Ronan Perry

Ronan Perry, Julius von Kügelgen, Bernhard Schölkopf · eth-zurich

Machine learning approaches commonly rely on the assumption of independent and identically distributed (i.i.d.) data. In reality, however, this assumption is almost always violated due to distribution shifts between environments. Although valuable learning signals can be provided by heterogeneous data from changing distributions, it is also known that learning under arbitrary (adversarial) changes is impossible. Causality provides a useful framework for modeling distribution shifts, since causal models encode both observational and interventional distributions. In this work, we explore the sparse mechanism shift hypothesis, which posits that distribution shifts occur due to a small number of changing causal conditionals. Motivated by this idea, we apply it to learning causal structure from heterogeneous environments, where i.i.d. data only allows for learning an equivalence class of graphs without restrictive assumptions. We propose the Mechanism Shift Score (MSS), a score-based approach amenable to various empirical estimators, which provably identifies the entire causal structure with high probability if the sparse mechanism shift hypothesis holds. Empirically, we verify behavior predicted by the theory and compare multiple estimators and score functions to identify the best approaches in practice. Compared to other methods, we show how MSS bridges a gap by both being nonparametric as well as explicitly leveraging sparse changes.

Ronan Perry, Gavin Mischler, Richard Guo et al.

As data are generated more and more from multiple disparate sources, multiview data sets, where each sample has features in distinct views, have ballooned in recent years. However, no comprehensive package exists that enables non-specialists to use these methods easily. mvlearn is a Python library which implements the leading multiview machine learning methods. Its simple API closely follows that of scikit-learn for increased ease-of-use. The package can be installed from Python Package Index (PyPI) and the conda package manager and is released under the MIT open-source license. The documentation, detailed examples, and all releases are available at https://mvlearn.github.io/.

Sambit Panda, Cencheng Shen, Ronan Perry et al.

The K-sample testing problem involves determining whether K groups of data points are each drawn from the same distribution. Analysis of variance is arguably the most classical method to test mean differences, along with several recent methods to test distributional differences. In this paper, we demonstrate the existence of a transformation that allows K-sample testing to be carried out using any dependence measure. Consequently, universally consistent K-sample testing can be achieved using a universally consistent dependence measure, such as distance correlation and the Hilbert-Schmidt independence criterion. This enables a wide range of dependence measures to be easily applied to K-sample testing.

Adam Li, Ronan Perry, Chester Huynh et al.

Decision forests (Forests), in particular random forests and gradient boosting trees, have demonstrated state-of-the-art accuracy compared to other methods in many supervised learning scenarios. In particular, Forests dominate other methods in tabular data, that is, when the feature space is unstructured, so that the signal is invariant to a permutation of the feature indices. However, in structured data lying on a manifold (such as images, text, and speech) deep networks (Networks), specifically convolutional deep networks (ConvNets), tend to outperform Forests. We conjecture that at least part of the reason for this is that the input to Networks is not simply the feature magnitudes, but also their indices. In contrast, naive Forest implementations fail to explicitly consider feature indices. A recently proposed Forest approach demonstrates that Forests, for each node, implicitly sample a random matrix from some specific distribution. These Forests, like some classes of Networks, learn by partitioning the feature space into convex polytopes corresponding to linear functions. We build on that approach and show that one can choose distributions in a manifold-aware fashion to incorporate feature locality. We demonstrate the empirical performance on data whose features live on three different manifolds: a torus, images, and time-series. Moreover, we demonstrate its strength in multivariate simulated settings and also show superiority in predicting surgical outcome in epilepsy patients and predicting movement direction from raw stereotactic EEG data from non-motor brain regions. In all simulations and real data, Manifold Oblique Random Forest (MORF) algorithm outperforms approaches that ignore feature space structure and challenges the performance of ConvNets. Moreover, MORF runs fast and maintains interpretability and theoretical justification.

Ronan Perry, Ronak Mehta, Richard Guo et al.

Information-theoretic quantities, such as conditional entropy and mutual information, are critical data summaries for quantifying uncertainty. Current widely used approaches for computing such quantities rely on nearest neighbor methods and exhibit both strong performance and theoretical guarantees in certain simple scenarios. However, existing approaches fail in high-dimensional settings and when different features are measured on different scales.We propose decision forest-based adaptive nearest neighbor estimators and show that they are able to effectively estimate posterior probabilities, conditional entropies, and mutual information even in the aforementioned settings.We provide an extensive study of efficacy for classification and posterior probability estimation, and prove certain forest-based approaches to be consistent estimators of the true posteriors and derived information-theoretic quantities under certain assumptions. In a real-world connectome application, we quantify the uncertainty about neuron type given various cellular features in the Drosophila larva mushroom body, a key challenge for modern neuroscience.