Uniformity testing is arguably one of the most fundamental distribution testing problems.

Reasons for score: ---------------------- Lack of clarity regarding some of the main theoretical and empirical results (see detailed comments and improvements for details). Assuming the authors address these points of clarification, my main concern is that the analyses that the authors present does not provide a practical method that practitioners can use: if I am understanding correctly, the conclusion is regularization might somewhat reduce the effects of confounding. But the authors do not provide a way to do sensitivity analysis to check how much confounding still exists or what to do about it; or what assumptions are required for their method to completely identify the causal estimands. Detailed comments: ------------------ Regarding the theory: - Some of my confusion arises from the fact that I do not fully understand what the authors mean by a "mixing matrix" and \ell "sources". I assumed that it is a random matrix based on their experimental setup where is drawn from a gaussian distribution.

This study explores the application of evolutionary generative algorithms in music production to preserve and enhance human creativity. By integrating human feedback into Differential Evolution algorithms, we produced six songs that were submitted to international record labels, all of which received contract offers. In addition to testing the commercial viability of these methods, this paper examines the long-term implications of content generation using traditional machine learning methods compared with evolutionary algorithms. Specifically, as current generative techniques continue to scale, the potential for computer-generated content to outpace human creation becomes likely. This trend poses a risk of exhausting the pool of human-created training data, potentially forcing generative machine learning models to increasingly depend on their random input functions for generating novel content. In contrast to a future of content generation guided by aimless random functions, our approach allows for individualized creative exploration, ensuring that computer-assisted content generation methods are human-centric and culturally relevant through time.

The Gromov-Wasserstein distance is a notable extension of optimal transport. In contrast to the classic Wasserstein distance, it solves a quadratic assignment problem that minimizes the pair-wise distance distortion under the transportation of distributions and thus could apply to distributions in different spaces. These properties make Gromov-Wasserstein widely applicable to many fields, such as computer graphics and machine learning. However, the computation of the Gromov-Wasserstein distance and transport plan is expensive. The well-known Entropic Gromov-Wasserstein approach has a cubic complexity since the matrix multiplication operations need to be repeated in computing the gradient of Gromov-Wasserstein loss. This becomes a key bottleneck of the method. Currently, existing methods accelerate the computation focus on sampling and approximation, which leads to low accuracy or incomplete transport plan. In this work, we propose a novel method to accelerate accurate gradient computation by dynamic programming techniques, reducing the complexity from cubic to quadratic. In this way, the original computational bottleneck is broken and the new entropic solution can be obtained with total quadratic time, which is almost optimal complexity. Furthermore, it can be extended to some variants easily. Extensive experiments validate the efficiency and effectiveness of our method.

We propose the Plaid Atoms Model (PAM), a novel Bayesian nonparametric model for grouped data. Founded on an idea of `atom skipping', PAM is part of a well-established category of models that generate dependent random distributions and clusters across multiple groups. Atom skipping referrs to stochastically assigning 0 weights to atoms in an infinite mixture. Deploying atom skipping across groups, PAM produces a dependent clustering pattern with overlapping and non-overlapping clusters across groups. As a result, interpretable posterior inference is possible such as reporting the posterior probability of a cluster being exclusive to a single group or shared among a subset of groups. We discuss the theoretical properties of the proposed and related models. Minor extensions of the proposed model for multivariate or count data are presented. Simulation studies and applications using real-world datasets illustrate the performance of the new models with comparison to existing models.

We develop a new technique for proving distribution testing lower bounds for properties defined by inequalities involving the bin probabilities of the distribution in question. Using this technique we obtain new lower bounds for monotonicity testing over discrete cubes and tight lower bounds for log-concavity testing. Our basic technique involves constructing a pair of moment-matching families of distributions by tweaking the probabilities of pairs of bins so that one family maintains the defining inequalities while the other violates them.

A reservoir computer is a type of dynamical system arranged to do computation. Typically, a reservoir computer is constructed by connecting a large number of nonlinear nodes in a network that includes recurrent connections. In order to achieve accurate results, the reservoir usually contains hundreds to thousands of nodes. This high dimensionality makes it difficult to analyze the reservoir computer using tools from dynamical systems theory. Additionally, the need to create and connect large numbers of nonlinear nodes makes it difficult to design and build analog reservoir computers that can be faster and consume less power than digital reservoir computers. We demonstrate here that a reservoir computer may be divided into two parts; a small set of nonlinear nodes (the reservoir), and a separate set of time-shifted reservoir output signals. The time-shifted output signals serve to increase the rank and memory of the reservoir computer, and the set of nonlinear nodes may create an embedding of the input dynamical system. We use this time-shifting technique to obtain excellent performance from an opto-electronic delay-based reservoir computer with only a small number of virtual nodes. Because only a few nonlinear nodes are required, construction of a reservoir computer becomes much easier, and delay-based reservoir computers can operate at much higher speeds.