Laboratory of Physics of Biological Systems

Laboratory

Symptom Prediction and Mortality Risk Calculation for COVID-19 Using Machine Learning

Background: Early prediction of symptoms and mortality risks for COVID-19 patients would improve healthcare outcomes, allow for the appropriate distribution of healthcare resources, reduce healthcare costs, aid in vaccine prioritization and self-isolation strategies, and thus reduce the prevalence of the disease. Such publicly accessible prediction models are lacking, however. Methods: Based on a comprehensive evaluation of existing machine learning (ML) methods, we created two models based solely on the age, gender, and medical histories of 23,749 hospital-confirmed COVID-19 patients from February to September 2020: a symptom prediction model (SPM) and a mortality prediction model (MPM). The SPM predicts 12 symptom groups for each patient: respiratory distress, consciousness disorders, chest pain, paresis or paralysis, cough, fever or chill, gastrointestinal symptoms, sore throat, headache, vertigo, loss of smell or taste, and muscular pain or fatigue. The MPM predicts the death of COVID-19-positive individuals. Results: The SPM yielded ROC-AUCs of 0.53-0.78 for symptoms. The most accurate prediction was for consciousness disorders at a sensitivity of 74% and a specificity of 70%. 2,440 deaths were observed in the study population. MPM had a ROC-AUC of 0.79 and could predict mortality with a sensitivity of 75% and a specificity of 70%. About 90% of deaths occurred in the top 21 percentile of risk groups. To allow patients and clinicians to use these models easily, we created a freely accessible online interface at www. aicovid.net. Conclusion: The ML models predict COVID-19-related symptoms and mortality using information that is readily available to patients as well as clinicians. Thus, both can rapidly estimate the severity of the disease, allowing shared and better healthcare decisions with regard to hospitalization, self-isolation strategy, and COVID-19 vaccine prioritization in the coming months.

FRONTIERS MEDIA SA2021

Principles of checkpoint override

Ahmad Sadeghi

Why biological quality-control systems fail is often mysterious. Specifically, checkpoints such as the DNA damage checkpoint or the spindle assembly checkpoint are overriden after prolonged arrests allowing cells to continue dividing despite the continued presence of errors.1â4 Although critical for biological systems, checkpoint override is poorly understood quantitatively by experiment or theory. Override may represent a trade-off between risk and speed, a fundamental principle explaining biological phenomena.5,6 Here, we derive the first, general theory of optimal checkpoint strategies, balancing risk and opportunities for growth. We demonstrate that the mathematical problem of finding the optimal strategy maps onto the question of calculating the optimal absorbing boundary for a random walk, which we show can be solved efficiently recursively. The theory predicts the optimal override strategy without any free parameters based on two inputs, the statistics i) of error correction and ii) of survival. We apply the theory to the prominent example of the DNA damage checkpoint in budding yeast (Saccharomyces cerevisiae) experimentally. Using a novel fluorescent construct which allowed cells with DNA breaks to be isolated by flow cytometry, we quantified i) the probability distribution function of repair for a double-strand DNA break (DSB), including for the critically important, rare events deep in the tail of the distribution, as well as ii) the survival probability if the checkpoint was overridden. Based on these two measurements, the optimal checkpoint theory predicted remarkably accurately the DNA damage checkpoint override times as a function of DSB numbers, which we measured precisely at the single-cell level. Our multi-DSB results refine well-known bulk culture measurements7 and show that override is a more general phenomenon than previously thought. Further, we show for the first time that override is an advantageous strategy in cells with wild-type DNA repair genes. The universal nature of the balance between risk and self-replication opportunity is in principle relevant to many other systems, including other checkpoints, developmental decisions8, or reprogramming of cancer cells9, suggesting potential further applications of the theory.

EPFL2022

Figlearn: Filter And Graph Learning Using Optimal Transport

Mireille El Gheche, Zahra Farsijani, Pascal Frossard, Matthias Minder

In many applications, a dataset can be considered as a set of observed signals that live on an unknown underlying graph structure. Some of these signals may be seen as white noise that has been filtered on the graph topology by a graph filter. Hence, the knowledge of the filter and the graph provides valuable information about the underlying data generation process and the complex interactions that arise in the dataset. We hence introduce a novel graph signal processing framework for jointly learning the graph and its generating filter from signal observations. We cast a new optimisation problem that minimises the Wasserstein distance between the distribution of the signal observations and the filtered signal distribution model. Our proposed method outperforms state-of-the-art graph learning frameworks on synthetic data. We then apply our method to a temperature anomaly dataset, and further show how this framework can be used to infer missing values if only very little information is available.

IEEE2021

Variants of Homomorphism Polynomials Complete for Algebraic Complexity Classes

Aditya Vardhan Varre

We present polynomial families complete for the well-studied algebraic complexity classes VF, VBP, VP, and VNP. The polynomial families are based on the homomorphism polynomials studied in the recent works of Durand et al. (2014) and Mahajan et al. (2018). We consider three different variants of graph homomorphisms, namely injective homomorphisms, directed homomorphisms, and injective directed homomorphisms, and obtain polynomial families complete for VF, VBP, VP, and VNP under each one of these. The polynomial families have the following properties: The polynomial families complete for VF, VBP, and VP are model independent, i.e., they do not use a particular instance of a formula, algebraic branching programs, or circuit for characterising VF, VBP, or VP, respectively. All the polynomial families are hard under p-projections.

ASSOC COMPUTING MACHINERY2021

Last iterate convergence of SGD for Least-Squares in the Interpolation regime

Nicolas Henri Bernard Flammarion, Loucas Pillaud-Vivien, Aditya Vardhan Varre

Motivated by the recent successes of neural networks that have the ability to fit the data perfectly \emph{and} generalize well, we study the noiseless model in the fundamental least-squares setup. We assume that an optimum predictor fits perfectly inputs and outputs

\langle \theta_* , \phi(X) \rangle = Y

, where

\phi(X)

stands for a possibly infinite dimensional non-linear feature map. To solve this problem, we consider the estimator given by the last iterate of stochastic gradient descent (SGD) with constant step-size. In this context, our contribution is two fold: (i) \emph{from a (stochastic) optimization perspective}, we exhibit an archetypal problem where we can show explicitly the convergence of SGD final iterate for a non-strongly convex problem with constant step-size whereas usual results use some form of average and (ii) \emph{from a statistical perspective}, we give explicit non-asymptotic convergence rates in the over-parameterized setting and leverage a \emph{fine-grained} parameterization of the problem to exhibit polynomial rates that can be faster than

O(1/T)

. The link with reproducing kernel Hilbert spaces is established.

2021

Adaptive model predictive control for linear time varying MIMO systems

Vojislav Gligorovski

A robust, adaptive Model Predictive Control (MPC) approach for asymptotically stable, constrained linear time-varying (LTV) systems with multiple inputs and outputs is proposed. The approach consists of two-steps, carried out on-line with a receding horizon strategy. In the first one, a real-time Set Membership identification algorithm exploits the measured input-output data and the available prior knowledge to build and refine a set of admissible models of the plant (Feasible Parameter Set, FPS). This set is guaranteed to contain also the true system dynamics under the considered working assumptions. In the second step, a robust finite-horizon optimal control problem is formulated and solved. The variation of system dynamics is taken into account by inflating the FPS over the prediction horizon, according to worst-case bounds, assumed a priori, on the parameters' rate of change. The resulting optimal control sequence guarantees that the outputs of all possible plants inside the FPS satisfy the operational constraints, also considering all possible future parameter changes. The main theoretical properties of the proposed approach are demonstrated and the method is showcased in numerical simulations, highlighting the fundamental improvement over previous approaches not designed for LTV systems. (C) 2019 Elsevier Ltd. All rights reserved.

2019

Last iterate convergence of SGD for Least-Squares in the Interpolation regime

Nicolas Henri Bernard Flammarion, Loucas Pillaud-Vivien, Aditya Vardhan Varre

\langle \theta_* , \phi(X) \rangle = Y

, where

\phi(X)

O(1/T)

. The link with reproducing kernel Hilbert spaces is established.

2021

Laboratory of Physics of Biological Systems

Symptom Prediction and Mortality Risk Calculation for COVID-19 Using Machine Learning

Using Machine Learning to Predict mortality for first-day COVID-19 patients presenting to the ICU

Principles of checkpoint override

Figlearn: Filter And Graph Learning Using Optimal Transport

Variants of Homomorphism Polynomials Complete for Algebraic Complexity Classes

Last iterate convergence of SGD for Least-Squares in the Interpolation regime

Adaptive model predictive control for linear time varying MIMO systems

Comparison against current standards of a DNA aptamer for the label-free quantification of tobramycin in human sera employed for therapeutic drug monitoring

Using Machine Learning to Predict mortality for first-day COVID-19 patients presenting to the ICU

Last iterate convergence of SGD for Least-Squares in the Interpolation regime

Comparison against current standards of a DNA aptamer for the label-free quantification of tobramycin in human sera employed for therapeutic drug monitoring

Symptom Prediction and Mortality Risk Calculation for COVID-19 Using Machine Learning

Principles of checkpoint override

Figlearn: Filter And Graph Learning Using Optimal Transport

Variants of Homomorphism Polynomials Complete for Algebraic Complexity Classes

Adaptive model predictive control for linear time varying MIMO systems