scholarly journals Weighted Model Integration with Orthogonal Transformations

2017 ◽  
Author(s):  
David Merrell ◽  
Aws Albarghouthi ◽  
Loris D'Antoni
Keyword(s):  
Satisfiability Modulo Theories ◽  
Exact Probability ◽  
Exact Inference ◽  
First Order ◽  
Probability Bounds ◽  
Model Counting ◽  
Weighted Model ◽  
Inference Techniques ◽  
Time Required ◽  
Probabilistic Programs

Weighted model counting and integration (WMC/WMI) are natural problems to which we can reduce many probabilistic inference tasks, e.g., in Bayesian networks, Markov networks, and probabilistic programs. Typically, we are given a first-order formula, where each satisfying assignment is associated with a weight---e.g., a probability of occurrence---and our goal is to compute the total weight of the formula. In this paper, we target exact inference techniques for WMI that leverage the power of satisfiability modulo theories (SMT) solvers to decompose a first-order formula in linear real arithmetic into a set of hyperrectangular regions whose weight is easy to compute. We demonstrate the challenges of hyperrectangular decomposition and present a novel technique that utilizes orthogonal transformations to transform formulas in order to enable efficient inference. Our evaluation demonstrates our technique's ability to improve the time required to achieve exact probability bounds.

scholarly journals Exploiting Structure in Weighted Model Counting Approaches to Probabilistic Inference

2011 ◽  
Vol 40 ◽  
pp. 729-765 ◽  
Author(s):  
W. Li ◽  
P. Poupart ◽  
P. Van Beek
Keyword(s):  
Bayesian Networks ◽  
Bayesian Network ◽  
Large Scale ◽  
Search Algorithm ◽  
Exact Inference ◽  
Backtracking Search ◽  
Space Efficiency ◽  
Counting Approach ◽  
Model Counting ◽  
Weighted Model

Previous studies have demonstrated that encoding a Bayesian network into a SAT formula and then performing weighted model counting using a backtracking search algorithm can be an effective method for exact inference. In this paper, we present techniques for improving this approach for Bayesian networks with noisy-OR and noisy-MAX relations---two relations that are widely used in practice as they can dramatically reduce the number of probabilities one needs to specify. In particular, we present two SAT encodings for noisy-OR and two encodings for noisy-MAX that exploit the structure or semantics of the relations to improve both time and space efficiency, and we prove the correctness of the encodings. We experimentally evaluated our techniques on large-scale real and randomly generated Bayesian networks. On these benchmarks, our techniques gave speedups of up to two orders of magnitude over the best previous approaches for networks with noisy-OR/MAX relations and scaled up to larger networks. As well, our techniques extend the weighted model counting approach for exact inference to networks that were previously intractable for the approach.

scholarly journals Properties of renin substrate in rabbit plasma with a note on its assay

1968 ◽  
Vol 108 (4) ◽  
pp. 687-692 ◽  
Author(s):  
J W Ryan ◽  
J. K. McKenzie
Keyword(s):  
Substrate Concentration ◽  
Rabbit Plasma ◽  
Selective Inhibitors ◽  
Angiotensin I ◽  
Renin Substrate ◽  
First Order ◽  
Plasma Enzymes ◽  
First Order Kinetics ◽  
Time Required ◽  
Substrate Concentrations

1. Rabbit plasma enzymes that degrade angiotensin I are inhibited completely by the combination of 2,3-dimercaptopropan-1-ol (10mm), EDTA (10mm) and chlorhexidine gluconate (0·005%, w/v). These compounds do not modify the reaction of renin with renin substrate and are termed the selective inhibitors. 2. The renin substrate concentration of plasma can be measured as angiotensin I content by incubating plasma plus the selective inhibitors with renin for a time sufficient to allow complete utilization of renin substrate. 3. This reaction obeys first-order kinetics to substrate concentrations of at least 1000ng. of angiotensin I content/ml. In general, the renin substrate concentrations of normal rabbit plasmas are less than 1000ng. of angiotensin I content/ml. Thus the time required for the complete release of angiotensin I from normal plasma is inversely related to renin activity and is independent of renin substrate concentration. 4. A method for the assay of renin substrate, taking these reaction kinetics into account, is presented.

scholarly journals VERIFYING PROBABILISTIC PROGRAMS USING A HOARE LIKE LOGIC

2002 ◽  
Vol 13 (03) ◽  
pp. 315-340 ◽  
Author(s):  
J. I. DEN HARTOG ◽  
E. P. DE VINK
Keyword(s):  
Programming Language ◽  
Denotational Semantics ◽  
Order Logic ◽  
First Order Logic ◽  
Proof System ◽  
Probabilistic Choice ◽  
First Order ◽  
Probabilistic Programs

Probability, be it inherent or explicitly introduced, has become an important issue in the verification of programs. In this paper we study a formalism which allows reasoning about programs which can act probabilistically. To describe probabilistic programs, a basic programming language with an operator for probabilistic choice is introduced and a denotational semantics is given for this language. To specify propertics of probabilistic programs, standard first order logic predicates are insufficient, so a notion of probabilistic predicates is introduced. A Hoare-style proof system to check properties of probabilistic programs is given. The proof system for a sublanguage is shown to be sound and complete; the properties that can be derived are exactly the valid properties. Finally some typical examples illustrate the use of the probabilistic predicates and the proof system.

Factors influencing the time required to shear Merino sheep and its importance as a breeding objective

1981 ◽  
Vol 21 (111) ◽  
pp. 387 ◽  
Author(s):  
BJ McGuirk ◽  
R Ponzoni ◽  
KD Atkins ◽  
AR Gilmour ◽  
FHW Morley ◽  
...  
Keyword(s):  
No Production ◽  
Merino Sheep ◽  
First Order ◽  
Merino Wool ◽  
Breeding Objective ◽  
Skin Fold ◽  
Fleece Weight ◽  
Time Required ◽  
Wool Industry ◽  
Australian Merino

Two sets of observations have been made on the time required to shear (TRS) Merino sheep. The first, in 1951, involved 98 rams and 75 ewes from one medium Peppin bloodline. Then, in 1975, TRS was recorded on 79 rams and 143 ewes from five different bloodlines, from a number of Merino strains. The effect of different production characters on TRS was estimated by least squares analysis, in models that included the effects of shearer, sex, bloodline (1975 only) and all first order interactions. In the 1951 data, TRS increased with increasing greasy fleece weight and with increasing skin fold in the rams (P <0.05). No production character had a significant effect on TRS in the ewes. In the 1975 data, TRS increased with increasing greasy fleece weight, skin fold, face cover and body weight in at least one sex, and when data from the two sexes were pooled (P <0.05). Skin fold and greasy fleece weight had the largest and most consistent effect. There were also significant differences between the bloodlines in TRS, which were found to be associated with differences between the bloodlines in skin fold, greasy fleece weight, and to a lesser extent, face cover. After studying the likely economic benefit of reducing TRS by selection, we concluded that under current economic situations, where any reduction in TRS would lower only the ancillary costs associated with shearing (shed hands, classing, etc.). TRS is not an important breeding objective for the Australian Merino wool industry.

scholarly journals Exact Inference Techniques for the Analysis of Bayesian Attack Graphs

2019 ◽  
Vol 16 (2) ◽  
pp. 231-244 ◽  
Author(s):  
Luis Munoz-Gonzalez ◽  
Daniele Sgandurra ◽  
Martin Barrere ◽  
Emil C. Lupu
Keyword(s):  
Attack Graphs ◽  
Exact Inference ◽  
Inference Techniques

scholarly journals Learning Probabilistic Termination Proofs

2021 ◽  
pp. 3-26
Author(s):  
Alessandro Abate ◽  
Mirco Giacobbe ◽  
Diptarko Roy
Keyword(s):  
Learning Strategy ◽  
Source Code ◽  
Satisfiability Modulo Theories ◽  
Smt Solver ◽  
Execution Traces ◽  
State Dependent ◽  
Polynomial Programs ◽  
Continuous State ◽  
Guided Inductive ◽  
Probabilistic Programs

AbstractWe present the first machine learning approach to the termination analysis of probabilistic programs. Ranking supermartingales (RSMs) prove that probabilistic programs halt, in expectation, within a finite number of steps. While previously RSMs were directly synthesised from source code, our method learns them from sampled execution traces. We introduce the neural ranking supermartingale: we let a neural network fit an RSM over execution traces and then we verify it over the source code using satisfiability modulo theories (SMT); if the latter step produces a counterexample, we generate from it new sample traces and repeat learning in a counterexample-guided inductive synthesis loop, until the SMT solver confirms the validity of the RSM. The result is thus a sound witness of probabilistic termination. Our learning strategy is agnostic to the source code and its verification counterpart supports the widest range of probabilistic single-loop programs that any existing tool can handle to date. We demonstrate the efficacy of our method over a range of benchmarks that include linear and polynomial programs with discrete, continuous, state-dependent, multi-variate, hierarchical distributions, and distributions with undefined moments.

scholarly journals SIMULATION OF A MANEUVERING AIRCRAFT USING A PANEL METHOD

2021 ◽  
Vol 61 (2) ◽  
pp. 378-390
Author(s):  
Pavel Schoř ◽  
Martin Kouřil ◽  
Vladimír Daněk
Keyword(s):  
Reasonable Agreement ◽  
Panel Method ◽  
Aerodynamic Forces ◽  
Local Pressure ◽  
First Order ◽  
Unsteady Panel Method ◽  
Flight Parameters ◽  
Time Required ◽  
Control Surfaces ◽  
Load Evaluation

We present a method for numerical simulations of a maneuvering aircraft, which uses a first-order unsteady panel method as the only source of aerodynamic forces and moments. By using the proposed method, it is possible to simulate a motion of an aircraft, while the only required inputs are geometry and inertia characteristics, which significantly reduces the time required to start the simulation. We validated the method by a comparison of recordings of flight parameters (position, velocities, accelerations) from an actual aerobatic flight of a glider and the results obtained from the simulations. The simulation was controlled by deflections of control surfaces recorded during the actual flight. We found a reasonable agreement between the experimental data and the simulation. The design of our method allows to evaluate not only the integral kinematic quantities but also instant local pressure and inertia loads. This makes our method useful also for a load evaluation of an aircraft. A significant advantage of the proposed method is that only an ordinary workstation computer is requiredto perform the simulation.

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