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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.
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We introduce Geomstats, an open-source Python toolbox for computations and statistics on nonlinear manifolds, such as hyperbolic spaces, spaces of symmetric positive definite matrices, Lie groups of transformations, and many more. We provide object-oriented and extensively unit-tested implementations. Among others, manifolds come equipped with families of Riemannian metrics, with associated exponential and logarithmic maps, geodesics and parallel transport. Statistics and learning algorithms provide methods for estimation, clustering and dimension reduction on manifolds. All associated operations are vectorized for batch computation and provide support for different execution backends, namely NumPy, PyTorch and TensorFlow, enabling GPU acceleration. This paper presents the package, compares it with related libraries and provides relevant code examples. We show that Geomstats provides reliable building blocks to foster research in differential geometry and statistics, and to democratize the use of Riemannian geometry in machine learning applications. The source code is freely available under the MIT license at url{geomstats.ai}.
Dealing with biased data samples is a common task across many statistical fields. In survey sampling, bias often occurs due to unrepresentative samples. In causal studies with observational data, the treated versus untreated group assignment is often correlated with covariates, i.e., not random. Empirical calibration is a generic weighting method that presents a unified view on correcting or reducing the data biases for the tasks mentioned above. We provide a Python library EC to compute the empirical calibration weights. The problem is formulated as convex optimization and solved efficiently in the dual form. Compared to existing software, EC is both more efficient and robust. EC also accommodates different optimization objectives, supports weight clipping, and allows inexact calibration, which improves usability. We demonstrate its usage across various experiments with both simulated and real-world data.
The R package MfUSampler provides Monte Carlo Markov Chain machinery for generating samples from multivariate probability distributions using univariate sampling algorithms such as Slice Sampler and Adaptive Rejection Sampler. The sampler function performs a full cycle of univariate sampling steps, one coordinate at a time. In each step, the latest sample values obtained for other coordinates are used to form the conditional distributions. The concept is an extension of Gibbs sampling where each step involves, not an independent sample from the conditional distribution, but a Markov transition for which the conditional distribution is invariant. The software relies on proportionality of conditional distributions to the joint distribution to implement a thin wrapper for producing conditionals. Examples illustrate basic usage as well as methods for improving performance. By encapsulating the multivariate-from-univariate logic, MfUSampler provides a reliable library for rapid prototyping of custom Bayesian models while allowing for incremental performance optimizations such as utilization of conjugacy, conditional independence, and porting function evaluations to compiled languages.
Complex data structures such as time series are increasingly present in modern data science problems. A fundamental question is whether two such time-series are statistically dependent. Many current approaches make parametric assumptions on the random processes, only detect linear association, require multiple tests, or forfeit power in high-dimensional, nonlinear settings. Estimating the distribution of any test statistic under the null is non-trivial, as the permutation test is invalid. This work juxtaposes distance correlation (Dcorr) and multiscale graph correlation (MGC) from independence testing literature and block permutation from time series analysis to address these challenges. The proposed nonparametric procedure is valid and consistent, building upon prior work by characterizing the geometry of the relationship, estimating the time lag at which dependence is maximized, avoiding the need for multiple testing, and exhibiting superior power in high-dimensional, low sample size, nonlinear settings. Neural connectivity is analyzed via fMRI data, revealing linear dependence of signals within the visual network and default mode network, and nonlinear relationships in other networks. This work uncovers a first-resort data analysis tool with open-source code available, directly impacting a wide range of scientific disciplines.
This is an up-to-date introduction to, and overview of, marginal likelihood computation for model selection and hypothesis testing. Computing normalizing constants of probability models (or ratio of constants) is a fundamental issue in many applications in statistics, applied mathematics, signal processing and machine learning. This article provides a comprehensive study of the state-of-the-art of the topic. We highlight limitations, benefits, connections and differences among the different techniques. Problems and possible solutions with the use of improper priors are also described. Some of the most relevant methodologies are compared through theoretical comparisons and numerical experiments.
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