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Ivan Paskov

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JMLR Journal 2022 Journal Article

Stable Classification

  • Dimitris Bertsimas
  • Jack Dunn
  • Ivan Paskov

We address the problem of instability of classification models: small changes in the training data leading to large changes in the resulting model and predictions. This phenomenon is especially well established for single tree based methods such as CART, however it is present in all classification methods. We apply robust optimization to improve the stability of four of the most commonly used classification methods: Random Forests, Logistic Regression, Support Vector Machines, and Optimal Classification Trees. Through experiments on 30 data sets with sizes ranging between 10^2 and 10^4 observations and features, we show that our approach (a) leads to improvements in stability, and in some cases accuracy, compared to the original methods, with the gains in stability being particularly significant (even, surprisingly, for those methods that were previously thought to be stable, such as Random Forests) and (b) has computational times comparable with (and indeed in some cases even faster than) the original methods allowing the method to be very scalable. [abs] [ pdf ][ bib ] &copy JMLR 2022. ( edit, beta )

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JMLR Journal 2020 Journal Article

Stable Regression: On the Power of Optimization over Randomization

  • Dimitris Bertsimas
  • Ivan Paskov

We investigate and ultimately suggest remediation to the widely held belief that the best way to train regression models is via random assignment of our data to training and validation sets. In particular, we show that taking a robust optimization approach, and optimally selecting such training and validation sets, leads to models that not only perform significantly better than their randomly constructed counterparts in terms of prediction error, but more importantly, are considerably more stable in the sense that the standard deviation of the resulting predictions, as well as of the model coefficients, is greatly reduced. Moreover, we show that this optimization approach to training is far more effective at recovering the true support of a given data set, i.e., correctly identifying important features while simultaneously excluding spurious ones. We further compare the robust optimization approach to cross validation and find that optimization continues to have a performance edge albeit smaller. Finally, we show that this optimization approach to training is equivalent to building models that are robust to all subpopulations in the data, and thus in particular are robust to the hardest subpopulation, which leads to interesting domain specific interpretations through the use of optimal classification trees. The proposed robust optimization algorithm is efficient and scales training to essentially any desired size. [abs] [ pdf ][ bib ] &copy JMLR 2020. ( edit, beta )

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