Tens of thousands of simultaneous hypothesis tests are routinely performed in genomic studies to identify differentially expressed genes. However, due to unmeasured confounders, many standard statistical approaches may be substantially biased. This paper investigates the large-scale hypothesis testing problem for multivariate generalized linear models in the presence of confounding effects. Under arbitrary confounding mechanisms, we propose a unified statistical estimation and inference framework that harnesses orthogonal structures and integrates linear projections into three key stages. It begins by disentangling marginal and uncorrelated confounding effects to recover the latent coefficients. Subsequently, latent factors and primary effects are jointly estimated through lasso-type optimization. Finally, we incorporate projected and weighted bias-correction steps for hypothesis testing. Theoretically, we establish the identification conditions of various effects and non-asymptotic error bounds. We show effective Type-I error control of asymptotic $z$-tests as sample and response sizes approach infinity. Numerical experiments demonstrate that the proposed method controls the false discovery rate by the Benjamini-Hochberg procedure and is more powerful than alternative methods. By comparing single-cell RNA-seq counts from two groups of samples, we demonstrate the suitability of adjusting confounding effects when significant covariates are absent from the model.
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This study compares the performance of (1) fine-tuned models and (2) extremely large language models on the task of check-worthy claim detection. For the purpose of the comparison we composed a multilingual and multi-topical dataset comprising texts of various sources and styles. Building on this, we performed a benchmark analysis to determine the most general multilingual and multi-topical claim detector. We chose three state-of-the-art models in the check-worthy claim detection task and fine-tuned them. Furthermore, we selected three state-of-the-art extremely large language models without any fine-tuning. We made modifications to the models to adapt them for multilingual settings and through extensive experimentation and evaluation. We assessed the performance of all the models in terms of accuracy, recall, and F1-score in in-domain and cross-domain scenarios. Our results demonstrate that despite the technological progress in the area of natural language processing, the models fine-tuned for the task of check-worthy claim detection still outperform the zero-shot approaches in a cross-domain settings.
The consistency of the maximum likelihood estimator for mixtures of elliptically-symmetric distributions for estimating its population version is shown, where the underlying distribution $P$ is nonparametric and does not necessarily belong to the class of mixtures on which the estimator is based. In a situation where $P$ is a mixture of well enough separated but nonparametric distributions it is shown that the components of the population version of the estimator correspond to the well separated components of $P$. This provides some theoretical justification for the use of such estimators for cluster analysis in case that $P$ has well separated subpopulations even if these subpopulations differ from what the mixture model assumes.
The study of moving particles (e.g. molecules, virus, vesicles, organelles, or whole cells) is crucial to decipher a plethora of cellular mechanisms within physiological and pathological conditions. Powerful live-imaging approaches enable life scientists to capture particle movements at different scale from cells to single molecules, that are collected in a series of frames. However, although these events can be captured, an accurate quantitative analysis of live-imaging experiments still remains a challenge. Two main approaches are currently used to study particle kinematics: kymographs, which are graphical representation of spatial motion over time, and single particle tracking (SPT) followed by linear linking. Both kymograph and SPT apply a space-time approximation in quantifying particle kinematics, considering the velocity constant either over several frames or between consecutive frames, respectively. Thus, both approaches intrinsically limit the analysis of complex motions with rapid changes in velocity. Therefore, we design, implement and validate a novel reconstruction algorithm aiming at supporting tracking particle trafficking analysis with mathematical foundations. Our method is based on polynomial reconstruction of 4D (3D+time) particle trajectories, enabling to assess particle instantaneous velocity and acceleration, at any time, over the entire trajectory. Here, the new algorithm is compared to state-of-the-art SPT followed by linear linking, demonstrating an increased accuracy in quantifying particle kinematics. Our approach is directly derived from the governing equations of motion, thus it arises from physical principles and, as such, it is a versatile and reliable numerical method for accurate particle kinematics analysis which can be applied to any live-imaging experiment where the space-time coordinates can be retrieved.
Generalized linear models (GLMs) are routinely used for modeling relationships between a response variable and a set of covariates. The simple form of a GLM comes with easy interpretability, but also leads to concerns about model misspecification impacting inferential conclusions. A popular semi-parametric solution adopted in the frequentist literature is quasi-likelihood, which improves robustness by only requiring correct specification of the first two moments. We develop a robust approach to Bayesian inference in GLMs through quasi-posterior distributions. We show that quasi-posteriors provide a coherent generalized Bayes inference method, while also approximating so-called coarsened posteriors. In so doing, we obtain new insights into the choice of coarsening parameter. Asymptotically, the quasi-posterior converges in total variation to a normal distribution and has important connections with the loss-likelihood bootstrap posterior. We demonstrate that it is also well-calibrated in terms of frequentist coverage. Moreover, the loss-scale parameter has a clear interpretation as a dispersion, and this leads to a consolidated method of moments estimator.
An iterative algorithm for high-dimensional linear models with both sparse and non-sparse structures
Numerous practical medical problems often involve data that possess a combination of both sparse and non-sparse structures. Traditional penalized regularizations techniques, primarily designed for promoting sparsity, are inadequate to capture the optimal solutions in such scenarios. To address these challenges, this paper introduces a novel algorithm named Non-sparse Iteration (NSI). The NSI algorithm allows for the existence of both sparse and non-sparse structures and estimates them simultaneously and accurately. We provide theoretical guarantees that the proposed algorithm converges to the oracle solution and achieves the optimal rate for the upper bound of the $l_2$-norm error. Through simulations and practical applications, NSI consistently exhibits superior statistical performance in terms of estimation accuracy, prediction efficacy, and variable selection compared to several existing methods. The proposed method is also applied to breast cancer data, revealing repeated selection of specific genes for in-depth analysis.
Throughout the life sciences we routinely seek to interpret measurements and observations using parameterised mechanistic mathematical models. A fundamental and often overlooked choice in this approach involves relating the solution of a mathematical model with noisy and incomplete measurement data. This is often achieved by assuming that the data are noisy measurements of the solution of a deterministic mathematical model, and that measurement errors are additive and normally distributed. While this assumption of additive Gaussian noise is extremely common and simple to implement and interpret, it is often unjustified and can lead to poor parameter estimates and non-physical predictions. One way to overcome this challenge is to implement a different measurement error model. In this review, we demonstrate how to implement a range of measurement error models in a likelihood-based framework for estimation, identifiability analysis, and prediction, called Profile-Wise Analysis. This frequentist approach to uncertainty quantification for mechanistic models leverages the profile likelihood for targeting parameters and understanding their influence on predictions. Case studies, motivated by simple caricature models routinely used in systems biology and mathematical biology literature, illustrate how the same ideas apply to different types of mathematical models. Open-source Julia code to reproduce results is available on GitHub.
Causal representation learning algorithms discover lower-dimensional representations of data that admit a decipherable interpretation of cause and effect; as achieving such interpretable representations is challenging, many causal learning algorithms utilize elements indicating prior information, such as (linear) structural causal models, interventional data, or weak supervision. Unfortunately, in exploratory causal representation learning, such elements and prior information may not be available or warranted. Alternatively, scientific datasets often have multiple modalities or physics-based constraints, and the use of such scientific, multimodal data has been shown to improve disentanglement in fully unsupervised settings. Consequently, we introduce a causal representation learning algorithm (causalPIMA) that can use multimodal data and known physics to discover important features with causal relationships. Our innovative algorithm utilizes a new differentiable parametrization to learn a directed acyclic graph (DAG) together with a latent space of a variational autoencoder in an end-to-end differentiable framework via a single, tractable evidence lower bound loss function. We place a Gaussian mixture prior on the latent space and identify each of the mixtures with an outcome of the DAG nodes; this novel identification enables feature discovery with causal relationships. Tested against a synthetic and a scientific dataset, our results demonstrate the capability of learning an interpretable causal structure while simultaneously discovering key features in a fully unsupervised setting.
We propose three test criteria each of which is appropriate for testing, respectively, the equivalence hypotheses of symmetry, of homogeneity, and of independence, with multivariate data. All quantities have the common feature of involving weighted--type distances between characteristic functions and are convenient from the computational point of view if the weight function is properly chosen. The asymptotic behavior of the tests under the null hypothesis is investigated, and numerical studies are conducted in order to examine the performance of the criteria in finite samples.
Complete observation of event histories is often impossible due to sampling effects such as right-censoring and left-truncation, but also due to reporting delays and incomplete event adjudication. This is for example the case during interim stages of clinical trials and for health insurance claims. In this paper, we develop a parametric method that takes the aforementioned effects into account, treating the latter two as partially exogenous. The method, which takes the form of a two-step M-estimation procedure, is applicable to multistate models in general, including competing risks and recurrent event models. The effect of reporting delays is derived via thinning, extending existing results for Poisson models. To address incomplete event adjudication, we propose an imputed likelihood approach which, compared to existing methods, has the advantage of allowing for dependencies between the event history and adjudication processes as well as allowing for unreported events and multiple event types. We establish consistency and asymptotic normality under standard identifiability, integrability, and smoothness conditions, and we demonstrate the validity of the percentile bootstrap. Finally, a simulation study shows favorable finite sample performance of our method compared to other alternatives, while an application to disability insurance data illustrates its practical potential.
Accelerated life-tests (ALTs) are applied for inferring lifetime characteristics of highly reliable products. In particular, step-stress ALTs increase the stress level at which units under test are subject at certain pre-fixed times, thus accelerating product wear and inducing its failure. In some cases, due to cost or product nature constraints, continuous monitoring of devices is infeasible but the units are inspected for failures at particular inspection time points. In such setups, the ALT response is interval-censored. Furthermore, when a test unit fails, there are often more than one fatal cause for the failure, known as competing risks. In this paper, we assume that all competing risks are independent and follow an exponential distribution with scale parameter depending on the stress level. Under this setup, we present a family of robust estimators based on the density power divergence, including the classical maximum likelihood estimator as a particular case. We derive asymptotic and robustness properties of the MDPDE, showing its consistency for large samples. Based on these MDPDEs, estimates of the lifetime characteristics of the product as well as estimates of cause-specific lifetime characteristics have been developed. Direct, transformed and bootstrap confidence intervals for the mean lifetime to failure, reliability at a mission time, and distribution quantiles are proposed, and their performance is empirically compared through simulations. Besides, the performance of the MDPDE family has been examined through an extensive numerical study and the methods of inference discussed here are illustrated with a real-data example regarding electronic devices.
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