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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.

Neil Ernst

May 29, 2018
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  1. 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
  2. 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.
  3. 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)
  4. 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.
  5. Hierarchical models Unpooled, linear regression y ⇠ N(µ, ) <latexit

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

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  7. 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
  8. 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); }
  9. 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
  10. 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”
  11. 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”