PSense: Automatic Sensitivity Analysis for Probabilistic Programs

Huang, Zixin; Wang, Zhenbang; Misailovíc, Saša

doi:10.1007/978-3-030-01090-4_23

Cited by 13 publications

(13 citation statements)

References 15 publications

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“…Below we compare our result in detail with the most related results, i.e., [Barthe et al 2018], [Huang et al 2018b] and also a recent arXiv submission [Aguirre et al 2019]. Recall that we have discussed the issue of conditional branches at the end of Section 1.…”

Section: Experimental Examplesmentioning

confidence: 67%

“…At each loop iteration, a data i is chosen uniformly from all n training data and the parameters in w are adjusted by the product of the step size and the gradient of the ith loss function G i . The loop guard Φ can either be practical so that a fixed number of iterations is performed (as is analyzed in existing approaches [Barthe et al 2018;Hardt et al 2016;Huang et al 2018b]), or the local criteria that the magnitude ∇G 2 of the gradient of the total loss function G is small enough, or the global criteria that the value of G is small enough. In this paper, we consider the global criteria, i.e., the loop guard is of the form G(w) ≥ ζ where ζ is the threshold for "small enough".…”

Section: Motivating Examplesmentioning

confidence: 99%

“…Several classical examples such as stochastic gradient descent, population dynamics or Glauber dynamics can be analyzed in the framework of [Barthe et al 2018]. Another method for the sensitivity analysis of probabilistic programs has been proposed in [Huang et al 2018b] and they analysed a linear-regression example derived from the SGD algorithm in [Barthe et al 2018]. For details of literature on relational analysis of probabilistic programs leading to the work of [Barthe et al 2018] see [Barthe et al 2018, Section 9].…”

Section: Experimental Examplesmentioning

confidence: 99%

“…Comparison with [Huang et al 2018b]. The result of [Huang et al 2018b] develops an automated tool based on computer algebra that calculates tight sensitivity bounds for probabilistic programs. As computer algebra requires to unroll every loop into its sequential counterpart without looping, the approach is suitable only for programs with a bounded number of loop iterations and cannot handle variable-dependent randomized loop iterations that typically lead to unbounded loop iterations.…”

Section: Experimental Examplesmentioning

confidence: 99%

“…For example, in previous approaches such as [Aguirre et al 2019; Barthe et al 2018], it must be manually ensured that the conditions of all conditional branches are either (i) both satisfied or (ii) both not satisfied by two close-by program valuations (i.e., the situation (**) above not allowed) (see [Barthe et al 2018, Figure 3] and [Aguirre et al 2019, Figure 1]). Moreover, in all the experimental examples from [Huang et al 2018b], conditional-branches within for-loops are either restricted to a finite set of values or directly transformed into probabilistic branches. For a possible extension to conditional branches see Remark 5.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Proving expected sensitivity of probabilistic programs with randomized variable-dependent termination time

Wang

Chatterjee

et al. 2019

Proc. ACM Program. Lang.

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The notion of program sensitivity (aka Lipschitz continuity) specifies that changes in the program input result in proportional changes to the program output. For probabilistic programs the notion is naturally extended to expected sensitivity. A previous approach develops a relational program logic framework for proving expected sensitivity of probabilistic while loops, where the number of iterations is fixed and bounded. In this work, we consider probabilistic while loops where the number of iterations is not fixed, but randomized and depends on the initial input values. We present a sound approach for proving expected sensitivity of such programs. Our sound approach is martingale-based and can be automated through existing martingale-synthesis algorithms. Furthermore, our approach is compositional for sequential composition of while loops under a mild side condition. We demonstrate the effectiveness of our approach on several classical examples from Gambler's Ruin, stochastic hybrid systems and stochastic gradient descent. We also present experimental results showing that our automated approach can handle various probabilistic programs in the literature.

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Section: Experimental Examplesmentioning

confidence: 67%

Section: Motivating Examplesmentioning

confidence: 99%

Section: Experimental Examplesmentioning

confidence: 99%

Section: Experimental Examplesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Proving expected sensitivity of probabilistic programs with randomized variable-dependent termination time

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Chatterjee

et al. 2019

Proc. ACM Program. Lang.

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Continualization of Probabilistic Programs With Correction

Laurel

Misailovíc

2020

Programming Languages and Systems

Self Cite

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Probabilistic Programming offers a concise way to represent stochastic models and perform automated statistical inference. However, many real-world models have discrete or hybrid discrete-continuous distributions, for which existing tools may suffer non-trivial limitations. Inference and parameter estimation can be exceedingly slow for these models because many inference algorithms compute results faster (or exclusively) when the distributions being inferred are continuous. To address this discrepancy, this paper presents Leios. Leios is the first approach for systematically approximating arbitrary probabilistic programs that have discrete, or hybrid discrete-continuous random variables. The approximate programs have all their variables fully continualized. We show that once we have the fully continuous approximate program, we can perform inference and parameter estimation faster by exploiting the existing support that many languages offer for continuous distributions. Furthermore, we show that the estimates obtained when performing inference and parameter estimation on the continuous approximation are still comparably close to both the true parameter values and the estimates obtained when performing inference on the original model.

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Latticed k-Induction with an Application to Probabilistic Programs

Batz

Chen

Kaminski

et al. 2021

Computer Aided Verification

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We revisit two well-established verification techniques, k-induction and bounded model checking (BMC), in the more general setting of fixed point theory over complete lattices. Our main theoretical contribution is latticed k-induction, which (i) generalizes classical k-induction for verifying transition systems, (ii) generalizes Park induction for bounding fixed points of monotonic maps on complete lattices, and (iii) extends from naturals k to transfinite ordinals $$\kappa $$ κ , thus yielding $$\kappa $$ κ -induction.The lattice-theoretic understanding of k-induction and BMC enables us to apply both techniques to the fully automatic verification of infinite-state probabilistic programs. Our prototypical implementation manages to automatically verify non-trivial specifications for probabilistic programs taken from the literature that—using existing techniques—cannot be verified without synthesizing a stronger inductive invariant first.

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PSense: Automatic Sensitivity Analysis for Probabilistic Programs

Cited by 13 publications

References 15 publications

Proving expected sensitivity of probabilistic programs with randomized variable-dependent termination time

Proving expected sensitivity of probabilistic programs with randomized variable-dependent termination time

Continualization of Probabilistic Programs With Correction

Latticed k-Induction with an Application to Probabilistic Programs

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