This letter focuses on estimating the average treatment effect within a high-dimensional single-index model framework. We employ the recently introduced concept of the rank average treatment effect (rank-ATE) as an alternative measure for assessing differences in potential outcomes. To estimate both the rank-ATE and the model parameters simultaneously, we propose the causal rank Lasso estimator. Specifically, our method involves regressing the outcome rank on both the the treatment indicator and the covariates. We demonstrate that our estimator consistently identifies the direction and support of the true model parameter. Additionally, we introduced a novel irrepresentable condition to establish the support recovery in causal rank Lasso. Simulation studies are provided to validate the efficacy of our approach.

Semi-supervised learning is devoted to using unlabeled data to improve the performance of machine learning algorithms. In this paper, we study the semi-supervised generalized linear model (GLM) in the distributed setup. In the cases of single or multiple machines containing unlabeled data, we propose two distributed semi-supervised algorithms based on the distributed approximate Newton method. When the labeled local sample size is small, our algorithms still give a consistent estimation, while fully supervised methods fail to converge. Moreover, we theoretically prove that the convergence rate is greatly improved when sufficient unlabeled data exists. Therefore, the proposed method requires much fewer rounds of communications to achieve the optimal rate than its fully-supervised counterpart. In the case of the linear model, we prove the rate lower bound after one round of communication, which shows that rate improvement is essential. Finally, several simulation analyses and real data studies are provided to demonstrate the effectiveness of our method.

The debiased estimator is a crucial tool in statistical inference for high-dimensional model parameters. However, constructing such an estimator involves estimating the high-dimensional inverse Hessian matrix, incurring significant computational costs. This challenge becomes particularly acute in distributed setups, where traditional methods necessitate computing a debiased estimator on every machine. This becomes unwieldy, especially with a large number of machines. In this paper, we delve into semi-supervised sparse statistical inference in a distributed setup. An efficient multi-round distributed debiased estimator, which integrates both labeled and unlabelled data, is developed. We will show that the additional unlabeled data helps to improve the statistical rate of each round of iteration. Our approach offers tailored debiasing methods forM-estimation and generalized linear models according to the specific form of the loss function. Our method also applies to a non-smooth loss like absolute deviation loss. Furthermore, our algorithm is computationally efficient since it requires only one estimation of a high-dimensional inverse covariance matrix. We demonstrate the effectiveness of our method by presenting simulation studies and real data applications that highlight the benefits of incorporating unlabeled data.

This paper develops an efficient distributed inference algorithm, which is robust against a moderate fraction of Byzantine nodes, namely arbitrary and possibly adversarial machines in a distributed learning system. In robust statistics, the median-of-means (MOM) has been a popular approach to hedge against Byzantine failures due to its ease of implementation and computational efficiency. However, the MOM estimator has the shortcoming in terms of statistical efficiency. The first main contribution of the paper is to propose a variance reduced median-of-means (VRMOM) estimator, which improves the statistical efficiency over the vanilla MOM estimator and is computationally as efficient as the MOM. Based on the proposed VRMOM estimator, we develop a general distributed inference algorithm that is robust against Byzantine failures. Theoretically, our distributed algorithm achieves a fast convergence rate with only a constant number of rounds of communications. We also provide the asymptotic normality result for the purpose of statistical inference. To the best of our knowledge, this is the first normality result in the setting of Byzantine-robust distributed learning. The simulation results are also presented to illustrate the effectiveness of our method.

A fuzzy neural network enhanced with evolutionary algorithms, based on the GRNNFA, is proposed that is able to accurately predict the effects of a single compartment fire, based on experimental data. This system is shown to make predictions with within 5% accuracy, thus demonstrating that it can learn the non-linear nature of fluid dynamics. Because of its speed it is able to quickly generate views of the nature of the fire, enabling users to interrogate it and gain intelligence as to what compartment geometries lead to greater fire hazards.