Consistency and convergence rate of phylogenetic inference via regularization

It is common in phylogenetics to have some, perhaps partial, information about the overall evolutionary tree of a group of organisms and wish to find an evolutionary tree of a specific gene for those organisms. There may not be enough information in the gene sequences alone to accurately reconstruct the correct "gene tree." Although the gene tree may deviate from the "species tree" due to a variety of genetic processes, in the absence of evidence to the contrary it is parsimonious to assume that they agree. A common statistical approach in these situations is to develop a likelihood penalty to incorporate such additional information. Recent studies using simulation and empirical data suggest that a likelihood penalty quantifying concordance with a species tree can significantly improve the accuracy of gene tree reconstruction compared to using sequence data alone. However, the consistency of such an approach has not yet been established, nor have convergence rates been bounded. Because phylogenetics is a non-standard inference problem, the standard theory does not apply. In this paper, we propose a penalized maximum likelihood estimator for gene tree reconstruction, where the penalty is the square of the Billera-Holmes-Vogtmann geodesic distance from the gene tree to the species tree. We prove that this method is consistent, and derive its convergence rate for estimating the discrete gene tree structure and continuous edge lengths (representing the amount of evolution that has occurred on that branch) simultaneously. We find that the regularized estimator is "adaptive fast converging," meaning that it can reconstruct all edges of length greater than any given threshold from gene sequences of polynomial length. Our method does not require the species tree to be known exactly; in fact, our asymptotic theory holds for any such guide tree.Comment: 34 pages, 5 figures. To appear on The Annals of Statistic

On the convergence of the maximum likelihood estimator for the transition rate under a 2-state symmetric model

Maximum likelihood estimators are used extensively to estimate unknown parameters of stochastic trait evolution models on phylogenetic trees. Although the MLE has been proven to converge to the true value in the independent-sample case, we cannot appeal to this result because trait values of different species are correlated due to shared evolutionary history. In this paper, we consider a $2$-state symmetric model for a single binary trait and investigate the theoretical properties of the MLE for the transition rate in the large-tree limit. Here, the large-tree limit is a theoretical scenario where the number of taxa increases to infinity and we can observe the trait values for all species. Specifically, we prove that the MLE converges to the true value under some regularity conditions. These conditions ensure that the tree shape is not too irregular, and holds for many practical scenarios such as trees with bounded edges, trees generated from the Yule (pure birth) process, and trees generated from the coalescent point process. Our result also provides an upper bound for the distance between the MLE and the true value

When can we reconstruct the ancestral state? Beyond Brownian motion

Reconstructing the ancestral state of a group of species helps answer many important questions in evolutionary biology. Therefore, it is crucial to understand when we can estimate the ancestral state accurately. Previous works provide a necessary and sufficient condition, called the big bang condition, for the existence of an accurate reconstruction method under discrete trait evolution models and the Brownian motion model. In this paper, we extend this result to a wide range of continuous trait evolution models. In particular, we consider a general setting where continuous traits evolve along the tree according to stochastic processes that satisfy some regularity conditions. We verify these conditions for popular continuous trait evolution models including Ornstein-Uhlenbeck, reflected Brownian Motion, and Cox-Ingersoll-Ross

Childhood Acute Poisoning at Haiphong Children\u27s Hospital: A 10-Year Retrospective Study

INTRODUCTION: Children are most often harmed by acute poisoning, which may cause disability or even death. This demonstrates the critical necessity for epidemiologic studies specific to each nation and area since they aid in developing plans for the prevention of acute poisoning. There are no data or outdated data on acute poisoning in children in Vietnam. This research would partly fill this existing gap and compare the trend with other places across the globe. METHODS: A retrospective study was conducted in the 10-year period from 2012 to 2021 in Haiphong Children\u27s Hospital, Vietnam. RESULTS: There were 771 children hospitalized due to acute poisoning. Children in the 1-5-year-old group accounted for the highest rate, at 506 (65.6%). The mean age was 4.5 ± 4.1 years old. The male-to-female ratio was 1.2/1. Nonpharmaceutical chemicals were the most common agent in 331 cases (42.9%), including cleaning products 63 (19.0%), rat poison 60 (18.1%), and petrol 42 (12.7%). Medications were the second most common agent in 290 cases (37.6%), mostly paracetamol 60 (20.7%) and sedatives 40 (13.8%). There were 633 (82.1%) children exposed to poisons unintentionally. CONCLUSION: Children between the ages of 1 and 5 are more likely to be exposed to harmful substances. The most common agents were nonpharmaceutical chemicals followed by pharmaceuticals. Most incidents were inadvertent. Finally, our research may provide insights that public health authorities might use to plan practical actions

Active disturbance rejection control-based anti-coupling method for conical magnetic bearings

Conical-shape magnetic bearings are currently a potential candidate for various magnetic force-supported applications due to their unique geometric nature reducing the number of required active magnets. However, the bearing structure places control-engineering related problems in view of underactuated and coupling phenomena. The paper proposes an Adaptive Disturbance Rejection Control (ADRC) for solving the above-mentioned problem in the conical magnetic bearing. At first, virtual current controls are identified to decouple the electrical sub-system, then the active disturbance rejection control is employed to eliminate coupling effects owing to rotational motions. Comprehensive simulations are provided to illustrate the control ability

Simple Transferability Estimation for Regression Tasks

We consider transferability estimation, the problem of estimating how well deep learning models transfer from a source to a target task. We focus on regression tasks, which received little previous attention, and propose two simple and computationally efficient approaches that estimate transferability based on the negative regularized mean squared error of a linear regression model. We prove novel theoretical results connecting our approaches to the actual transferability of the optimal target models obtained from the transfer learning process. Despite their simplicity, our approaches significantly outperform existing state-of-the-art regression transferability estimators in both accuracy and efficiency. On two large-scale keypoint regression benchmarks, our approaches yield 12% to 36% better results on average while being at least 27% faster than previous state-of-the-art methods.Comment: Paper published at The 39th Conference on Uncertainty in Artificial Intelligence (UAI) 202