Gaussian processes (GPs) furnish accurate nonlinear predictions with well-calibrated uncertainty. However, the typical GP setup has a built-in stationarity assumption, making it ill-suited for modeling data from processes with sudden changes, or "jumps" in the output variable. The "jump GP" (JGP) was developed for modeling data from such processes, combining local GPs and latent "level" variables under a joint inferential framework. But joint modeling can be fraught with difficulty. We aim to simplify by suggesting a more modular setup, eschewing joint inference but retaining the main JGP themes: (a) learning optimal neighborhood sizes that locally respect manifolds of discontinuity; and (b) a new cluster-based (latent) feature to capture regions of distinct output levels on both sides of the manifold. We show that each of (a) and (b) separately leads to dramatic improvements when modeling processes with jumps. In tandem (but without requiring joint inference) that benefit is compounded, as illustrated on real and synthetic benchmark examples from the recent literature.

While progress has been made in identifying common genetic variants associated with human diseases, for most of common complex diseases, the identified genetic variants only account for a small proportion of heritability. Challenges remain in finding additional unknown genetic variants predisposing to complex diseases. With the advance in next-generation sequencing technologies, sequencing studies have become commonplace in genetic research. The ongoing exome-sequencing and whole-genome-sequencing studies generate a massive amount of sequencing variants and allow researchers to comprehensively investigate their role in human diseases. The discovery of new disease-associated variants can be enhanced by utilizing powerful and computationally efficient statistical methods. In this paper, we propose a functional analysis of variance (FANOVA) method for testing an association of sequence variants in a genomic region with a qualitative trait. The FANOVA has a number of advantages: (1) it tests for a joint effect of gene variants, including both common and rare; (2) it fully utilizes linkage disequilibrium and genetic position information; and (3) allows for either protective or risk-increasing causal variants. Through simulations, we show that FANOVA outperform two popularly used methods - SKAT and a previously proposed method based on functional linear models (FLM), - especially if a sample size of a study is small and/or sequence variants have low to moderate effects. We conduct an empirical study by applying three methods (FANOVA, SKAT and FLM) to sequencing data from Dallas Heart Study. While SKAT and FLM respectively detected ANGPTL 4 and ANGPTL 3 associated with obesity, FANOVA was able to identify both genes associated with obesity.

The paper studies the DIverse MultiPLEx Signed Generalized Random Dot Product Graph (DIMPLE-SGRDPG) network model (Pensky (2024)), where all layers of the network have the same collection of nodes. In addition, all layers can be partitioned into groups such that the layers in the same group are embedded in the same ambient subspace but otherwise matrices of connection probabilities can be all different. This setting includes majority of multilayer network models as its particular cases. The key task in this model is to recover the groups of layers with unique subspace structures, since the case where all layers of the network are embedded in the same subspace has been fairly well studied. Until now, clustering of layers in such networks was based on the layer-per-layer analysis, which required the multilayer network to be sufficiently dense. Nevertheless, in this paper we succeeded in pooling information in all layers together and providing a tensor-based methodology that ensures perfect clustering for a much sparser network. Our theoretical results, established under intuitive non-restrictive assumptions, assert that the new technique achieves perfect clustering under sparsity conditions that, up to logarithmic factors, coincide with the computational lower bound derived for a much simpler model.

The evaluation of large language model (LLM) outputs is increasingly performed by other LLMs, a setup commonly known as "LLM-as-a-judge", or autograders. While autograders offer a scalable alternative to human evaluation, they have shown mixed reliability and may exhibit systematic biases, depending on response type, scoring methodology, domain specificity, or other factors. Here we propose a statistical framework based on Bayesian generalised linear models (GLMs) that enables researchers to simultaneously assess their autograders while addressing their primary research questions (e.g., LLM evaluation). Our approach models evaluation outcomes (e.g., scores or pairwise preferences) as a function of properties of the grader (e.g., human vs. autograder) and the evaluated item (e.g., response length or the LLM that generated it), allowing for explicit quantification of scoring differences and potential biases within a unified framework. In addition, our method can be used to augment traditional metrics such as inter-rater agreement, by providing uncertainty estimates and clarifying sources of disagreement. Overall, this approach contributes to more robust and interpretable use of autograders in LLM evaluation, enabling both performance analysis and bias detection.

The Transiting Exoplanet Survey Satellite (TESS) has surveyed nearly the entire sky in Full-Frame Image mode with a time resolution of 200 seconds to 30 minutes and a temporal baseline of at least 27 days. In addition to the primary goal of discovering new exoplanets, TESS is exceptionally capable at detecting variable stars, and in particular short-period eclipsing binaries which are relatively common, making up a few percent of all stars, and represent powerful astrophysical laboratories for deep investigations of stellar formation and evolution. We combed Sectors 1-82 of TESS Full-Frame Image data searching for eclipsing binary stars using a neural network that identified ~1.2 million stars with eclipse-like features. Of these, we have performed an in-depth analysis on ~60,000 targets using automated methods and manual inspection by citizen scientists. Here we present a catalog of 10001 uniformly-vetted and -validated eclipsing binary stars that passed all our ephemeris and photocenter tests, as well as complementary visual inspection. Of these, 7936 are new eclipsing binaries while the remaining 2065 are known systems for which we update the published ephemerides. We outline the detection and analysis of the targets, discuss the properties of the sample, and highlight potentially interesting systems. Finally, we also provide a list of ~900,000 unvetted and unvalidated targets for which the neural network found eclipse-like features with a score higher than 0.9, and for which there are no known eclipsing binaries within a sky-projected separation of a TESS pixel (~21 arcsec).

Current Multimodal Large Language Models (MLLMs) excel in general visual reasoning but remain underexplored in Abstract Visual Reasoning (AVR), which demands higher-order reasoning to identify abstract rules beyond simple perception. Existing AVR benchmarks focus on single-step reasoning, emphasizing the end result but neglecting the multi-stage nature of reasoning process. Past studies found MLLMs struggle with these benchmarks, but it doesn't explain how they fail. To address this gap, we introduce MultiStAR, a Multi-Stage AVR benchmark, based on RAVEN, designed to assess reasoning across varying levels of complexity. Additionally, existing metrics like accuracy only focus on the final outcomes while do not account for the correctness of intermediate steps. Therefore, we propose a novel metric, MSEval, which considers the correctness of intermediate steps in addition to the final outcomes. We conduct comprehensive experiments on MultiStAR using 17 representative close-source and open-source MLLMs. The results reveal that while existing MLLMs perform adequately on basic perception tasks, they continue to face challenges in more complex rule detection stages.

The decomposition of a signal is a fundamental tool in many fields of research, including signal processing, geophysics, astrophysics, engineering, medicine, and many more. By breaking down complex signals into simpler oscillatory components we can enhance the understanding and processing of the data, unveiling hidden information contained in them. Traditional methods, such as Fourier analysis and wavelet transforms, which are effective in handling mono-dimensional stationary signals struggle with non-stationary data sets and they require, this is the case of the wavelet, the selection of predefined basis functions. In contrast, the Empirical Mode Decomposition (EMD) method and its variants, such as Iterative Filtering (IF), have emerged as effective nonlinear approaches, adapting to signals without any need for a priori assumptions. To accelerate these methods, the Fast Iterative Filtering (FIF) algorithm was developed, and further extensions, such as Multivariate FIF (MvFIF) and Multidimensional FIF (FIF2), have been proposed to handle higher-dimensional data. In this work, we introduce the Multidimensional and Multivariate Fast Iterative Filtering (MdMvFIF) technique, an innovative method that extends FIF to handle data that vary simultaneously in space and time. This new algorithm is capable of extracting Intrinsic Mode Functions (IMFs) from complex signals that vary in both space and time, overcoming limitations found in prior methods. The potentiality of the proposed method is demonstrated through applications to artificial and real-life signals, highlighting its versatility and effectiveness in decomposing multidimensional and multivariate nonstationary signals. The MdMvFIF method offers a powerful tool for advanced signal analysis across many scientific and engineering disciplines.