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We describe group sequential tests which efficiently incorporate information from multiple endpoints allowing for early stopping at pre-planned interim analyses. We formulate a testing procedure where several outcomes are examined, and interim decisions are based on a global summary statistic. An error spending approach to this problem is defined which allows for unpredictable group sizes and nuisance parameters such as the correlation between endpoints. We present and compare three methods for implementation of the testing procedure including numerical integration, the Delta approximation and Monte Carlo simulation. In our evaluation, numerical integration techniques performed best for implementation with error rate calculations accurate to five decimal places. Our proposed testing method is flexible and accommodates summary statistics derived from general, non-linear functions of endpoints informed by the statistical model. Type 1 error rates are controlled, and sample size calculations can easily be performed to satisfy power requirements.

Popular artificial neural networks (ANN) optimize parameters for unidirectional value propagation, assuming some guessed parametrization type like Multi-Layer Perceptron (MLP) or Kolmogorov-Arnold Network (KAN). In contrast, for biological neurons e.g. "it is not uncommon for axonal propagation of action potentials to happen in both directions" \cite{axon} - suggesting they are optimized to continuously operate in multidirectional way. Additionally, statistical dependencies a single neuron could model is not just (expected) value dependence, but entire joint distributions including also higher moments. Such agnostic joint distribution neuron would allow for multidirectional propagation (of distributions or values) e.g. $\rho(x|y,z)$ or $\rho(y,z|x)$ by substituting to $\rho(x,y,z)$ and normalizing. There will be discussed Hierarchical Correlation Reconstruction (HCR) for such neuron model: assuming $\rho(x,y,z)=\sum_{ijk} a_{ijk} f_i(x) f_j(y) f_k(z)$ type parametrization of joint distribution with polynomial basis $f_i$, which allows for flexible, inexpensive processing including nonlinearities, direct model estimation and update, trained through standard backpropagation or novel ways for such structure up to tensor decomposition. Using only pairwise (input-output) dependencies, its expected value prediction becomes KAN-like with trained activation functions as polynomials, can be extended by adding higher order dependencies through included products - in conscious interpretable way, allowing for multidirectional propagation of both values and probability densities.

The high dimensional nature of genomics data complicates feature selection, in particular in low sample size studies - not uncommon in clinical prediction settings. It is widely recognized that complementary data on the features, `co-data', may improve results. Examples are prior feature groups or p-values from a related study. Such co-data are ubiquitous in genomics settings due to the availability of public repositories. Yet, the uptake of learning methods that structurally use such co-data is limited. We review guided adaptive shrinkage methods: a class of regression-based learners that use co-data to adapt the shrinkage parameters, crucial for the performance of those learners. We discuss technical aspects, but also the applicability in terms of types of co-data that can be handled. This class of methods is contrasted with several others. In particular, group-adaptive shrinkage is compared with the better-known sparse group-lasso by evaluating feature selection. Finally, we demonstrate the versatility of the guided shrinkage methodology by showing how to `do-it-yourself': we integrate implementations of a co-data learner and the spike-and-slab prior for the purpose of improving feature selection in genetics studies.

Community detection algorithms try to extract a mesoscale structure from the available network data, generally avoiding any explicit assumption regarding the quantity and quality of information conveyed by specific sets of edges. In this paper, we show that the core of ideological/discursive communities on X/Twitter can be effectively identified by uncovering the most informative interactions in an authors-audience bipartite network through a maximum-entropy null model. The analysis is performed considering three X/Twitter datasets related to the main political events of 2022 in Italy, using as benchmarks four state-of-the-art algorithms - three descriptive, one inferential -, and manually annotating nearly 300 verified users based on their political affiliation. In terms of information content, the communities obtained with the entropy-based algorithm are comparable to those obtained with some of the benchmarks. However, such a methodology on the authors-audience bipartite network: uses just a small sample of the available data to identify the central users of each community; returns a neater partition of the user set in just a few, easy to interpret, communities; clusters well-known political figures in a way that better matches the political alliances when compared with the benchmarks. Our results provide an important insight into online debates, highlighting that online interaction networks are mostly shaped by the activity of a small set of users who enjoy public visibility even outside social media.

The problem of community detection in multi-layer undirected networks has received considerable attention in recent years. However, practical scenarios often involve multi-layer bipartite networks, where each layer consists of two distinct types of nodes. Existing community detection algorithms tailored for multi-layer undirected networks are not directly applicable to multi-layer bipartite networks. To address this challenge, this paper introduces a novel multi-layer degree-corrected stochastic co-block model specifically designed to capture the underlying community structure within multi-layer bipartite networks. Within this framework, we propose an efficient debiased spectral co-clustering algorithm for detecting nodes' communities. We establish the consistent estimation property of our proposed algorithm and demonstrate that an increased number of layers in bipartite networks improves the accuracy of community detection. Through extensive numerical experiments, we showcase the superior performance of our algorithm compared to existing methods. Additionally, we validate our algorithm by applying it to real-world multi-layer network datasets, yielding meaningful and insightful results.

A fundamental problem associated with the task of network reconstruction from dynamical or behavioral data consists in determining the most appropriate model complexity in a manner that prevents overfitting, and produces an inferred network with a statistically justifiable number of edges. The status quo in this context is based on $L_{1}$ regularization combined with cross-validation. However, besides its high computational cost, this commonplace approach unnecessarily ties the promotion of sparsity with weight "shrinkage". This combination forces a trade-off between the bias introduced by shrinkage and the network sparsity, which often results in substantial overfitting even after cross-validation. In this work, we propose an alternative nonparametric regularization scheme based on hierarchical Bayesian inference and weight quantization, which does not rely on weight shrinkage to promote sparsity. Our approach follows the minimum description length (MDL) principle, and uncovers the weight distribution that allows for the most compression of the data, thus avoiding overfitting without requiring cross-validation. The latter property renders our approach substantially faster to employ, as it requires a single fit to the complete data. As a result, we have a principled and efficient inference scheme that can be used with a large variety of generative models, without requiring the number of edges to be known in advance. We also demonstrate that our scheme yields systematically increased accuracy in the reconstruction of both artificial and empirical networks. We highlight the use of our method with the reconstruction of interaction networks between microbial communities from large-scale abundance samples involving in the order of $10^{4}$ to $10^{5}$ species, and demonstrate how the inferred model can be used to predict the outcome of interventions in the system.

The notion of Laplacian of a graph can be generalized to simplicial complexes and hypergraphs, and contains information on the topology of these structures. Even for a graph, the consideration of associated simplicial complexes is interesting to understand its shape. Whereas the Laplacian of a graph has a simple probabilistic interpretation as the generator of a continuous time Markov chain on the graph, things are not so direct when considering simplicial complexes. We define here new Markov chains on simplicial complexes. For a given order~$k$, the state space is the set of $k$-cycles that are chains of $k$-simplexes with null boundary. This new framework is a natural generalization of the canonical Markov chains on graphs. We show that the generator of our Markov chain is the upper Laplacian defined in the context of algebraic topology for discrete structure. We establish several key properties of this new process: in particular, when the number of vertices is finite, the Markov chain is positive recurrent. This result is not trivial, since the cycles can loop over themselves an unbounded number of times. We study the diffusive limits when the simplicial complexes under scrutiny are a sequence of ever refining triangulations of the flat torus. Using the analogy between singular and Hodge homologies, we express this limit as valued in the set of currents. The proof of tightness and the identification of the limiting martingale problem make use of the flat norm and carefully controls of the error terms in the convergence of the generator. Uniqueness of the solution to the martingale problem is left open. An application to hole detection is carried.

This manuscript derives locally weighted ensemble Kalman methods from the point of view of ensemble-based function approximation. This is done by using pointwise evaluations to build up a local linear or quadratic approximation of a function, tapering off the effect of distant particles via local weighting. This introduces a candidate method (the locally weighted Ensemble Kalman method for inversion) with the motivation of combining some of the strengths of the particle filter (ability to cope with nonlinear maps and non-Gaussian distributions) and the Ensemble Kalman filter (no filter degeneracy).

Classical sequential recommendation models generally adopt ID embeddings to store knowledge learned from user historical behaviors and represent items. However, these unique IDs are challenging to be transferred to new domains. With the thriving of pre-trained language model (PLM), some pioneer works adopt PLM for pre-trained recommendation, where modality information (e.g., text) is considered universal across domains via PLM. Unfortunately, the behavioral information in ID embeddings is still verified to be dominating in PLM-based recommendation models compared to modality information and thus limits these models' performance. In this work, we propose a novel ID-centric recommendation pre-training paradigm (IDP), which directly transfers informative ID embeddings learned in pre-training domains to item representations in new domains. Specifically, in pre-training stage, besides the ID-based sequential model for recommendation, we also build a Cross-domain ID-matcher (CDIM) learned by both behavioral and modality information. In the tuning stage, modality information of new domain items is regarded as a cross-domain bridge built by CDIM. We first leverage the textual information of downstream domain items to retrieve behaviorally and semantically similar items from pre-training domains using CDIM. Next, these retrieved pre-trained ID embeddings, rather than certain textual embeddings, are directly adopted to generate downstream new items' embeddings. Through extensive experiments on real-world datasets, both in cold and warm settings, we demonstrate that our proposed model significantly outperforms all baselines. Codes will be released upon acceptance.

Recent advances in 3D fully convolutional networks (FCN) have made it feasible to produce dense voxel-wise predictions of volumetric images. In this work, we show that a multi-class 3D FCN trained on manually labeled CT scans of several anatomical structures (ranging from the large organs to thin vessels) can achieve competitive segmentation results, while avoiding the need for handcrafting features or training class-specific models. To this end, we propose a two-stage, coarse-to-fine approach that will first use a 3D FCN to roughly define a candidate region, which will then be used as input to a second 3D FCN. This reduces the number of voxels the second FCN has to classify to ~10% and allows it to focus on more detailed segmentation of the organs and vessels. We utilize training and validation sets consisting of 331 clinical CT images and test our models on a completely unseen data collection acquired at a different hospital that includes 150 CT scans, targeting three anatomical organs (liver, spleen, and pancreas). In challenging organs such as the pancreas, our cascaded approach improves the mean Dice score from 68.5 to 82.2%, achieving the highest reported average score on this dataset. We compare with a 2D FCN method on a separate dataset of 240 CT scans with 18 classes and achieve a significantly higher performance in small organs and vessels. Furthermore, we explore fine-tuning our models to different datasets. Our experiments illustrate the promise and robustness of current 3D FCN based semantic segmentation of medical images, achieving state-of-the-art results. Our code and trained models are available for download: //github.com/holgerroth/3Dunet_abdomen_cascade.