Efficient and scalable non-parametric or semi-parametric regression analysis and density estimation are of crucial importance to the fields of statistics and machine learning. However, available methods are limited in their ability to handle large-scale data. We address this issue by developing a novel coreset construction for multivariate conditional transformation models (MCTMs) to enhance their scalability and training efficiency. To the best of our knowledge, these are the first coresets for semi-parametric distributional models. Our approach yields substantial data reduction via importance sampling. It ensures with high probability that the log-likelihood remains within multiplicative error bounds of $(1\pm\varepsilon)$ and thereby maintains statistical model accuracy. Compared to conventional full-parametric models, where coresets have been incorporated before, our semi-parametric approach exhibits enhanced adaptability, particularly in scenarios where complex distributions and non-linear relationships are present, but not fully understood. To address numerical problems associated with normalizing logarithmic terms, we follow a geometric approximation based on the convex hull of input data. This ensures feasible, stable, and accurate inference in scenarios involving large amounts of data. Numerical experiments demonstrate substantially improved computational efficiency when handling large and complex datasets, thus laying the foundation for a broad range of applications within the statistics and machine learning communities.

Concurrent measurements of neural activity at multiple scales, sometimes performed with multimodal techniques, become increasingly important for studying brain function. However, statistical methods for their concurrent analysis are currently lacking.

First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. The paper describes a number of new models for representing a joint distribution over integer-count variables. The authors argue that the default model that arises from Yang et al. is not satisfactory because it can only model negative correlations in order for the distribution to be normalized. They then consider a series of fixes for this including a new truncation method, using a quadratic base measure statistic (which they prove is necessary with everything else fixed), and finally a sub-linear sufficient statistic. This is a well written paper describing some nice solutions for representing count data.

Kernel embedding of distributions has led to many recent advances in machine learning. However, latent and low rank structures prevalent in real world distributions have rarely been taken into account in this setting. Furthermore, no prior work in kernel embedding literature has addressed the issue of robust embedding when the latent and low rank information are misspecified. In this paper, we propose a hierarchical low rank decomposition of kernels embeddings which can exploit such low rank structures in data while being robust to model misspecification. We also illustrate with empirical evidence that the estimated low rank embeddings lead to improved performance in density estimation.

The field of numerical optimization has recently seen a surge in the development of "novel" metaheuristic algorithms, inspired by metaphors derived from natural or human-made processes, which have been widely criticized for obscuring meaningful innovations and failing to distinguish themselves from existing approaches. Aiming to address these concerns, we investigate the applicability of statistical tests for comparing algorithms based on their search behavior. We utilize the cross-match statistical test to compare multivariate distributions and assess the solutions produced by 114 algorithms from the MEALPY library. These findings are incorporated into an empirical analysis aiming to identify algorithms with similar search behaviors.

Positioning is a prominent field of study, notably focusing on Visual Inertial Odometry (VIO) and Simultaneous Localization and Mapping (SLAM) methods. Despite their advancements, these methods often encounter dead-reckoning errors that leads to considerable drift in estimated platform motion especially during long traverses. In such cases, the drift error is not negligible and should be rectified. Our proposed approach minimizes the drift error by correcting the estimated motion generated by any SLAM method at each epoch. Our methodology treats positioning measurements rendered by the SLAM solution as random variables formulated jointly in a multivariate distribution. In this setting, The correction of the drift becomes equivalent to finding the mode of this multivariate distribution which jointly maximizes the likelihood of a set of relevant geo-spatial priors about the platform motion and environment. Our method is integrable into any SLAM/VIO method as an correction module. Our experimental results shows the effectiveness of our approach in minimizing the drift error by 10x in long treverses.

We present a reformulation of the information bottleneck (IB) problem in terms of copula, using the equivalence between mutual information and negative copula entropy. Focusing on the Gaussian copula we extend the analytical IB solution available for the multivariate Gaussian case to distributions with a Gaussian dependence structure but arbitrary marginal densities, also called meta-Gaussian distributions. This opens new possibles applications of IB to continuous data and provides a solution more robust to outliers.

Concurrent measurements of neural activity at multiple scales, sometimes performed with multimodal techniques, become increasingly important for studying brain function. However, statistical methods for their concurrent analysis are currently lacking. Here we introduce such techniques in a framework based on vine copulas with mixed margins to construct multivariate stochastic models. These models can describe detailed mixed interactions between discrete variables such as neural spike counts, and continuous variables such as local field potentials. We propose efficient methods for likelihood calculation, inference, sampling and mutual information estimation within this framework. We test our methods on simulated data and demonstrate applicability on mixed data generated by a biologically realistic neural network. Our methods hold the promise to considerably improve statistical analysis of neural data recorded simultaneously at different scales.

Some defenders of so-called'artificial intelligence' believe that machines can understand language. In particular, Søgaard has argued in this journal for a thesis of this sort, on the basis of the idea (1) that where there is semantics there is also understanding and (2) that machines are not only capable of what he calls'inferential semantics', but even that they can (with the help of inputs from sensors) 'learn' referential semantics (Søgaard, 2022). We show that he goes wrong because he pays insufficient attention to the difference between language as used by humans and the sequences of inert of symbols which arise when language is stored on hard drives or in books in libraries. So-called large language models (LLMs), such as the ones built into chatGPT and GPT-4, contain encodings of natural language symbol sequences which represent morphological and syntactic relationships between their constituent symbols. This means that a model of this sort can represent both the internal structure of words and the ways in which words are put together to form phrases, sentences and paragraphs.

We introduce a new approach to nonlinear sufficient dimension reduction in cases where both the predictor and the response are distributional data, modeled as members of a metric space. Our key step is to build universal kernels (cc-universal) on the metric spaces, which results in reproducing kernel Hilbert spaces for the predictor and response that are rich enough to characterize the conditional independence that determines sufficient dimension reduction. For univariate distributions, we construct the universal kernel using the Wasserstein distance, while for multivariate distributions, we resort to the sliced Wasserstein distance. The sliced Wasserstein distance ensures that the metric space possesses similar topological properties to the Wasserstein space while also offering significant computation benefits. Numerical results based on synthetic data show that our method outperforms possible competing methods. The method is also applied to several data sets, including fertility and mortality data and Calgary temperature data.