In Bayesian accelerated life testing, the most used tool for model comparison is the deviance information criterion. An alternative and more formal approach is to use Bayes factors to compare models. However, Bayesian accelerated life testing models with more than one stressor often have mathematically intractable posterior distributions and Markov chain Monte Carlo methods are employed to obtain posterior samples to base inference on. The computation of the marginal likelihood is challenging when working with such complex models. In this paper, methods for approximating the marginal likelihood and the application thereof in the accelerated life testing paradigm are explored for dual-stress models.
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The Covid-19 pandemic has been a scourge upon humanity, claiming the lives of more than 5 million people worldwide. Although vaccines are being distributed worldwide, there is an apparent need for affordable screening techniques to serve parts of the world that do not have access to traditional medicine. Artificial Intelligence can provide a solution utilizing cough sounds as the primary screening mode. This paper presents multiple models that have achieved relatively respectable perfor mance on the largest evaluation dataset currently presented in academic literature. Moreover, we also show that performance increases with training data size, showing the need for the world wide collection of data to help combat the Covid-19 pandemic with non-traditional means.
There is a need for new models for characterizing dependence in multivariate data. The multivariate Gaussian distribution is routinely used, but cannot characterize nonlinear relationships in the data. Most non-linear extensions tend to be highly complex; for example, involving estimation of a non-linear regression model in latent variables. In this article, we propose a relatively simple class of Ellipsoid-Gaussian multivariate distributions, which are derived by using a Gaussian linear factor model involving latent variables having a von Mises-Fisher distribution on a unit hyper-sphere. We show that the Ellipsoid-Gaussian distribution can flexibly model curved relationships among variables with lower-dimensional structures. Taking a Bayesian approach, we propose a hybrid of gradient-based geodesic Monte Carlo and adaptive Metropolis for posterior sampling. We derive basic properties and illustrate the utility of the Ellipsoid-Gaussian distribution on a variety of simulated and real data applications.
Multilevel regression and poststratification (MRP) is a flexible modeling technique that has been used in a broad range of small-area estimation problems. Traditionally, MRP studies have been focused on non-causal settings, where estimating a single population value using a nonrepresentative sample was of primary interest. In this manuscript, MRP-style estimators will be evaluated in an experimental causal inference setting. We simulate a large-scale randomized control trial with a stratified cluster sampling design, and compare traditional and nonparametric treatment effect estimation methods with MRP methodology. Using MRP-style estimators, treatment effect estimates for areas as small as 1.3$\%$ of the population have lower bias and variance than standard causal inference methods, even in the presence of treatment effect heterogeneity. The design of our simulation studies also requires us to build upon a MRP variant that allows for non-census covariates to be incorporated into poststratification.
Missing values in covariates due to censoring by signal interference or lack of sensitivity in the measuring devices are common in industrial problems. We propose a full Bayesian solution to the prediction problem with an efficient Markov Chain Monte Carlo (MCMC) algorithm that updates all the censored covariate values jointly in a random scan Gibbs sampler. We show that the joint updating of missing covariate values can be at least two orders of magnitude more efficient than univariate updating. This increased efficiency is shown to be crucial for quickly learning the missing covariate values and their uncertainty in a real-time decision making context, in particular when there is substantial correlation in the posterior for the missing values. The approach is evaluated on simulated data and on data from the telecom sector. Our results show that the proposed Bayesian imputation gives substantially more accurate predictions than na\"ive imputation, and that the use of auxiliary variables in the imputation gives additional predictive power.
The Student-$t$ distribution is widely used in statistical modeling of datasets involving outliers since its longer-than-normal tails provide a robust approach to hand such data. Furthermore, data collected over time may contain censored or missing observations, making it impossible to use standard statistical procedures. This paper proposes an algorithm to estimate the parameters of a censored linear regression model when the regression errors are autocorrelated and the innovations follow a Student-$t$ distribution. To fit the proposed model, maximum likelihood estimates are obtained throughout the SAEM algorithm, which is a stochastic approximation of the EM algorithm useful for models in which the E-step does not have an analytic form. The methods are illustrated by the analysis of a real dataset that has left-censored and missing observations. We also conducted two simulations studies to examine the asymptotic properties of the estimates and the robustness of the model.
Deep Learning (DL) methods have emerged as one of the most powerful tools for functional approximation and prediction. While the representation properties of DL have been well studied, uncertainty quantification remains challenging and largely unexplored. Data augmentation techniques are a natural approach to provide uncertainty quantification and to integrate stochastic MCMC search with stochastic gradient descent (SGD) methods. The purpose of our paper is to show that training DL architectures with data augmentation leads to efficiency gains. To demonstrate our methodology, we develop data augmentation algorithms for a variety of commonly used activation functions: logit, ReLU and SVM. Our methodology is compared with traditional stochastic gradient descent with back-propagation. Our optimization procedure leads to a version of iteratively re-weighted least squares and can be implemented at scale with accelerated linear algebra methods providing substantial performance improvement. We illustrate our methodology on a number of standard datasets. Finally, we conclude with directions for future research.
Statistical inference on the explained variation of an outcome by a set of covariates is of particular interest in practice. When the covariates are of moderate to high-dimension and the effects are not sparse, several approaches have been proposed for estimation and inference. One major problem with the existing approaches is that the inference procedures are not robust to the normality assumption on the covariates and the residual errors. In this paper, we propose an estimating equation approach to the estimation and inference on the explained variation in the high-dimensional linear model. Unlike the existing approaches, the proposed approach does not rely on the restrictive normality assumptions for inference. It is shown that the proposed estimator is consistent and asymptotically normally distributed under reasonable conditions. Simulation studies demonstrate better performance of the proposed inference procedure in comparison with the existing approaches. The proposed approach is applied to studying the variation of glycohemoglobin explained by environmental pollutants in a National Health and Nutrition Examination Survey data set.
Spatio-temporal forecasting has numerous applications in analyzing wireless, traffic, and financial networks. Many classical statistical models often fall short in handling the complexity and high non-linearity present in time-series data. Recent advances in deep learning allow for better modelling of spatial and temporal dependencies. While most of these models focus on obtaining accurate point forecasts, they do not characterize the prediction uncertainty. In this work, we consider the time-series data as a random realization from a nonlinear state-space model and target Bayesian inference of the hidden states for probabilistic forecasting. We use particle flow as the tool for approximating the posterior distribution of the states, as it is shown to be highly effective in complex, high-dimensional settings. Thorough experimentation on several real world time-series datasets demonstrates that our approach provides better characterization of uncertainty while maintaining comparable accuracy to the state-of-the art point forecasting methods.
Deep convolutional neural networks (CNNs) have recently achieved great success in many visual recognition tasks. However, existing deep neural network models are computationally expensive and memory intensive, hindering their deployment in devices with low memory resources or in applications with strict latency requirements. Therefore, a natural thought is to perform model compression and acceleration in deep networks without significantly decreasing the model performance. During the past few years, tremendous progress has been made in this area. In this paper, we survey the recent advanced techniques for compacting and accelerating CNNs model developed. These techniques are roughly categorized into four schemes: parameter pruning and sharing, low-rank factorization, transferred/compact convolutional filters, and knowledge distillation. Methods of parameter pruning and sharing will be described at the beginning, after that the other techniques will be introduced. For each scheme, we provide insightful analysis regarding the performance, related applications, advantages, and drawbacks etc. Then we will go through a few very recent additional successful methods, for example, dynamic capacity networks and stochastic depths networks. After that, we survey the evaluation matrix, the main datasets used for evaluating the model performance and recent benchmarking efforts. Finally, we conclude this paper, discuss remaining challenges and possible directions on this topic.
We introduce an algorithmic method for population anomaly detection based on gaussianization through an adversarial autoencoder. This method is applicable to detection of `soft' anomalies in arbitrarily distributed highly-dimensional data. A soft, or population, anomaly is characterized by a shift in the distribution of the data set, where certain elements appear with higher probability than anticipated. Such anomalies must be detected by considering a sufficiently large sample set rather than a single sample. Applications include, but not limited to, payment fraud trends, data exfiltration, disease clusters and epidemics, and social unrests. We evaluate the method on several domains and obtain both quantitative results and qualitative insights.
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