scholarly journals Formal verification of higher-order probabilistic programs: reasoning about approximation, convergence, Bayesian inference, and optimization

2019 ◽  
Vol 3 (POPL) ◽  
pp. 1-30 ◽  
Author(s):  
Tetsuya Sato ◽  
Alejandro Aguirre ◽  
Gilles Barthe ◽  
Marco Gaboardi ◽  
Deepak Garg ◽  
...  
Keyword(s):  
Bayesian Inference ◽  
Formal Verification ◽  
Higher Order ◽  
Probabilistic Programs

scholarly journals Probabilistic Reasoning Across the Causal Hierarchy

2020 ◽  
Vol 34 (06) ◽  
pp. 10170-10177 ◽  
Author(s):  
Duligur Ibeling ◽  
Thomas Icard
Keyword(s):  
Bayesian Inference ◽  
Conditional Independence ◽  
Probabilistic Reasoning ◽  
Causal Models ◽  
Causal Effects ◽  
Polynomial Space ◽  
The Third ◽  
Probabilistic Programs

We propose a formalization of the three-tier causal hierarchy of association, intervention, and counterfactuals as a series of probabilistic logical languages. Our languages are of strictly increasing expressivity, the first capable of expressing quantitative probabilistic reasoning—including conditional independence and Bayesian inference—the second encoding do-calculus reasoning for causal effects, and the third capturing a fully expressive do-calculus for arbitrary counterfactual queries. We give a corresponding series of finitary axiomatizations complete over both structural causal models and probabilistic programs, and show that satisfiability and validity for each language are decidable in polynomial space.

scholarly journals Formal verification of Matrix based MATLAB models using interactive theorem proving

2021 ◽  
Vol 7 ◽  
pp. e440
Author(s):  
Ayesha Gauhar ◽  
Adnan Rashid ◽  
Osman Hasan ◽  
João Bispo ◽  
João M.P. Cardoso
Keyword(s):  
Formal Verification ◽  
Finite Impulse Response ◽  
Formal Analysis ◽  
Digital Signal ◽  
Interactive Theorem Proving ◽  
Higher Order ◽  
Order Logic ◽  
Theorem Prover ◽  
Formal Models ◽  
Higher Order Logic

MATLAB is a software based analysis environment that supports a high-level programing language and is widely used to model and analyze systems in various domains of engineering and sciences. Traditionally, the analysis of MATLAB models is done using simulation and debugging/testing frameworks. These methods provide limited coverage due to their inherent incompleteness. Formal verification can overcome these limitations, but developing the formal models of the underlying MATLAB models is a very challenging and time-consuming task, especially in the case of higher-order-logic models. To facilitate this process, we present a library of higher-order-logic functions corresponding to the commonly used matrix functions of MATLAB as well as a translator that allows automatic conversion of MATLAB models to higher-order logic. The formal models can then be formally verified in an interactive theorem prover. For illustrating the usefulness of the proposed library and approach, we present the formal analysis of a Finite Impulse Response (FIR) filter, which is quite commonly used in digital signal processing applications, within the sound core of the HOL Light theorem prover.

scholarly journals Denotational validation of higher-order Bayesian inference

2018 ◽  
Vol 2 (POPL) ◽  
pp. 1-29 ◽  
Author(s):  
Adam Ścibior ◽  
Ohad Kammar ◽  
Matthijs Vákár ◽  
Sam Staton ◽  
Hongseok Yang ◽  
...  
Keyword(s):  
Bayesian Inference ◽  
Higher Order

scholarly journals An Efficient Improved OGWSBI Algorithm for Accurate Off-Grid DOA Estimation of Coherent Signals

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Xiangjun Xu ◽  
Mingwei Shen ◽  
Di Wu ◽  
Daiyin Zhu
Keyword(s):  
Bayesian Inference ◽  
Unitary Transformation ◽  
Order Approximation ◽  
Doa Estimation ◽  
Higher Order ◽  
Estimation Accuracy ◽  
Real Field ◽  
Coherent Signals ◽  
Steering Vector ◽  
Grid Model

The performance of the weighted sparse Bayesian inference (OGWSBI) algorithm for off-grid coherent DOA estimation is not satisfactory due to the inaccurate weighting information. To increase the estimation accuracy and efficiency, an improved OGWSBI algorithm based on a higher-order off-grid model and unitary transformation for off-grid coherent DOA estimation is proposed in this paper. Firstly, to reduce the approximate error of the first-order off-grid model, the steering vector is reformulated by the second-order Taylor expansion. Then, the received data is transformed from complex value to real value and the coherent signals are decorrelated via utilizing unitary transformation, which can increase the computational efficiency and restore the rank of the covariance matrix. Finally, in the real field, the steering vector higher-order approximation model and weighted sparse Bayesian inference are combined together to realize the estimation of DOA. Extensive simulation results indicate that under the condition of coherent signals and low SNR, the estimation accuracy of the proposed algorithm is about 50% higher than that of the OGWSBI algorithm, and the calculation time is reduced by about 60%.

scholarly journals Higher-order probabilistic perceptrons as Bayesian inference engines

1999 ◽  
Vol 59 (5) ◽  
pp. 6161-6174 ◽  
Author(s):  
J. W. Clark ◽  
K. A. Gernoth ◽  
S. Dittmar ◽  
M. L. Ristig
Keyword(s):  
Bayesian Inference ◽  
Higher Order ◽  
Inference Engines
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