Sambit Panda

Eric W. Bridgeford, Jaewon Chung, Brian Gilbert et al.

Causal inference studies whether the presence of a variable influences an observed outcome. As measured by quantities such as the "average treatment effect," this paradigm is employed across numerous biological fields, from vaccine and drug development to policy interventions. Unfortunately, the majority of these methods are often limited to univariate outcomes. Our work generalizes causal estimands to outcomes with any number of dimensions or any measurable space, and formulates traditional causal estimands for nominal variables as causal discrepancy tests. We propose a simple technique for adjusting universally consistent conditional independence tests and prove that these tests are universally consistent causal discrepancy tests. Numerical experiments illustrate that our method, Causal CDcorr, leads to improvements in both finite sample validity and power when compared to existing strategies. Our methods are all open source and available at github.com/ebridge2/cdcorr.

Haoyin Xu, Jayanta Dey, Sambit Panda et al.

Decision forests, including random forests and gradient boosting trees, remain the leading machine learning methods for many real-world data problems, especially on tabular data. However, most of the current implementations only operate in batch mode, and therefore cannot incrementally update when more data arrive. Several previous works developed streaming trees and ensembles to overcome this limitation. Nonetheless, we found that those state-of-the-art algorithms suffer from a number of drawbacks, including low accuracy on some problems and high memory usage on others. We therefore developed an extremely simple extension of decision trees: given new data, simply update existing trees by continuing to grow them, and replace some old trees with new ones to control the total number of trees. In a benchmark suite containing 72 classification problems (the OpenML-CC18 data suite), we illustrate that our approach, $\textit{Extremely Simple Streaming Forest}$ (XForest), does not suffer from either of the aforementioned limitations. On those datasets, we also demonstrate that our approach often performs as well as, and sometimes even better than, conventional batch decision forest algorithms. With a $\textit{zero-added-node}$ approach, XForest-Zero, we also further extend existing splits to new tasks, and this very efficient method only requires inference time. Thus, XForests establish a simple standard for streaming trees and forests that could readily be applied to many real-world problems.

Haoyin Xu, Kaleab A. Kinfu, Will LeVine et al.

Deep networks and decision forests (such as random forests and gradient boosted trees) are the leading machine learning methods for structured and tabular data, respectively. Many papers have empirically compared large numbers of classifiers on one or two different domains (e.g., on 100 different tabular data settings). However, a careful conceptual and empirical comparison of these two strategies using the most contemporary best practices has yet to be performed. Conceptually, we illustrate that both can be profitably viewed as "partition and vote" schemes. Specifically, the representation space that they both learn is a partitioning of feature space into a union of convex polytopes. For inference, each decides on the basis of votes from the activated nodes. This formulation allows for a unified basic understanding of the relationship between these methods. Empirically, we compare these two strategies on hundreds of tabular data settings, as well as several vision and auditory settings. Our focus is on datasets with at most 10,000 samples, which represent a large fraction of scientific and biomedical datasets. In general, we found forests to excel at tabular and structured data (vision and audition) with small sample sizes, whereas deep nets performed better on structured data with larger sample sizes. This suggests that further gains in both scenarios may be realized via further combining aspects of forests and networks. We will continue revising this technical report in the coming months with updated results.

Cencheng Shen, Sambit Panda, Joshua T. Vogelstein

Distance correlation has gained much recent attention in the data science community: the sample statistic is straightforward to compute and asymptotically equals zero if and only if independence, making it an ideal choice to discover any type of dependency structure given sufficient sample size. One major bottleneck is the testing process: because the null distribution of distance correlation depends on the underlying random variables and metric choice, it typically requires a permutation test to estimate the null and compute the p-value, which is very costly for large amount of data. To overcome the difficulty, in this paper we propose a chi-square test for distance correlation. Method-wise, the chi-square test is non-parametric, extremely fast, and applicable to bias-corrected distance correlation using any strong negative type metric or characteristic kernel. The test exhibits a similar testing power as the standard permutation test, and can be utilized for K-sample and partial testing. Theory-wise, we show that the underlying chi-square distribution well approximates and dominates the limiting null distribution in upper tail, prove the chi-square test can be valid and universally consistent for testing independence, and establish a testing power inequality with respect to the permutation test.

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.

Sambit Panda, Satish Palaniappan, Junhao Xiong et al.

We introduce hyppo, a unified library for performing multivariate hypothesis testing, including independence, two-sample, and k-sample testing. While many multivariate independence tests have R packages available, the interfaces are inconsistent and most are not available in Python. hyppo includes many state of the art multivariate testing procedures. The package is easy-to-use and is flexible enough to enable future extensions. The documentation and all releases are available at https://hyppo.neurodata.io.

Sambit Panda, Cencheng Shen, Joshua T. Vogelstein

Decision forests are widely used for classification and regression tasks. A lesser known property of tree-based methods is that one can construct a proximity matrix from the tree(s), and these proximity matrices are induced kernels. While there has been extensive research on the applications and properties of kernels, there is relatively little research on kernels induced by decision forests. We construct Kernel Mean Embedding Random Forests (KMERF), which induce kernels from random trees and/or forests using leaf-node proximity. We introduce the notion of an asymptotically characteristic kernel, and prove that KMERF kernels are asymptotically characteristic for both discrete and continuous data. Because KMERF is data-adaptive, we suspected it would outperform kernels selected a priori on finite sample data. We illustrate that KMERF nearly dominates current state-of-the-art kernel-based tests across a diverse range of high-dimensional two-sample and independence testing settings. Furthermore, our forest-based approach is interpretable, and provides feature importance metrics that readily distinguish important dimensions, unlike other high-dimensional non-parametric testing procedures. Hence, this work demonstrates the decision forest-based kernel can be more powerful and more interpretable than existing methods, flying in the face of conventional wisdom of the trade-off between the two.