We provide four case studies that use Bayesian machinery to making inductive reasoning. Our main motivation relies in offering several instances where the Bayesian approach to data analysis is exploited at its best to perform complex tasks, such as description, testing, estimation, and prediction. This work is not meant to be either a reference text or a survey in Bayesian statistical inference. Our goal is simply to provide several examples that use Bayesian methodology to solve data-driven problems. The topics we cover here, include problems in Bayesian nonparametrics, Bayesian analysis of times series, and Bayesian analysis of spatial data.
Electroencephalogram (EEG) is an important diagnostic test that physicians use to record brain activity and detect seizures by monitoring the signals. There have been several attempts to detect seizures and abnormalities in EEG signals with modern deep learning models to reduce the clinical burden. However, they cannot be fairly compared against each other as they were tested in distinct experimental settings. Also, some of them are not trained in real-time seizure detection tasks, making it hard for on-device applications. Therefore in this work, for the first time, we extensively compare multiple state-of-the-art models and signal feature extractors in a real-time seizure detection framework suitable for real-world application, using various evaluation metrics including a new one we propose to evaluate more practical aspects of seizure detection models. Our code is available at //github.com/AITRICS/EEG_real_time_seizure_detection.
In countries where population census and sample survey data are limited, generating accurate subnational estimates of health and demographic indicators is challenging. Existing model-based geostatistical methods leverage covariate information and spatial smoothing to reduce the variability of estimates but often assume the survey design is ignorable, which may be inappropriate given the complex design of household surveys typically used in this context. On the other hand, small area estimation approaches common in the survey statistics literature do not incorporate both unit-level covariate information and spatial smoothing in a design-consistent way. We propose a new smoothed model-assisted estimator that accounts for survey design and leverages both unit-level covariates and spatial smoothing, bridging the survey statistics and model-based geostatistics perspectives. Under certain assumptions, the new estimator can be viewed as both design-consistent and model-consistent, offering potential benefits from both perspectives. We demonstrate our estimator's performance using both real and simulated data, comparing it with existing design-based and model-based estimators.
This paper provides an experimentally validated, probabilistic model of file behavior when consumed by a set of pre-existing parsers. File behavior is measured by way of a standardized set of Boolean "messages" produced as the files are read. By thresholding the posterior probability that a file exhibiting a particular set of messages is from a particular dialect, our model yields a practical classification algorithm for two dialects. We demonstrate that this thresholding algorithm for two dialects can be bootstrapped from a training set consisting primarily of one dialect. Both the (parametric) theoretical and the (non-parametric) empirical distributions of file behaviors for one dialect yield good classification performance, and outperform classification based on simply counting messages. Our theoretical framework relies on statistical independence of messages within each dialect. Violations of this assumption are detectable and allow a format analyst to identify "boundaries" between dialects. A format analyst can therefore greatly reduce the number of files they need to consider when crafting new criteria for dialect detection, since they need only consider the files that exhibit ambiguous message patterns.
Ensembles of networks arise in various fields where multiple independent networks are observed on the same set of nodes, for example, a collection of brain networks constructed on the same brain regions for different individuals. However, there are few models that describe both the variations and characteristics of networks in an ensemble at the same time. In this paper, we propose to model the ensemble of networks using a Dirichlet Process Mixture of Exponential Random Graph Models (DPM-ERGMs), which divides the ensemble into different clusters and models each cluster of networks using a separate Exponential Random Graph Model (ERGM). By employing a Dirichlet process mixture, the number of clusters can be determined automatically and changed adaptively with the data provided. Moreover, in order to perform full Bayesian inference for DPM-ERGMs, we employ the intermediate importance sampling technique inside the Metropolis-within-slice sampling scheme, which addressed the problem of sampling from the intractable ERGMs on an infinite sample space. We also demonstrate the performance of DPM-ERGMs with both simulated and real datasets.
Deep learning models have shown great potential for image-based diagnosis assisting clinical decision making. At the same time, an increasing number of reports raise concerns about the potential risk that machine learning could amplify existing health disparities due to human biases that are embedded in the training data. It is of great importance to carefully investigate the extent to which biases may be reproduced or even amplified if we wish to build fair artificial intelligence systems. Seyyed-Kalantari et al. advance this conversation by analysing the performance of a disease classifier across population subgroups. They raise performance disparities related to underdiagnosis as a point of concern; we identify areas from this analysis which we believe deserve additional attention. Specifically, we wish to highlight some theoretical and practical difficulties associated with assessing model fairness through testing on data drawn from the same biased distribution as the training data, especially when the sources and amount of biases are unknown.
Study of the interaction between computation and society often focuses on how researchers model social and physical systems in order to specify problems and propose solutions. However, the social effects of computing can depend just as much on obscure and opaque technical caveats, choices, and qualifiers. These artifacts are products of the particular algorithmic techniques and theory applied to solve a problem once it has been modeled, and their nature can imperil thorough sociotechnical scrutiny of the often discretionary decisions made to manage them. We describe three classes of objects used to encode these choices and qualifiers: heuristic models, assumptions, and parameters, and discuss selection of the last for differential privacy as an illustrative example. We raise six reasons these objects may be hazardous to comprehensive analysis of computing and argue they deserve deliberate consideration as researchers explain scientific work.
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.
Community detection, a fundamental task for network analysis, aims to partition a network into multiple sub-structures to help reveal their latent functions. Community detection has been extensively studied in and broadly applied to many real-world network problems. Classical approaches to community detection typically utilize probabilistic graphical models and adopt a variety of prior knowledge to infer community structures. As the problems that network methods try to solve and the network data to be analyzed become increasingly more sophisticated, new approaches have also been proposed and developed, particularly those that utilize deep learning and convert networked data into low dimensional representation. Despite all the recent advancement, there is still a lack of insightful understanding of the theoretical and methodological underpinning of community detection, which will be critically important for future development of the area of network analysis. In this paper, we develop and present a unified architecture of network community-finding methods to characterize the state-of-the-art of the field of community detection. Specifically, we provide a comprehensive review of the existing community detection methods and introduce a new taxonomy that divides the existing methods into two categories, namely probabilistic graphical model and deep learning. We then discuss in detail the main idea behind each method in the two categories. Furthermore, to promote future development of community detection, we release several benchmark datasets from several problem domains and highlight their applications to various network analysis tasks. We conclude with discussions of the challenges of the field and suggestions of possible directions for future research.
Attention-based neural networks have achieved state-of-the-art results on a wide range of tasks. Most such models use deterministic attention while stochastic attention is less explored due to the optimization difficulties or complicated model design. This paper introduces Bayesian attention belief networks, which construct a decoder network by modeling unnormalized attention weights with a hierarchy of gamma distributions, and an encoder network by stacking Weibull distributions with a deterministic-upward-stochastic-downward structure to approximate the posterior. The resulting auto-encoding networks can be optimized in a differentiable way with a variational lower bound. It is simple to convert any models with deterministic attention, including pretrained ones, to the proposed Bayesian attention belief networks. On a variety of language understanding tasks, we show that our method outperforms deterministic attention and state-of-the-art stochastic attention in accuracy, uncertainty estimation, generalization across domains, and robustness to adversarial attacks. We further demonstrate the general applicability of our method on neural machine translation and visual question answering, showing great potential of incorporating our method into various attention-related tasks.
We propose a new method of estimation in topic models, that is not a variation on the existing simplex finding algorithms, and that estimates the number of topics K from the observed data. We derive new finite sample minimax lower bounds for the estimation of A, as well as new upper bounds for our proposed estimator. We describe the scenarios where our estimator is minimax adaptive. Our finite sample analysis is valid for any number of documents (n), individual document length (N_i), dictionary size (p) and number of topics (K), and both p and K are allowed to increase with n, a situation not handled well by previous analyses. We complement our theoretical results with a detailed simulation study. We illustrate that the new algorithm is faster and more accurate than the current ones, although we start out with a computational and theoretical disadvantage of not knowing the correct number of topics K, while we provide the competing methods with the correct value in our simulations.