problem of constrained sampling is to sample satisfying assignments of F conditioned on W. Constrained sampling is a fundamental problem with applications in probabilistic reasoning, synthesis, software and hardware testing. Consequently, the problem of sampling has been subject to intense theoretical and practical investigations over the years. Despite such intense investigations, there still remains a gap between theory and practice. In particular, there has been significant progress in the development of sampling techniques when W is a uniform distribution, but such techniques fail to handle general weight functions W. Furthermore, we are, often, interested in Σ 1 1 formulas, i.e., G(X) := ∃Y F (X, Y) for some F ; typically the set of variables Y are introduced as auxiliary variables during encoding of constraints to F. In this context, one wonders whether it is possible to design sampling techniques whose runtime performance is agnostic to the underlying weight distribution and can handle Σ 1 1 formulas? The primary contribution of this work is a novel technique, called WAPS, for sampling over Σ 1 1 whose runtime is agnostic to W. WAPS is based on our recently discovered connection between knowledge compilation and uniform sampling. WAPS proceeds by compiling F into a well studied compiled form, d-DNNF, which allows sampling operations to be conducted in linear time in the size of the compiled form. We demonstrate that WAPS can significantly outperform existing state-of-the-art weighted and projected sampler WeightGen, by up to 3 orders of magnitude in runtime while achieving a geometric speedup of 296× and solving 564 more instances out of 773. The distribution generated by WAPS is statistically indistinguishable from that generated by an ideal weighted and projected sampler. Furthermore, WAPS is almost oblivious to the number of samples requested.

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Section: Related Workmentioning

confidence: 99%

Section: Samplingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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$$\mathsf {WAPS}$$ : Weighted and Projected Sampling

Gupta

Sharma

Roy

et al. 2019

Lecture Notes in Computer Science

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“…To evaluate the runtime performance of Barbarik and test the uniformity of the state of the art samplers, we implemented a prototype of Barbarik and employed SPUR (Achlioptas, Hammoudeh, and Theodoropoulos 2018) as the ideal uniform sampler, i.e., U in the Algorithm 1. Note that Barbarik allows choice of any other available samplers such as KUS (Sharma et al 2018). The experiments were conducted on a high-performance computer cluster, where each node consists of E5-2690 v3 CPU with 24 cores and 96GB of RAM.…”

Section: Discussionmentioning

confidence: 99%

“…With the proposal of every new sampling techniques, a significant effort is put for the evaluation of the proposed techniques. The literature bears testimony to the focus on runtime performance comparison of the proposed technique with the previous state of the art (See, for example (Chakraborty, Meel, and Vardi 2013;Ermon et al 2013a;Meel 2014;Chakraborty et al 2015a;Meel 2017;Dutra et al 2018;Sharma et al 2018;Achlioptas, Hammoudeh, and Theodoropoulos 2018)). On the other hand, there is a less rigorous evaluation of the quality of generated samples.…”

Section: Introductionmentioning

confidence: 99%

On Testing of Uniform Samplers

Chakraborty

Meel

2019

AAAI

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Recent years have seen an unprecedented adoption of artificial intelligence in a wide variety of applications ranging from medical diagnosis, automobile industry, security to aircraft collision avoidance. Probabilistic reasoning is a key component of such modern artificial intelligence systems. Sampling techniques form the core of the state of the art probabilistic reasoning systems. The divide between the existence of sampling techniques that have strong theoretical guarantees but fail to scale and scalable techniques with weak or no theoretical guarantees mirrors the gap in software engineering between poor scalability of classical program synthesis techniques and billions of programs that are routinely used by practitioners. One bridge connecting the two extremes in the context of software engineering has been program testing. In contrast to testing for deterministic programs, where one trace is sufficient to prove the existence of a bug, in case of samplers one sample is typically not sufficient to prove non-conformity of the sampler to the desired distribution. This makes one wonder whether it is possible to design testing methodology to test whether a sampler under test generates samples close to a given distribution. The primary contribution of this paper is an affirmative answer to the above question when the given distribution is a uniform distribution: We design, to the best of our knowledge, the first algorithmic framework, Barbarik, to test whether the distribution generated is ε−close or η−far from the uniform distribution. In contrast to the sampling techniques that require an exponential or sub-exponential number of samples for sampler whose support can be represented by n bits, Barbarik requires only O(1/(η−ε)4) samples. We present a prototype implementation of Barbarik and use it to test three state of the art uniform samplers over the support defined by combinatorial constraints. Barbarik can provide a certificate of uniformity to one sampler and demonstrate nonuniformity for the other two samplers.

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Manthan: A Data-Driven Approach for Boolean Function Synthesis

Golia

Roy

Meel

2020

Computer Aided Verification

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Boolean functional synthesis is a fundamental problem in computer science with wide-ranging applications and has witnessed a surge of interest resulting in progressively improved techniques over the past decade. Despite intense algorithmic development, a large number of problems remain beyond the reach of the state of the art techniques. Motivated by the progress in machine learning, we propose Manthan, a novel data-driven approach to Boolean functional synthesis. Manthan views functional synthesis as a classification problem, relying on advances in constrained sampling for data generation, and advances in automated reasoning for a novel proof-guided refinement and provable verification. On an extensive and rigorous evaluation over 609 benchmarks, we demonstrate that Manthan significantly improves upon the current state of the art, solving 356 benchmarks in comparison to 280, which is the most solved by a state of the art technique; thereby, we demonstrate an increase of 76 benchmarks over the current state of the art. Furthermore, Manthan solves 60 benchmarks that none of the current state of the art techniques could solve. The significant performance improvements, along with our detailed analysis, highlights several interesting avenues of future work at the intersection of machine learning, constrained sampling, and automated reasoning.

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Knowledge Compilation meets Uniform Sampling

Cited by 23 publications

References 24 publications

$$\mathsf {WAPS}$$ : Weighted and Projected Sampling

$$\mathsf {WAPS}$$ : Weighted and Projected Sampling

On Testing of Uniform Samplers

Manthan: A Data-Driven Approach for Boolean Function Synthesis

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