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In current applied research the most-used route to an analysis of composition is through log-ratios -- that is, contrasts among log-transformed measurements. Here we argue instead for a more direct approach, using a statistical model for the arithmetic mean on the original scale of measurement. Central to the approach is a general variance-covariance function, derived by assuming multiplicative measurement error. Quasi-likelihood analysis of logit models for composition is then a general alternative to the use of multivariate linear models for log-ratio transformed measurements, and it has important advantages. These include robustness to secondary aspects of model specification, stability when there are zero-valued or near-zero measurements in the data, and more direct interpretation. The usual efficiency property of quasi-likelihood estimation applies even when the error covariance matrix is unspecified. We also indicate how the derived variance-covariance function can be used, instead of the variance-covariance matrix of log-ratios, with more general multivariate methods for the analysis of composition. A specific feature is that the notion of `null correlation' -- for compositional measurements on their original scale -- emerges naturally.

Block majorization-minimization (BMM) is a simple iterative algorithm for nonconvex optimization that sequentially minimizes a majorizing surrogate of the objective function in each block coordinate while the other block coordinates are held fixed. We consider a family of BMM algorithms for minimizing smooth nonconvex objectives, where each parameter block is constrained within a subset of a Riemannian manifold. We establish that this algorithm converges asymptotically to the set of stationary points, and attains an $\epsilon$-stationary point within $\widetilde{O}(\epsilon^{-2})$ iterations. In particular, the assumptions for our complexity results are completely Euclidean when the underlying manifold is a product of Euclidean or Stiefel manifolds, although our analysis makes explicit use of the Riemannian geometry. Our general analysis applies to a wide range of algorithms with Riemannian constraints: Riemannian MM, block projected gradient descent, optimistic likelihood estimation, geodesically constrained subspace tracking, robust PCA, and Riemannian CP-dictionary-learning. We experimentally validate that our algorithm converges faster than standard Euclidean algorithms applied to the Riemannian setting.

Ensemble methods such as bagging and random forests are ubiquitous in various fields, from finance to genomics. Despite their prevalence, the question of the efficient tuning of ensemble parameters has received relatively little attention. This paper introduces a cross-validation method, ECV (Extrapolated Cross-Validation), for tuning the ensemble and subsample sizes in randomized ensembles. Our method builds on two primary ingredients: initial estimators for small ensemble sizes using out-of-bag errors and a novel risk extrapolation technique that leverages the structure of prediction risk decomposition. By establishing uniform consistency of our risk extrapolation technique over ensemble and subsample sizes, we show that ECV yields $\delta$-optimal (with respect to the oracle-tuned risk) ensembles for squared prediction risk. Our theory accommodates general ensemble predictors, only requires mild moment assumptions, and allows for high-dimensional regimes where the feature dimension grows with the sample size. As a practical case study, we employ ECV to predict surface protein abundances from gene expressions in single-cell multiomics using random forests. In comparison to sample-split cross-validation and $K$-fold cross-validation, ECV achieves higher accuracy avoiding sample splitting. At the same time, its computational cost is considerably lower owing to the use of the risk extrapolation technique. Additional numerical results validate the finite-sample accuracy of ECV for several common ensemble predictors under a computational constraint on the maximum ensemble size.

Spatial data can come in a variety of different forms, but two of the most common generating models for such observations are random fields and point processes. Whilst it is known that spectral analysis can unify these two different data forms, specific methodology for the related estimation is yet to be developed. In this paper, we solve this problem by extending multitaper estimation, to estimate the spectral density matrix function for multivariate spatial data, where processes can be any combination of either point processes or random fields. We discuss finite sample and asymptotic theory for the proposed estimators, as well as specific details on the implementation, including how to perform estimation on non-rectangular domains and the correct implementation of multitapering for processes sampled in different ways, e.g. continuously vs on a regular grid.

In this article, we study nonparametric inference for a covariate-adjusted regression function. This parameter captures the average association between a continuous exposure and an outcome after adjusting for other covariates. In particular, under certain causal conditions, this parameter corresponds to the average outcome had all units been assigned to a specific exposure level, known as the causal dose-response curve. We propose a debiased local linear estimator of the covariate-adjusted regression function, and demonstrate that our estimator converges pointwise to a mean-zero normal limit distribution. We use this result to construct asymptotically valid confidence intervals for function values and differences thereof. In addition, we use approximation results for the distribution of the supremum of an empirical process to construct asymptotically valid uniform confidence bands. Our methods do not require undersmoothing, permit the use of data-adaptive estimators of nuisance functions, and our estimator attains the optimal rate of convergence for a twice differentiable function. We illustrate the practical performance of our estimator using numerical studies and an analysis of the effect of air pollution exposure on cardiovascular mortality.

Generative models inspired by dynamical transport of measure -- such as flows and diffusions -- construct a continuous-time map between two probability densities. Conventionally, one of these is the target density, only accessible through samples, while the other is taken as a simple base density that is data-agnostic. In this work, using the framework of stochastic interpolants, we formalize how to \textit{couple} the base and the target densities, whereby samples from the base are computed conditionally given samples from the target in a way that is different from (but does preclude) incorporating information about class labels or continuous embeddings. This enables us to construct dynamical transport maps that serve as conditional generative models. We show that these transport maps can be learned by solving a simple square loss regression problem analogous to the standard independent setting. We demonstrate the usefulness of constructing dependent couplings in practice through experiments in super-resolution and in-painting.

The field of adversarial textual attack has significantly grown over the last few years, where the commonly considered objective is to craft adversarial examples (AEs) that can successfully fool the target model. However, the imperceptibility of attacks, which is also essential for practical attackers, is often left out by previous studies. In consequence, the crafted AEs tend to have obvious structural and semantic differences from the original human-written text, making them easily perceptible. In this work, we advocate leveraging multi-objectivization to address such issue. Specifically, we reformulate the problem of crafting AEs as a multi-objective optimization problem, where the attack imperceptibility is considered as an auxiliary objective. Then, we propose a simple yet effective evolutionary algorithm, dubbed HydraText, to solve this problem. To the best of our knowledge, HydraText is currently the only approach that can be effectively applied to both score-based and decision-based attack settings. Exhaustive experiments involving 44237 instances demonstrate that HydraText consistently achieves competitive attack success rates and better attack imperceptibility than the recently proposed attack approaches. A human evaluation study also shows that the AEs crafted by HydraText are more indistinguishable from human-written text. Finally, these AEs exhibit good transferability and can bring notable robustness improvement to the target model by adversarial training.

We use Stein characterisations to derive new moment-type estimators for the parameters of several multivariate distributions in the i.i.d. case; we also derive the asymptotic properties of these estimators. Our examples include the multivariate truncated normal distribution and several spherical distributions. The estimators are explicit and therefore provide an interesting alternative to the maximum-likelihood estimator. The quality of these estimators is assessed through competitive simulation studies in which we compare their behaviour to the performance of other estimators available in the literature.

Dynamical systems across the sciences, from electrical circuits to ecological networks, undergo qualitative and often catastrophic changes in behavior, called bifurcations, when their underlying parameters cross a threshold. Existing methods predict oncoming catastrophes in individual systems but are primarily time-series-based and struggle both to categorize qualitative dynamical regimes across diverse systems and to generalize to real data. To address this challenge, we propose a data-driven, physically-informed deep-learning framework for classifying dynamical regimes and characterizing bifurcation boundaries based on the extraction of topologically invariant features. We focus on the paradigmatic case of the supercritical Hopf bifurcation, which is used to model periodic dynamics across a wide range of applications. Our convolutional attention method is trained with data augmentations that encourage the learning of topological invariants which can be used to detect bifurcation boundaries in unseen systems and to design models of biological systems like oscillatory gene regulatory networks. We further demonstrate our method's use in analyzing real data by recovering distinct proliferation and differentiation dynamics along pancreatic endocrinogenesis trajectory in gene expression space based on single-cell data. Our method provides valuable insights into the qualitative, long-term behavior of a wide range of dynamical systems, and can detect bifurcations or catastrophic transitions in large-scale physical and biological systems.

In the study of the brain, there is a hypothesis that sparse coding is realized in information representation of external stimuli, which is experimentally confirmed for visual stimulus recently. However, unlike the specific functional region in the brain, sparse coding in information processing in the whole brain has not been clarified sufficiently. In this study, we investigate the validity of sparse coding in the whole human brain by applying various matrix factorization methods to functional magnetic resonance imaging data of neural activities in the whole human brain. The result suggests sparse coding hypothesis in information representation in the whole human brain, because extracted features from sparse MF method, SparsePCA or MOD under high sparsity setting, or approximate sparse MF method, FastICA, can classify external visual stimuli more accurately than non-sparse MF method or sparse MF method under low sparsity setting.