Context-dependent feature analysis with random forests

In many cases, feature selection is often more complicated than identifying a single subset of input variables that would together explain the output. There may be interactions that depend on contextual information, i.e., variables that reveal to be relevant only in some specific circumstances. In this setting, the contribution of this paper is to extend the random forest variable importances framework in order (i) to identify variables whose relevance is context-dependent and (ii) to characterize as precisely as possible the effect of contextual information on these variables. The usage and the relevance of our framework for highlighting context-dependent variables is illustrated on both artificial and real datasets.Comment: Accepted for presentation at UAI 201

Understanding Random Forests: From Theory to Practice

Data analysis and machine learning have become an integrative part of the modern scientific methodology, offering automated procedures for the prediction of a phenomenon based on past observations, unraveling underlying patterns in data and providing insights about the problem. Yet, caution should avoid using machine learning as a black-box tool, but rather consider it as a methodology, with a rational thought process that is entirely dependent on the problem under study. In particular, the use of algorithms should ideally require a reasonable understanding of their mechanisms, properties and limitations, in order to better apprehend and interpret their results. Accordingly, the goal of this thesis is to provide an in-depth analysis of random forests, consistently calling into question each and every part of the algorithm, in order to shed new light on its learning capabilities, inner workings and interpretability. The first part of this work studies the induction of decision trees and the construction of ensembles of randomized trees, motivating their design and purpose whenever possible. Our contributions follow with an original complexity analysis of random forests, showing their good computational performance and scalability, along with an in-depth discussion of their implementation details, as contributed within Scikit-Learn. In the second part of this work, we analyse and discuss the interpretability of random forests in the eyes of variable importance measures. The core of our contributions rests in the theoretical characterization of the Mean Decrease of Impurity variable importance measure, from which we prove and derive some of its properties in the case of multiway totally randomized trees and in asymptotic conditions. In consequence of this work, our analysis demonstrates that variable importances [...].Comment: PhD thesis. Source code available at https://github.com/glouppe/phd-thesi

Exploring helical dynamos with machine learning

We use ensemble machine learning algorithms to study the evolution of magnetic fields in magnetohydrodynamic (MHD) turbulence that is helically forced. We perform direct numerical simulations of helically forced turbulence using mean field formalism, with electromotive force (EMF) modeled both as a linear and non-linear function of the mean magnetic field and current density. The form of the EMF is determined using regularized linear regression and random forests. We also compare various analytical models to the data using Bayesian inference with Markov Chain Monte Carlo (MCMC) sampling. Our results demonstrate that linear regression is largely successful at predicting the EMF and the use of more sophisticated algorithms (random forests, MCMC) do not lead to significant improvement in the fits. We conclude that the data we are looking at is effectively low dimensional and essentially linear. Finally, to encourage further exploration by the community, we provide all of our simulation data and analysis scripts as open source IPython notebooks.Comment: accepted by A&A, 11 pages, 6 figures, 3 tables, data + IPython notebooks: https://github.com/fnauman/ML_alpha

Sparsity Oriented Importance Learning for High-dimensional Linear Regression

With now well-recognized non-negligible model selection uncertainty, data analysts should no longer be satisfied with the output of a single final model from a model selection process, regardless of its sophistication. To improve reliability and reproducibility in model choice, one constructive approach is to make good use of a sound variable importance measure. Although interesting importance measures are available and increasingly used in data analysis, little theoretical justification has been done. In this paper, we propose a new variable importance measure, sparsity oriented importance learning (SOIL), for high-dimensional regression from a sparse linear modeling perspective by taking into account the variable selection uncertainty via the use of a sensible model weighting. The SOIL method is theoretically shown to have the inclusion/exclusion property: When the model weights are properly around the true model, the SOIL importance can well separate the variables in the true model from the rest. In particular, even if the signal is weak, SOIL rarely gives variables not in the true model significantly higher important values than those in the true model. Extensive simulations in several illustrative settings and real data examples with guided simulations show desirable properties of the SOIL importance in contrast to other importance measures

From global to local MDI variable importances for random forests and when they are Shapley values

peer reviewedRandom forests have been widely used for their ability to provide so-called importance measures, which give insight at a global (per dataset) level on the relevance of input variables to predict a certain output. On the other hand, methods based on Shapley values have been introduced to refine the analysis of feature relevance in tree-based models to a local (per instance) level. In this context, we first show that the global Mean Decrease of Impurity (MDI) variable importance scores correspond to Shapley values under some conditions. Then, we derive a local MDI importance measure of variable relevance, which has a very natural connection with the global MDI measure and can be related to a new notion of local feature relevance. We further link local MDI importances with Shapley values and discuss them in the light of related measures from the literature. The measures are illustrated through experiments on several classification and regression problems

Modeling Customer Engagement with churn and upgrade prediction

Modeling customer engagement assists a business in identifying the high risk and high potential customers. A way to define high risk and high potential customers in a Software-as-a-Service (SaaS) business is to define them as customers with high potential to churn or upgrade. Identifying the high risk and high potential customers in time can help the business retain and grow revenue. This thesis uses churn and upgrade prediction classifiers to define a customer engagement score for a SaaS business. The classifiers used and compared in the research were logistic regression, random forest and XGBoost. The classifiers were trained using data from the case-company containing customer data such as user count and feature usage. To tackle class imbalance, the models were also trained with oversampled training data. The hyperparameters of each classifier were optimised using grid search. After training the models, performance of the classifiers on a test data was evaluated. In the end, the XGBoost classifiers outperformed the other classifiers in churn prediction. In predicting customer upgrades, the results were more mixed. Feature importances were also calculated, and the results showed that the importances differ for churn and upgrade prediction

SPLIT DECISIONS: PRACTICAL MACHINE LEARNING FOR EMPIRICAL LEGAL SCHOLARSHIP

Multivariable regression may be the most prevalent and useful task in social science. Empirical legal studies rely heavily on the ordinary least squares method. Conventional regression methods have attained credibility in court, but by no means do they dictate legal outcomes. Using the iconic Boston housing study as a source of price data, this Article introduces machine-learning regression methods. Although decision trees and forest ensembles lack the overt interpretability of linear regression, these methods reduce the opacity of black-box techniques by scoring the relative importance of dataset features. This Article will also address the theoretical tradeoff between bias and variance, as well as the importance of training, cross-validation, and reserving a holdout dataset for testing