Real world data is an increasingly utilized resource for post-market monitoring of vaccines and provides insight into real world effectiveness. However, outside of the setting of a clinical trial, heterogeneous mechanisms may drive observed breakthrough infection rates among vaccinated individuals; for instance, waning vaccine-induced immunity as time passes and the emergence of a new strain against which the vaccine has reduced protection. Analyses of infection incidence rates are typically predicated on a presumed mechanism in their choice of an "analytic time zero" after which infection rates are modeled. In this work, we propose an explicit test for driving mechanism situated in a standard Cox proportional hazards framework. We explore the test's performance in simulation studies and in an illustrative application to real world data. We additionally introduce subgroup differences in infection incidence and evaluate the impact of time zero misspecification on bias and coverage of model estimates. In this study we observe strong power and controlled type I error of the test to detect the correct infection-driving mechanism under various settings. Similar to previous studies, we find mitigated bias and greater coverage of estimates when the analytic time zero is correctly specified or accounted for.
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Since coral reef ecosystems face threats from human activities and climate change, coral conservation programs are implemented worldwide. Monitoring coral health provides references for guiding conservation activities. However, current labor-intensive methods result in a backlog of unsorted images, highlighting the need for automated classification. Few studies have simultaneously utilized accurate annotations along with updated algorithms and datasets. This study aimed to create a dataset representing common coral conditions and associated stressors in the Indo-Pacific. Concurrently, it assessed existing classification algorithms and proposed a new multi-label method for automatically detecting coral conditions and extracting ecological information. A dataset containing over 20,000 high-resolution coral images of different health conditions and stressors was constructed based on the field survey. Seven representative deep learning architectures were tested on this dataset, and their performance was quantitatively evaluated using the F1 metric and the match ratio. Based on this evaluation, a new method utilizing the ensemble learning approach was proposed. The proposed method accurately classified coral conditions as healthy, compromised, dead, and rubble; it also identified corresponding stressors, including competition, disease, predation, and physical issues. This method can help develop the coral image archive, guide conservation activities, and provide references for decision-making for reef managers and conservationists. The proposed ensemble learning approach outperforms others on the dataset, showing State-Of-The-Art (SOTA) performance. Future research should improve its generalizability and accuracy to support global coral conservation efforts.
For factor analysis, many estimators, starting with the maximum likelihood estimator, are developed, and the statistical properties of most estimators are well discussed. In the early 2000s, a new estimator based on matrix factorization, called Matrix Decomposition Factor Analysis (MDFA), was developed. Although the estimator is obtained by minimizing the principal component analysis-like loss function, this estimator empirically behaves like other consistent estimators of factor analysis, not principal component analysis. Since the MDFA estimator cannot be formulated as a classical M-estimator, the statistical properties of the MDFA estimator have not yet been discussed. To explain this unexpected behavior theoretically, we establish the consistency of the MDFA estimator as the factor analysis. That is, we show that the MDFA estimator has the same limit as other consistent estimators of factor analysis.
We consider the chance-constrained binary knapsack problem (CKP), where the item weights are independent and normally distributed. We introduce a continuous relaxation for the CKP, represented as a non-convex optimization problem, which we call the non-convex relaxation. A comparative study shows that the non-convex relaxation provides an upper bound for the CKP, at least as tight as those obtained from other continuous relaxations for the CKP. Furthermore, the quality of the obtained upper bound is guaranteed to be at most twice the optimal objective value of the CKP. Despite its non-convex nature, we show that the non-convex relaxation can be solved in polynomial time. Subsequently, we proposed a polynomial-time 1/2-approximation algorithm for the CKP based on this relaxation, providing a lower bound for the CKP. Computational test results demonstrate that the non-convex relaxation and the proposed approximation algorithm yields tight lower and upper bounds for the CKP within a short computation time, ensuring the quality of the obtained bounds.
Three equivalent characterizations of probability measures through independence criteria are given. These characterizations lead to a family of Brascamp--Lieb-type inequalities for relative entropy, determine equilibrium states and sharp rates of convergence for certain linear Boltzmann-type dynamics, and unify an assortment of $L^2$ inequalities in probability.
The purpose of anonymizing structured data is to protect the privacy of individuals in the data while retaining the statistical properties of the data. There is a large body of work that examines anonymization vulnerabilities. Focusing on strong anonymization mechanisms, this paper examines a number of prominent attack papers and finds several problems, all of which lead to overstating risk. First, some papers fail to establish a correct statistical inference baseline (or any at all), leading to incorrect measures. Notably, the reconstruction attack from the US Census Bureau that led to a redesign of its disclosure method made this mistake. We propose the non-member framework, an improved method for how to compute a more accurate inference baseline, and give examples of its operation. Second, some papers don't use a realistic membership base rate, leading to incorrect precision measures if precision is reported. Third, some papers unnecessarily report measures in such a way that it is difficult or impossible to assess risk. Virtually the entire literature on membership inference attacks, dozens of papers, make one or both of these errors. We propose that membership inference papers report precision/recall values using a representative range of base rates.
Optimal estimation and inference for both the minimizer and minimum of a convex regression function under the white noise and nonparametric regression models are studied in a nonasymptotic local minimax framework, where the performance of a procedure is evaluated at individual functions. Fully adaptive and computationally efficient algorithms are proposed and sharp minimax lower bounds are given for both the estimation accuracy and expected length of confidence intervals for the minimizer and minimum. The nonasymptotic local minimax framework brings out new phenomena in simultaneous estimation and inference for the minimizer and minimum. We establish a novel uncertainty principle that provides a fundamental limit on how well the minimizer and minimum can be estimated simultaneously for any convex regression function. A similar result holds for the expected length of the confidence intervals for the minimizer and minimum.
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.
Mendelian randomization is an instrumental variable method that utilizes genetic information to investigate the causal effect of a modifiable exposure on an outcome. In most cases, the exposure changes over time. Understanding the time-varying causal effect of the exposure can yield detailed insights into mechanistic effects and the potential impact of public health interventions. Recently, a growing number of Mendelian randomization studies have attempted to explore time-varying causal effects. However, the proposed approaches oversimplify temporal information and rely on overly restrictive structural assumptions, limiting their reliability in addressing time-varying causal problems. This paper considers a novel approach to estimate time-varying effects through continuous-time modelling by combining functional principal component analysis and weak-instrument-robust techniques. Our method effectively utilizes available data without making strong structural assumptions and can be applied in general settings where the exposure measurements occur at different timepoints for different individuals. We demonstrate through simulations that our proposed method performs well in estimating time-varying effects and provides reliable inference results when the time-varying effect form is correctly specified. The method could theoretically be used to estimate arbitrarily complex time-varying effects. However, there is a trade-off between model complexity and instrument strength. Estimating complex time-varying effects requires instruments that are unrealistically strong. We illustrate the application of this method in a case study examining the time-varying effects of systolic blood pressure on urea levels.
Temporal network data is often encoded as time-stamped interaction events between senders and receivers, such as co-authoring scientific articles or communication via email. A number of relational event frameworks have been proposed to address specific issues raised by complex temporal dependencies. These models attempt to quantify how individual behaviour, endogenous and exogenous factors, as well as interactions with other individuals modify the network dynamics over time. It is often of interest to determine whether changes in the network can be attributed to endogenous mechanisms reflecting natural relational tendencies, such as reciprocity or triadic effects. The propensity to form or receive ties can also, at least partially, be related to actor attributes. Nodal heterogeneity in the network is often modelled by including actor-specific or dyadic covariates. However, comprehensively capturing all personality traits is difficult in practice, if not impossible. A failure to account for heterogeneity may confound the substantive effect of key variables of interest. This work shows that failing to account for node level sender and receiver effects can induce ghost triadic effects. We propose a random-effect extension of the relational event model to deal with these problems. We show that it is often effective over more traditional approaches, such as in-degree and out-degree statistics. These results that the violation of the hierarchy principle due to insufficient information about nodal heterogeneity can be resolved by including random effects in the relational event model as a standard.
Knowledge graphs (KGs) of real-world facts about entities and their relationships are useful resources for a variety of natural language processing tasks. However, because knowledge graphs are typically incomplete, it is useful to perform knowledge graph completion or link prediction, i.e. predict whether a relationship not in the knowledge graph is likely to be true. This paper serves as a comprehensive survey of embedding models of entities and relationships for knowledge graph completion, summarizing up-to-date experimental results on standard benchmark datasets and pointing out potential future research directions.
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