Predictability, computability, and stability for interpretable and reproducible data science

Karl Kumbier

Joint work with Bin Yu

Domain insights through supervised learning

Natural phenomena

Supervised learning

Domain insights

Prediction error

Interpretation error

The PCS framework: transparently evaluate human judgement calls

  • Predictability: does my model capture external reality? (Popper, 1959; Allen, 1974; Stone, 1974; Breiman, 2001)
  • Computability: can I tractably build/train my model? (Turing 1937; Hartmanis and Stearns, 1965)
  • Stability: are my results consistent with respect to "reasonable" perturbations of the data/model? (Fisher, 1937; Popper 1959; Donoho et al., 2009; Yu, 2013; Stark 2018)

 iterative Random Forest to identify genomic interactions

  1. Iteratively re-weighted Random Forests (Breiman, 20001; Amaratunga et al., 2008)
  2. Generalized random intersection trees (Shah and Meinshausen, 2014)
  3. Stability bagging (Breiman, 1996)

Joint work with Sumanta Basu, James B. Brown, and Bin Yu

iterative Random Forests (iRF) build on PCS to identify genomic interactions in developing Drosophila embryos 

iterative re-weighting stabilizes RF decision paths

Sampling features based on their importance acts as soft regularization and maintains predictive accuracy of RF

Gini importance

Generalized random intersection trees search for high-order interactions

Features selected on RF decision paths

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Intersect features on randomly selected decision paths to identify frequently co-occurring combinations

Bagging evaluates stability of interactions

Outer-layer bootstrap samples evaluate how consistently interactions are recovered across bootstrap perturbations of the data

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\{\{1,4\},\{1,3\}\}
{{1,4},{1,3}}\{\{1,4\},\{1,3\}\}

Predicting early stage cancers

  • 1817 patients (1005 cancer, 812 control)
  • 8 cancer types: 

    ovary, liver, stomach, pancreas, lung, breast,

    esophagus, and colorectum

  • 61  genetic mutations and 39 protein biomarkers

Cancer detection: incorporating rules for better prediction

P(y=1)=\frac{1}{K} \sum_{k=1}^K r_k(x;S_k)
P(y=1)=1K∑k=1Krk(x;Sk)P(y=1)=\frac{1}{K} \sum_{k=1}^K r_k(x;S_k)
  • iRF can extract predictive rules from a Random Forest
  • Individual rules are interpretable (e.g. sparse, simulatable, modular) and can be screened based on domain constraints

Probability of cancer

Decision rule

iRF interaction

Rule-based predictions consistently improve predictive accuracy

Rule-based models successfully diagnose an additional 123/1000 patients under domain-specific constraints

Rule-based predictions improve predictive accuracy over all cancer types

Additional 12 / 100 patients successfully diagnosed

Additional 11 / 100 patients successfully diagnosed

Summary

Ackowledgements

Defining interpretability

Interpretable machine learning: The extraction of relevant knowledge about domain relationships contained in data.

 

Relevant knowledge: provides insight for a particular audience into a chosen problem. These insights guide actions, discovery, and communication.

Encourage our model to learn interpretable relationships that can be [easily] read off by a practitioner.

Allow our model to learn complex relationships and develop methods to extract portions of these relationships.

Model based

Post hoc

Graphic for prediction accuracy vs interpretation accuracy

Model based interpretability

  • Sparsity: how many components does my model have?
  • Simulatability: can a human reasonably internalize the decision making process?
  • Modularity: can the model be broken down into components that can be interpreted independently?
  • Feature engineering
  • Unsupervised learning

iRF builds in interpretability

iterative re-weighting encourages model to use sparse set of stable features

Recovered interactions represent predictive, simulatable "modules" (almost)

Post hoc interpretability

  • Local interpretability: what relationship(s) does my model learn for an individual observation
  • Global interpretability: what relationship(s) does my model learn across the entire dataset

Evaluating interpretability

  • Interpretation accuracy: how well does my interpretation represent the model [image data relationship, prediction accuracy, interpretation accuracy]
  • Interpretation stability: how consistent is my interpretation relative to reasonable perturbation(s) of the model/data
  • Relevancy: does my interpretation address the task at hand without convoluting

Interpretability constraints in early-stage cancer prediction

Biomarkers known associations with cancer

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