Identification of high-risk COVID-19 patients using machine learning

The current COVID-19 public health crisis, caused by SARS-CoV-2 (severe acute respiratory syndrome coronavirus 2), has produced a devastating toll both in terms of human life loss and economic disruption. In this paper we present a machine-learning algorithm capable of identifying whether a given patient (actually infected or suspected to be infected) is more likely to survive than to die, or vice-versa. We train this algorithm with historical data, including medical history, demographic data, as well as COVID-19-related information. This is extracted from a database of confirmed and suspected COVID-19 infections in Mexico, constituting the official COVID-19 data compiled and made publicly available by the Mexican Federal Government. We demonstrate that the proposed method can detect high-risk patients with high accuracy, in each of four identified clinical stages, thus improving hospital capacity planning and timely treatment. Furthermore, we show that our method can be extended to provide optimal estimators for hypothesis-testing techniques commonly-used in biological and medical statistics. We believe that our work could be of use in the context of the current pandemic in assisting medical professionals with real-time assessments so as to determine health care priorities.

Neural Networks for self-adjusting Mutation Rate Estimation when the Recombination Rate is unknown

Estimating the mutation rate, or equivalently effective population size, is a common task in population genetics. If recombination is low or high, the optimal linear estimation methods, namely Fu’s and Watterson’s estimator, are known and well understood. For intermediate recombination rates, the calculation of optimal estimators is more involved. As an alternative to model-based estimation, neural networks and other machine learning tools could help to develop good estimators in these involved scenarios. However, if no benchmark is available it is difficult to assess how well suited these tools are for different applications in population genetics.Here we investigate feedforward neural networks for the estimation of the mutation rate and compare their performance with the frequently used optimal estimators introduced by Fu and Watterson. We find that neural networks can reproduce the optimal estimators if provided with the appropriate features and training sets. Remarkably, only one hidden layer is necessary to obtain a single estimator that performs almost as well as the optimal estimators for both, low and high recombination rates and provides a superior estimation method for intermediate recombination rates at the same time.

\({\mathbb{T}}\)-Proper Hypercomplex Centralized Fusion Estimation for Randomly Multiple Sensor Delays Systems with Correlated Noises

The centralized fusion estimation problem for discrete-time vectorial tessarine signals in multiple sensor stochastic systems with random one-step delays and correlated noises is analyzed under different T-properness conditions. Based on Tk, k=1,2, linear processing, new centralized fusion filtering, prediction, and fixed-point smoothing algorithms are devised. These algorithms have the advantage of providing optimal estimators with a significant reduction in computational cost compared to that obtained through a real or a widely linear processing approach. Simulation examples illustrate the effectiveness and applicability of the algorithms proposed, in which the superiority of the Tk linear estimators over their counterparts in the quaternion domain is apparent.

T-proper Hypercomplex Centralized Fusion Estimation for Randomly Multiple Sensor Delays Systems with Correlated Noises

The centralized fusion estimation problem for discrete-time vectorial tessarine signals in multiple sensor stochastic systems with random one-step delays and correlated noises is analyzed under different T-properness conditions. Based on Tk, k=1,2, linear processing, new centralized fusion filtering, prediction, and fixed-point smoothing algorithms are devised. These algorithms have the advantage of providing optimal estimators with a significant reduction in computational cost compared to that obtained through a real or widely linear processing approach. Simulation examples illustrate the effectiveness and applicability of the algorithms proposed, in which the superiority of the Tk linear estimators over their counterparts in the quaternion domain is apparent.

Identification of high-risk COVID-19 patients using machine learning

The current COVID-19 public health crisis, caused by SARSCoV-2 (severe acute respiratory syndrome coronavirus 2), has produced a devastating toll both in terms of human life loss and economic disruption. In this paper we present a machine-learning algorithm capable of identifying whether a given patient (actually infected or suspected to be infected) is more likely to survive than to die, or vice-versa. We train this algorithm with historical data, including medical history, demographic data, as well as COVID-19-related information. This is extracted from a database of confirmed and suspected COVID-19 infections in Mexico, constituting the official COVID-19 data compiled and made publicly available by the Mexican Federal Government. We demonstrate that the proposed method can detect high-risk patients with high accuracy, in each of four identified treatment stages, thus improving hospital capacity planning and timely treatment. Furthermore, we show that our method can be extended to provide optimal estimators for hypothesis-testing techniques commonly-used in biological and medical statistics. We believe that our work could be of use in the context of the current pandemic in assisting medical professionals with real-time assessments so as to determine health care priorities.

Generalized Inequalities to Optimize the Fitting Method for Track Reconstruction

A standard criterium in statistics is to define an optimal estimator as the one with the minimum variance. Thus, the optimality is proved with inequality among variances of competing estimators. The demonstrations of inequalities among estimators are essentially based on the Cramer, Rao and Frechet methods. They require special analytical properties of the probability functions, globally indicated as regular models. With an extension of the Cramer–Rao–Frechet inequalities and Gaussian distributions, it was proved the optimality (efficiency) of the heteroscedastic estimators compared to any other linear estimator. However, the Gaussian distributions are a too restrictive selection to cover all the realistic properties of track fitting. Therefore, a well-grounded set of inequalities must overtake the limitations to regular models. Hence, the inequalities for least-squares estimators are generalized to any model of probabilities. The new inequalities confirm the results obtained for the Gaussian distributions and generalize them to any irregular or regular model. Estimators for straight and curved tracks are considered. The second part deals with the shapes of the distributions of simplified heteroscedastic track models, reconstructed with optimal estimators and the standard (non-optimal) estimators. A comparison among the distributions of these different estimators shows the large loss in resolution of the standard least-squares estimators.

Optimal estimation of bacterial growth rates based on a permuted monotone matrix

Motivated by the problem of estimating the bacterial growth rates for genome assemblies from shotgun metagenomic data, we consider the permuted monotone matrix model Y = ΘΠ + Z, where Y ∈ ℝ n × p is observed, Θ ∈ ℝ n × p is an unknown approximately rank-one signal matrix with monotone rows, Π ∈ ℝ p × p is an unknown permutation matrix, and Z ∈ ℝ n × p is the noise matrix. This paper studies the estimation of the extreme values associated to the signal matrix Θ, including its first and last columns, as well as their difference. Treating these estimation problems as compound decision problems, minimax rate-optimal estimators are constructed using the spectral column sorting method. Numerical experiments through simulated and synthetic microbiome metagenomic data are presented, showing the superiority of the proposed methods over the alternatives. The methods are illustrated by comparing the growth rates of gut bacteria between inflammatory bowel disease patients and normal controls.