arXiv subjects

Daniel Spencer

Publications and source records attributed to Daniel Spencer.

6 recordsLinked to original sources

arXiv2024

Proximal Byzantine Consensus

Distributed control systems require high reliability and availability guarantees despite often being deployed at the edge of network infrastructure. Edge computing resources are less secure and less reliable than centralized resources in data centers. Replication and consensus protocols improve robustness to network faults and crashed or corrupted nodes, but these volatile environments can cause non-faulty nodes to temporarily diverge, increasing the time needed for replicas to converge on a consensus value, and give Byzantine attackers too much influence over the convergence process. This paper proposes proximal Byzantine consensus, a new approximate consensus protocol where clients use statistical models of streaming computations to decide a consensus value. In addition, it provides an interval around the decision value and the probability that the true (non-faulty, noise-free) value falls within this interval. Proximal consensus (PC) tolerates unreliable network conditions, Byzantine behavior, and other sources of noise that cause honest replica states to diverge. We evaluate our approach for scalar values, and compare PC simulations against a vector consensus (VC) protocol simulation. Our simulations demonstrate that consensus values selected by PC have lower error and are more robust against Byzantine attacks. We formally characterize the security guarantees against Byzantine attacks and demonstrate attacker influence is bound with high probability. Additionally, an informal complexity analysis suggests PC scales better to higher dimensions than convex hull-based protocols such as VC.

cs.DC↗

arXiv2023

Leveraging population information in brain connectivity via Bayesian ICA with a novel informative prior for correlation matrices

Brain functional connectivity (FC), the temporal synchrony between brain networks, is essential to understand the functional organization of the brain and to identify changes due to neurological disorders, development, treatment, and other phenomena. Independent component analysis (ICA) is a matrix decomposition method used extensively for simultaneous estimation of functional brain topography and connectivity. However, estimation of FC via ICA is often sub-optimal due to the use of ad-hoc estimation methods or temporal dimension reduction prior to ICA. Bayesian ICA can avoid dimension reduction, estimate latent variables and model parameters more accurately, and facilitate posterior inference. In this paper, we develop a novel, computationally feasible Bayesian ICA method with population-derived priors on both the spatial ICs and their temporal correlation, i.e. FC. For the latter we consider two priors: the inverse-Wishart, which is conjugate but is not ideally suited for modeling correlation matrices; and a novel informative prior for correlation matrices. For each prior, we derive a variational Bayes algorithm to estimate the model variables and facilitate posterior inference. Through extensive simulation studies, we evaluate the performance of the proposed methods and benchmark against existing approaches. We also analyze fMRI data from over 400 healthy adults in the Human Connectome Project. We find that our Bayesian ICA model and algorithms result in more accurate measures of functional connectivity and spatial brain features. Our novel prior for correlation matrices is more computationally intensive than the inverse-Wishart but provides improved accuracy and inference. The proposed framework is applicable to single-subject analysis, making it potentially clinically viable.

stat.AP↗

arXiv2022

Bayesian tensor regression using the Tucker decomposition for sparse spatial modeling

Modeling with multidimensional arrays, or tensors, often presents a problem due to high dimensionality. In addition, these structures typically exhibit inherent sparsity, requiring the use of regularization methods to properly characterize an association between a tensor covariate and a scalar response. We propose a Bayesian method to efficiently model a scalar response with a tensor covariate using the Tucker tensor decomposition in order to retain the spatial relationship within a tensor coefficient, while reducing the number of parameters varying within the model and applying regularization methods. Simulated data are analyzed to compare the model to recently proposed methods. A neuroimaging analysis using data from the Alzheimer's Data Neuroimaging Initiative is included to illustrate the benefits of the model structure in making inference.

stat.ME↗

arXiv2022

Fast Bayesian estimation of brain activation with cortical surface and subcortical fMRI data using EM

Analysis of brain imaging scans is critical to understanding the way the human brain functions, which can be leveraged to treat injuries and conditions that affect the quality of life for a significant portion of the human population. In particular, functional magnetic resonance imaging (fMRI) scans give detailed data on a living subject at high spatial and temporal resolutions. Due to the high cost involved in the collection of these scans, robust methods of analysis are of critical importance in order to produce meaningful inference. Bayesian methods in particular allow for the inclusion of expected behavior from prior study into an analysis, increasing the power of the results while circumventing problems that arise in classical analyses, including the effects of smoothing results and sensitivity to multiple comparison testing corrections. Recent development of a surface-based spatial Bayesian general linear model for cortical surface fMRI (cs-fMRI) data provides the desired power increase in task fMRI data using stochastic partial differential equation (SPDE) priors. This model relies on the computational efficiencies of the integrated nested Laplace approximation (INLA) to perform powerful analyses that have been validated to outperform classical analyses. In this article, we develop an exact Bayesian analysis method for the GLM, employing an expectation-maximization (EM) algorithm to find maximum a posteriori (MAP) estimates of task-based regressors on cs-fMRI and subcortical fMRI data while using minimal computational resources. Our proposed method is compared to the INLA implementation of the Bayesian GLM, as well as a classical GLM on simulated data. A validation of the method on data from the Human Connectome Project is also provided.

stat.ME↗

arXiv2021

Spatial Bayesian GLM on the cortical surface produces reliable task activations in individuals and groups

The general linear model (GLM) is a widely popular and convenient tool for estimating the functional brain response and identifying areas of significant activation during a task or stimulus. However, the classical GLM is based on a massive univariate approach that does not explicitly leverage the similarity of activation patterns among neighboring brain locations. As a result, it tends to produce noisy estimates and be underpowered to detect significant activations, particularly in individual subjects and small groups. A recent alternative, a cortical surface-based spatial Bayesian GLM, leverages spatial dependencies among neighboring cortical vertices to produce more accurate estimates and areas of functional activation. The spatial Bayesian GLM can be applied to individual and group-level analysis. In this study, we assess the reliability and power of individual and group-average measures of task activation produced via the surface-based spatial Bayesian GLM. We analyze motor task data from 45 subjects in the Human Connectome Project (HCP) and HCP Retest datasets. We also extend the model to multi-run analysis and employ subject-specific cortical surfaces rather than surfaces inflated to a sphere for more accurate distance-based modeling. Results show that the surface-based spatial Bayesian GLM produces highly reliable activations in individual subjects and is powerful enough to detect trait-like functional topologies. Additionally, spatial Bayesian modeling enhances reliability of group-level analysis even in moderately sized samples (n=45). The power of the spatial Bayesian GLM to detect activations above a scientifically meaningful effect size is nearly invariant to sample size, exhibiting high power even in small samples (n=10). The spatial Bayesian GLM is computationally efficient in individuals and groups and is convenient to implement with the open-source BayesfMRI R package.

stat.ME↗

arXiv2019

Bayesian Mixed Effect Sparse Tensor Response Regression Model with Joint Estimation of Activation and Connectivity

Brain activation and connectivity analyses in task-based functional magnetic resonance imaging (fMRI) experiments with multiple subjects are currently at the forefront of data-driven neuroscience. In such experiments, interest often lies in understanding activation of brain voxels due to external stimuli and strong association or connectivity between the measurements on a set of pre-specified group of brain voxels, also known as regions of interest (ROI). This article proposes a joint Bayesian additive mixed modeling framework that simultaneously assesses brain activation and connectivity patterns from multiple subjects. In particular, fMRI measurements from each individual obtained in the form of a multi-dimensional array/tensor at each time are regressed on functions of the stimuli. We impose a low-rank PARAFAC decomposition on the tensor regression coefficients corresponding to the stimuli to achieve parsimony. Multiway stick breaking shrinkage priors are employed to infer activation patterns and associated uncertainties in each voxel. Further, the model introduces region specific random effects which are jointly modeled with a Bayesian Gaussian graphical prior to account for the connectivity among pairs of ROIs. Empirical investigations under various simulation studies demonstrate the effectiveness of the method as a tool to simultaneously assess brain activation and connectivity. The method is then applied to a multi-subject fMRI dataset from a balloon-analog risk-taking experiment in order to make inference about how the brain processes risk.

stat.AP↗