Fluid limit theorems for stochastic hybrid systems with application to neuron models

This paper establishes limit theorems for a class of stochastic hybrid systems (continuous deterministic dynamic coupled with jump Markov processes) in the fluid limit (small jumps at high frequency), thus extending known results for jump Markov processes. We prove a functional law of large numbers with exponential convergence speed, derive a diffusion approximation and establish a functional central limit theorem. We apply these results to neuron models with stochastic ion channels, as the number of channels goes to infinity, estimating the convergence to the deterministic model. In terms of neural coding, we apply our central limit theorems to estimate numerically impact of channel noise both on frequency and spike timing coding.Comment: 42 pages, 4 figure

Comparative performances of machine learning methods for classifying Crohn Disease patients using genome-wide genotyping data

© 2019, The Author(s). Crohn Disease (CD) is a complex genetic disorder for which more than 140 genes have been identified using genome wide association studies (GWAS). However, the genetic architecture of the trait remains largely unknown. The recent development of machine learning (ML) approaches incited us to apply them to classify healthy and diseased people according to their genomic information. The Immunochip dataset containing 18,227 CD patients and 34,050 healthy controls enrolled and genotyped by the international Inflammatory Bowel Disease genetic consortium (IIBDGC) has been re-analyzed using a set of ML methods: penalized logistic regression (LR), gradient boosted trees (GBT) and artificial neural networks (NN). The main score used to compare the methods was the Area Under the ROC Curve (AUC) statistics. The impact of quality control (QC), imputing and coding methods on LR results showed that QC methods and imputation of missing genotypes may artificially increase the scores. At the opposite, neither the patient/control ratio nor marker preselection or coding strategies significantly affected the results. LR methods, including Lasso, Ridge and ElasticNet provided similar results with a maximum AUC of 0.80. GBT methods like XGBoost, LightGBM and CatBoost, together with dense NN with one or more hidden layers, provided similar AUC values, suggesting limited epistatic effects in the genetic architecture of the trait. ML methods detected near all the genetic variants previously identified by GWAS among the best predictors plus additional predictors with lower effects. The robustness and complementarity of the different methods are also studied. Compared to LR, non-linear models such as GBT or NN may provide robust complementary approaches to identify and classify genetic markers

Echo State Property of Deep Reservoir Computing Networks

In the last years, the Reservoir Computing (RC) framework has emerged as a state of-the-art approach for efficient learning in temporal domains. Recently, within the RC context, deep Echo State Network (ESN) models have been proposed. Being composed of a stack of multiple non-linear reservoir layers, deep ESNs potentially allow to exploit the advantages of a hierarchical temporal feature representation at different levels of abstraction, at the same time preserving the training efficiency typical of the RC methodology. In this paper, we generalize to the case of deep architectures the fundamental RC conditions related to the Echo State Property (ESP), based on the study of stability and contractivity of the resulting dynamical system. Besides providing a necessary condition and a sufficient condition for the ESP of layered RC networks, the results of our analysis provide also insights on the nature of the state dynamics in hierarchically organized recurrent models. In particular, we find out that by adding layers to a deep reservoir architecture, the regime of network’s dynamics can only be driven towards (equally or) less stable behaviors. Moreover, our investigation shows the intrinsic ability of temporal dynamics differentiation at the different levels in a deep recurrent architecture, with higher layers in the stack characterized by less contractive dynamics. Such theoretical insights are further supported by experimental results that show the effect of layering in terms of a progressively increased short-term memory capacity of the recurrent models

Comparative performances of machine learning methods for classifying Crohn Disease patients using genome-wide genotyping data

Abstract: Crohn Disease (CD) is a complex genetic disorder for which more than 140 genes have been identified using genome wide association studies (GWAS). However, the genetic architecture of the trait remains largely unknown. The recent development of machine learning (ML) approaches incited us to apply them to classify healthy and diseased people according to their genomic information. The Immunochip dataset containing 18,227 CD patients and 34,050 healthy controls enrolled and genotyped by the international Inflammatory Bowel Disease genetic consortium (IIBDGC) has been re-analyzed using a set of ML methods: penalized logistic regression (LR), gradient boosted trees (GBT) and artificial neural networks (NN). The main score used to compare the methods was the Area Under the ROC Curve (AUC) statistics. The impact of quality control (QC), imputing and coding methods on LR results showed that QC methods and imputation of missing genotypes may artificially increase the scores. At the opposite, neither the patient/control ratio nor marker preselection or coding strategies significantly affected the results. LR methods, including Lasso, Ridge and ElasticNet provided similar results with a maximum AUC of 0.80. GBT methods like XGBoost, LightGBM and CatBoost, together with dense NN with one or more hidden layers, provided similar AUC values, suggesting limited epistatic effects in the genetic architecture of the trait. ML methods detected near all the genetic variants previously identified by GWAS among the best predictors plus additional predictors with lower effects. The robustness and complementarity of the different methods are also studied. Compared to LR, non-linear models such as GBT or NN may provide robust complementary approaches to identify and classify genetic markers

External control arm analysis: an evaluation of propensity score approaches, G-computation, and doubly debiased machine learning

Abstract Background An external control arm is a cohort of control patients that are collected from data external to a single-arm trial. To provide an unbiased estimation of efficacy, the clinical profiles of patients from single and external arms should be aligned, typically using propensity score approaches. There are alternative approaches to infer efficacy based on comparisons between outcomes of single-arm patients and machine-learning predictions of control patient outcomes. These methods include G-computation and Doubly Debiased Machine Learning (DDML) and their evaluation for External Control Arms (ECA) analysis is insufficient. Methods We consider both numerical simulations and a trial replication procedure to evaluate the different statistical approaches: propensity score matching, Inverse Probability of Treatment Weighting (IPTW), G-computation, and DDML. The replication study relies on five type 2 diabetes randomized clinical trials granted by the Yale University Open Data Access (YODA) project. From the pool of five trials, observational experiments are artificially built by replacing a control arm from one trial by an arm originating from another trial and containing similarly-treated patients. Results Among the different statistical approaches, numerical simulations show that DDML has the smallest bias followed by G-computation. In terms of mean squared error, G-computation usually minimizes mean squared error. Compared to other methods, DDML has varying Mean Squared Error performances that improves with increasing sample sizes. For hypothesis testing, all methods control type I error and DDML is the most conservative. G-computation is the best method in terms of statistical power, and DDML has comparable power at $$n=1000$$ n = 1000 but inferior ones for smaller sample sizes. The replication procedure also indicates that G-computation minimizes mean squared error whereas DDML has intermediate performances in between G-computation and propensity score approaches. The confidence intervals of G-computation are the narrowest whereas confidence intervals obtained with DDML are the widest for small sample sizes, which confirms its conservative nature. Conclusions For external control arm analyses, methods based on outcome prediction models can reduce estimation error and increase statistical power compared to propensity score approaches