Bayesian Hierarchical Modeling for Software Metrics

Bayesian Hierarchical Modeling for Software Metrics

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At MSR18 in Gothenburg, I presented [my work](https://arxiv.org/abs/1804.02443) on using Bayesian inference to set software metrics thresholds. We want to set thresholds because for many software metrics, like coupling between objects (CBO), a single, global metric value ("all software objects with this value or below are maintainable") is nonsensical, if only because programming language choice is important. So we want to tailor threshold values to some contextually relevant value (e.g., perhaps all Java code should be X or less). The question I answered is how we do the tailoring, given some contextual features.

141272f109fbf660ffa001647f17d368?s=128

Neil Ernst

May 29, 2018
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  1. Bayesian Hierarchical Models for Tailoring Metrics Thresholds Neil Ernst University

    of Victoria Software Engineering @neilernst
  2. Bayesian Hierarchical Models for X Neil Ernst University of Victoria

    Software Engineering @neilernst
  3. Bottom line (SE) We can use hierarchical models to tailor

    metrics to specific contexts → In this case, with 50% drop in RMSE (Method) Hierarchical modeling with Bayesian inference fit SE data very well
  4. Local vs global properties GLOBAL: All software is the same.

    Lessons from one project directly apply to others. LOCAL: No software is the same: → (my Javascript startup, dev team, and business context are different than your Javascript startup, dev team, and business context). Lessons are not transferable. Tim Menzies and others showed you can in fact transfer (software) lessons.
  5. Software hierarchies • Look at data as having levels/hierarchies: →

    Radon samples by county, students per school → Ecosystems: Projects: Files: Methods • Incredibly useful when one “pool” is under-represented in dataset • This case: predicting mean log CBO for a given Spring project (to set thresholds) (files/projects)
  6. Bayesian regression Bayesian approach models a posterior distribution by conditioning

    on data, given some explicit prior assumptions. → Posterior P(H | D) is proportional to the likelihood P(D|H) times the prior P(D). → A machine for producing posterior distributions. More data = tighter estimates. Less data = more influence from priors.
  7. Hierarchical models Unpooled, linear regression y ⇠ N(µ, ) <latexit

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  8. Hierarchical models Unpooled, linear regression y ⇠ N(µ, ) <latexit

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sha1_base64="ZHIsLPnE/luMTe1lLAiuIlArZZ8=">AAACznichVJda9swFJW9ry77SrvHvYglgXgbwc7L+lIoXR8Cg+HB0hZiY64VOVEr2Z4ll3qq2et+3972A/Y/JqVmH21hFwRH55wr3aurtORMKt//4bh37t67/2DrYe/R4ydPn/W3d45kUVeEzknBi+okBUk5y+lcMcXpSVlRECmnx+nZO6sfn9NKsiL/pJqSxgJWOcsYAWWopP9zNGxwJJnAkQC1JsD1h3YcifqNIVcCvGFvNAzHM3yJDz28h6OsAqJxOD40zMzDrwycea02hNdar0m1tpQqSAL8ukNTfJEwKzcJszLwcg2JPl2wuP1t6rYXiWaGjGgpGTc1mrxba/zvGX9aSPoDf+JvAt8EQQcGqIsw6X+PlgWpBc0V4SDlIvBLFWuoFCOctr2olrQEcgYrujAwB0FlrDfjaPHIMEucFZVZucIb9u8MDULKRqTGafuR1zVL3qYtapXtxprlZa1oTq4uymqOVYHtbPGSVZQo3hgApGKmVkzWYAamzA+wjxBcb/kmOJpOAn8SfJwO9g+659hCL9BLNEYBeov20QyFaI6I89757HxxtBu6527rfr2yuk6X8xz9E+63X9e81qc=</latexit> <latexit sha1_base64="ZHIsLPnE/luMTe1lLAiuIlArZZ8=">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</latexit> Aka multilevel models, partial pooling models, varying slope and intercept models
  9. Src: https://bit.ly/2G04hN2

  10. Src: https://bit.ly/2G04hN2 Pooled

  11. Src: https://bit.ly/2G04hN2 Pooled Un-Pooled

  12. Src: https://bit.ly/2G04hN2 Pooled Un-Pooled Partially pooled

  13. Conditioning Finding closed form solutions is difficult or impossible Simulate

    using Hamiltonian Monte Carlo with a probabilistic program (Stan) Model checking vital: does our model converge
  14. Partial pooling model model { mu_a ~ normal(0, 100); #

    hyperprior mu_b ~ normal(0, 100); # hyperprior a ~ normal(mu_a, sigma_a); # prior b ~ normal(mu_b, sigma_b); # prior # likelihood: y ~ normal(a[project] + b[project]*x, sigma); }
  15. None
  16. Validation: RMSE per project up to 50% lower with partial

    pooling
  17. None
  18. None
  19. Modeling and stating explicit priors (theories) increase replicability

  20. Modeling and stating explicit priors (theories) increase replicability Tooling support

    for Bayesian hierarchical models (Stan, PyMC3, Edward)
  21. Modeling and stating explicit priors (theories) increase replicability Tooling support

    for Bayesian hierarchical models (Stan, PyMC3, Edward) Partial pooling matches intuition of software development analysis
  22. Modeling and stating explicit priors (theories) increase replicability Tooling support

    for Bayesian hierarchical models (Stan, PyMC3, Edward) Partial pooling matches intuition of software development analysis “multi-level modeling deserves to be the default form of regression”
  23. Modeling and stating explicit priors (theories) increase replicability Tooling support

    for Bayesian hierarchical models (Stan, PyMC3, Edward) Partial pooling matches intuition of software development analysis More info: neilernst.net and @neilernst ArXiv: https://arxiv.org/abs/1804.02443 Jupyter notebook: https://doi.org/10.6084/m9.figshare.4892852.v1 Dataset: http://www.mauricioaniche.com/scam2016/ “multi-level modeling deserves to be the default form of regression”