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Compositional data arise in many real-life applications and versatile methods for properly analyzing this type of data in the regression context are needed. When parametric assumptions do not hold or are difficult to verify, non-parametric regression models can provide a convenient alternative method for prediction. To this end, we consider an extension to the classical $k$--$NN$ regression, termed $\alpha$--$k$--$NN$ regression, that yields a highly flexible non-parametric regression model for compositional data through the use of the $\alpha$-transformation. Unlike many of the recommended regression models for compositional data, zeros values (which commonly occur in practice) are not problematic and they can be incorporated into the proposed models without modification. Extensive simulation studies and real-life data analyses highlight the advantage of using these non-parametric regressions for complex relationships between the compositional response data and Euclidean predictor variables. Both suggest that $\alpha$--$k$--$NN$ regression can lead to more accurate predictions compared to current regression models which assume a, sometimes restrictive, parametric relationship with the predictor variables. In addition, the $\alpha$--$k$--$NN$ regression, in contrast to current regression techniques, enjoys a high computational efficiency rendering it highly attractive for use with large scale, massive, or big data.

Several new network information dimension definitions have been proposed in recent decades, expanding the scope of applicability of this seminal tool. This paper proposes a new definition based on Deng entropy and d-summability (a concept from geometric measure theory). We will prove to what extent the new formulation will be useful in the theoretical and applied points of view.

Nominal assortativity (or discrete assortativity) is widely used to characterize group mixing patterns and homophily in networks, enabling researchers to analyze how groups interact with one another. Here we demonstrate that the measure presents severe shortcomings when applied to networks with unequal group sizes and asymmetric mixing. We characterize these shortcomings analytically and use synthetic and empirical networks to show that nominal assortativity fails to account for group imbalance and asymmetric group interactions, thereby producing an inaccurate characterization of mixing patterns. We propose adjusted nominal assortativity and show that this adjustment recovers the expected assortativity in networks with various level of mixing. Furthermore, we propose an analytical method to assess asymmetric mixing by estimating the tendency of inter- and intra-group connectivities. Finally, we discuss how this approach enables uncovering hidden mixing patterns in real-world networks.

Correlation matrix visualization is essential for understanding the relationships between variables in a dataset, but missing data can pose a significant challenge in estimating correlation coefficients. In this paper, we compare the effects of various missing data methods on the correlation plot, focusing on two common missing patterns: random and monotone. We aim to provide practical strategies and recommendations for researchers and practitioners in creating and analyzing the correlation plot. Our experimental results suggest that while imputation is commonly used for missing data, using imputed data for plotting the correlation matrix may lead to a significantly misleading inference of the relation between the features. We recommend using DPER, a direct parameter estimation approach, for plotting the correlation matrix based on its performance in the experiments.

Recent architectural developments have enabled recurrent neural networks (RNNs) to reach and even surpass the performance of Transformers on certain sequence modeling tasks. These modern RNNs feature a prominent design pattern: linear recurrent layers interconnected by feedforward paths with multiplicative gating. Here, we show how RNNs equipped with these two design elements can exactly implement (linear) self-attention, the main building block of Transformers. By reverse-engineering a set of trained RNNs, we find that gradient descent in practice discovers our construction. In particular, we examine RNNs trained to solve simple in-context learning tasks on which Transformers are known to excel and find that gradient descent instills in our RNNs the same attention-based in-context learning algorithm used by Transformers. Our findings highlight the importance of multiplicative interactions in neural networks and suggest that certain RNNs might be unexpectedly implementing attention under the hood.

Bayesian binary regression is a prosperous area of research due to the computational challenges encountered by currently available methods either for high-dimensional settings or large datasets, or both. In the present work, we focus on the expectation propagation (EP) approximation of the posterior distribution in Bayesian probit regression under a multivariate Gaussian prior distribution. Adapting more general derivations in Anceschi et al. (2023), we show how to leverage results on the extended multivariate skew-normal distribution to derive an efficient implementation of the EP routine having a per-iteration cost that scales linearly in the number of covariates. This makes EP computationally feasible also in challenging high-dimensional settings, as shown in a detailed simulation study.

Many researchers have identified distribution shift as a likely contributor to the reproducibility crisis in behavioral and biomedical sciences. The idea is that if treatment effects vary across individual characteristics and experimental contexts, then studies conducted in different populations will estimate different average effects. This paper uses ``generalizability" methods to quantify how much of the effect size discrepancy between an original study and its replication can be explained by distribution shift on observed unit-level characteristics. More specifically, we decompose this discrepancy into ``components" attributable to sampling variability (including publication bias), observable distribution shifts, and residual factors. We compute this decomposition for several directly-replicated behavioral science experiments and find little evidence that observable distribution shifts contribute appreciably to non-replicability. In some cases, this is because there is too much statistical noise. In other cases, there is strong evidence that controlling for additional moderators is necessary for reliable replication.

Deep neural networks have shown remarkable performance when trained on independent and identically distributed data from a fixed set of classes. However, in real-world scenarios, it can be desirable to train models on a continuous stream of data where multiple classification tasks are presented sequentially. This scenario, known as Continual Learning (CL) poses challenges to standard learning algorithms which struggle to maintain knowledge of old tasks while learning new ones. This stability-plasticity dilemma remains central to CL and multiple metrics have been proposed to adequately measure stability and plasticity separately. However, none considers the increasing difficulty of the classification task, which inherently results in performance loss for any model. In that sense, we analyze some limitations of current metrics and identify the presence of setup-induced forgetting. Therefore, we propose new metrics that account for the task's increasing difficulty. Through experiments on benchmark datasets, we demonstrate that our proposed metrics can provide new insights into the stability-plasticity trade-off achieved by models in the continual learning environment.

Hawkes processes are often applied to model dependence and interaction phenomena in multivariate event data sets, such as neuronal spike trains, social interactions, and financial transactions. In the nonparametric setting, learning the temporal dependence structure of Hawkes processes is generally a computationally expensive task, all the more with Bayesian estimation methods. In particular, for generalised nonlinear Hawkes processes, Monte-Carlo Markov Chain methods applied to compute the doubly intractable posterior distribution are not scalable to high-dimensional processes in practice. Recently, efficient algorithms targeting a mean-field variational approximation of the posterior distribution have been proposed. In this work, we first unify existing variational Bayes approaches under a general nonparametric inference framework, and analyse the asymptotic properties of these methods under easily verifiable conditions on the prior, the variational class, and the nonlinear model. Secondly, we propose a novel sparsity-inducing procedure, and derive an adaptive mean-field variational algorithm for the popular sigmoid Hawkes processes. Our algorithm is parallelisable and therefore computationally efficient in high-dimensional setting. Through an extensive set of numerical simulations, we also demonstrate that our procedure is able to adapt to the dimensionality of the parameter of the Hawkes process, and is partially robust to some type of model mis-specification.