arXiv subjects

Austin Brown

Publications and source records attributed to Austin Brown.

15 recordsLinked to original sources

arXiv2026

Markov Chain CLTs: Resolving Open Problems

Markov chain central limit theorems (CLTs) and their associated variances are very important for implementing Markov chain Monte Carlo algorithms among other applications. H\"aggstr\"om and Rosenthal (2007) presented various results regarding the equality of different formulae for this variance and also posed seven open problems. We resolve all seven in this paper. For stationary, ergodic and reversible chains, we prove that whenever the normalized partial sums satisfy a $\sqrt{n}$-CLT, the variance limit is finite if the function is square-integrable, otherwise undefined. Moreover, failure of the $\sqrt{n}$-CLT forces the normalized partial sums to be non-tight. We also show that Roberts' holding-probability condition precludes a CLT even without assuming reversibility or square-integrability. Finally, we develop a general principle that expresses Fourier coefficients as the autocovariances of an ergodic nonreversible Markov chain.

math.PR↗

arXiv2026

Hyper-V uniform ergodicity of Markov chains

We develop a new uniform drift condition and local minorization that implies a stronger weighted form of uniform ergodicity for Markov chains we call hyper-V uniform ergodicity. The convergence guarantees geometric decay of the bias towards the invariant measure independently of the initialization for all functions controlled by a dominating function V. A key advantage of the approach is that it bypasses the need to establish a global minorization condition, which is often substantially more difficult to verify in practice, while yielding stronger convergence guarantees than global minorization. Optimal convergence bounds in a minimax sense of the framework are established. The utility of the framework is demonstrated through applications to the P'olya-Gamma and Kolmogorov-Gamma Gibbs samplers. We also show qualitative hyper-V uniform ergodicity convergence for two-variable Gibbs samplers can be inferred by the form of the invariant measure, bypassing convergence analysis entirely.

math.ST↗

arXiv2026

Implications of weak convergence rates of Markov transition kernels

This article extends weak convergence bounds of Markov transition kernels to convergence bounds on the variance of the Markov kernel applied to Lipschitz functions. In the reversible case, weak convergence rates of the transition kernels imply chi-squared divergence convergence bounds if the density of the initialization measure is Lipschitz. These results provide new tools to establish central limit theorems for Lipschitz functions used in Markov chain Monte Carlo simulations. Applications are explored to the stability of Metropolis-Hastings algorithms in high dimensions, stochastic gradient descent, and solutions to stochastic delay equations.

math.ST↗

arXiv2026

A Nonparametric Adaptive EWMA Control Chart for Binary Monitoring of Multiple Stream Processes

Monitoring binomial proportions across multiple independent streams is a critical challenge in Statistical Process Control (SPC), with applications from manufacturing to cybersecurity. While EWMA charts offer sensitivity to small shifts, existing implementations rely on asymptotic variance approximations that fail during early-phase monitoring. We introduce a Cumulative Standardized Binomial EWMA (CSB-EWMA) chart that overcomes this limitation by deriving the exact time-varying variance of the EWMA statistic for binary multiple-stream data, enabling adaptive control limits that ensure statistical rigor from the first sample. Through extensive simulations, we identify optimal smoothing ({\lambda}) and limit (L) parameters to achieve target in-control average run length (ARL0) of 370 and 500. The CSB-EWMA chart demonstrates rapid shift detection across both ARL0 targets, with out-of-control average run length (ARL1) dropping to 3-7 samples for moderate shifts ({\delta}=0.2), and exhibits exceptional robustness across different data distributions, with low ARL1 Coefficients of Variation (CV < 0.10 for small shifts) for both ARL0 = 370 and 500. This work provides practitioners with a distribution-free, sensitive, and theoretically sound tool for early change detection in binomial multiple-stream processes.

stat.ML↗

arXiv2026

Derivations for the Cumulative Standardized Binomial EWMA (CSB-EWMA) Control Chart

This paper presents the exact mathematical derivation of the mean and variance properties for the Exponentially Weighted Moving Average (EWMA) statistic applied to binomial proportion monitoring in Multiple Stream Processes (MSPs). We develop a Cumulative Standardized Binomial EWMA (CSB-EWMA) formulation that provides adaptive control limits based on exact time-varying variance calculations, overcoming the limitations of asymptotic approximations during early-phase monitoring. The derivations are rigorously validated through Monte Carlo simulations, demonstrating remarkable agreement between theoretical predictions and empirical results. This work establishes a theoretical foundation for distribution-free monitoring of binary outcomes across parallel data streams, with applications in statistical process control across diverse domains including manufacturing, healthcare, and cybersecurity.

stat.ME↗

arXiv2024

Upper and lower bounds on the subgeometric convergence of adaptive Markov chain Monte Carlo

We investigate lower bounds on the subgeometric convergence of adaptive Markov chain Monte Carlo under any adaptation strategy. In particular, we prove general lower bounds in total variation and on the weak convergence rate under general adaptation plans. If the adaptation diminishes sufficiently fast, we also develop comparable convergence rate upper bounds that are capable of approximately matching the convergence rate in the subgeometric lower bound. These results provide insight into the optimal design of adaptation strategies and also limitations on the convergence behavior of adaptive Markov chain Monte Carlo. Applications to an adaptive unadjusted Langevin algorithm as well as adaptive Metropolis-Hastings with independent proposals and random-walk proposals are explored.

math.ST↗

arXiv2024

Fast and Modular Autonomy Software for Autonomous Racing Vehicles

Autonomous motorsports aim to replicate the human racecar driver with software and sensors. As in traditional motorsports, Autonomous Racing Vehicles (ARVs) are pushed to their handling limits in multi-agent scenarios at extremely high ($\geq 150mph$) speeds. This Operational Design Domain (ODD) presents unique challenges across the autonomy stack. The Indy Autonomous Challenge (IAC) is an international competition aiming to advance autonomous vehicle development through ARV competitions. While far from challenging what a human racecar driver can do, the IAC is pushing the state of the art by facilitating full-sized ARV competitions. This paper details the MIT-Pitt-RW Team's approach to autonomous racing in the IAC. In this work, we present our modular and fast approach to agent detection, motion planning and controls to create an autonomy stack. We also provide analysis of the performance of the software stack in single and multi-agent scenarios for rapid deployment in a fast-paced competition environment. We also cover what did and did not work when deployed on a physical system the Dallara AV-21 platform and potential improvements to address these shortcomings. Finally, we convey lessons learned and discuss limitations and future directions for improvement.

cs.RO↗

arXiv2024

Weak convergence of adaptive Markov chain Monte Carlo

This article develops general conditions for weak convergence of adaptive Markov chain Monte Carlo processes and is shown to imply a weak law of large numbers for bounded Lipschitz continuous functions. This allows an estimation theory for adaptive Markov chain Monte Carlo where previously developed theory in total variation may fail or be difficult to establish. Extensions of weak convergence to general Wasserstein distances are established along with a weak law of large numbers for possibly unbounded Lipschitz functions. Applications are applied to auto-regressive processes in various settings, unadjusted Langevin processes, and adaptive Metropolis-Hastings.

math.ST↗

arXiv2024

A non-asymptotic error analysis for parallel Monte Carlo estimation from many short Markov chains

Single-chain Markov chain Monte Carlo simulates realizations from a Markov chain to estimate expectations with the empirical average. The single-chain simulation is generally of considerable length and restricts many advantages of modern parallel computation. This paper constructs a novel many-short-chains Monte Carlo (MSC) estimator by averaging over multiple independent sums from Markov chains of a guaranteed short length. The computational advantage is the independent Markov chain simulations can be fast and may be run in parallel. The MSC estimator requires an importance sampling proposal and a drift condition on the Markov chain without requiring convergence analysis on the Markov chain. A non-asymptotic error analysis is developed for the MSC estimator under both geometric and multiplicative drift conditions. Empirical performance is illustrated on an autoregressive process and the P\'olya-Gamma Gibbs sampler for Bayesian logistic regression to predict cardiovascular disease.

math.ST↗

arXiv2023

Estimating MCMC convergence rates using common random number simulation

This paper presents how to use common random number (CRN) simulation to evaluate Markov chain Monte Carlo (MCMC) convergence to stationarity. We provide an upper bound on the Wasserstein distance of a Markov chain to its stationary distribution after $N$ steps in terms of averages over CRN simulations. We apply our bound to Gibbs samplers on a model related to James-Stein estimators, a variance component model, and a Bayesian linear regression model. Using our examples, we show that the CRN-based simulation combined with a coalescing condition to generate a total variation bound converges to zero much more faster than the available drift and minorization bounds, while also converging at the same rate as the one-shot coupling bound.

stat.CO↗

arXiv2023

Automated Machine Learning for Deep Learning based Malware Detection

Deep learning (DL) has proven to be effective in detecting sophisticated malware that is constantly evolving. Even though deep learning has alleviated the feature engineering problem, finding the most optimal DL model, in terms of neural architecture search (NAS) and the model's optimal set of hyper-parameters, remains a challenge that requires domain expertise. In addition, many of the proposed state-of-the-art models are very complex and may not be the best fit for different datasets. A promising approach, known as Automated Machine Learning (AutoML), can reduce the domain expertise required to implement a custom DL model. AutoML reduces the amount of human trial-and-error involved in designing DL models, and in more recent implementations can find new model architectures with relatively low computational overhead. This work provides a comprehensive analysis and insights on using AutoML for static and online malware detection. For static, our analysis is performed on two widely used malware datasets: SOREL-20M to demonstrate efficacy on large datasets; and EMBER-2018, a smaller dataset specifically curated to hinder the performance of machine learning models. In addition, we show the effects of tuning the NAS process parameters on finding a more optimal malware detection model on these static analysis datasets. Further, we also demonstrate that AutoML is performant in online malware detection scenarios using Convolutional Neural Networks (CNNs) for cloud IaaS. We compare an AutoML technique to six existing state-of-the-art CNNs using a newly generated online malware dataset with and without other applications running in the background during malware execution.In general, our experimental results show that the performance of AutoML based static and online malware detection models are on par or even better than state-of-the-art models or hand-designed models presented in literature.

cs.CR↗

arXiv2022

Lower bounds on the rate of convergence for accept-reject-based Markov chains in Wasserstein and total variation distances

To avoid poor empirical performance in Metropolis-Hastings and other accept-reject-based algorithms practitioners often tune them by trial and error. Lower bounds on the convergence rate are developed in both total variation and Wasserstein distances in order to identify how the simulations will fail so these settings can be avoided, providing guidance on tuning. Particular attention is paid to using the lower bounds to study the convergence complexity of accept-reject-based Markov chains and to constrain the rate of convergence for geometrically ergodic Markov chains. The theory is applied in several settings. For example, if the target density concentrates with a parameter n (e.g. posterior concentration, Laplace approximations), it is demonstrated that the convergence rate of a Metropolis-Hastings chain can be arbitrarily slow if the tuning parameters do not depend carefully on n. This is demonstrated with Bayesian logistic regression with Zellner's g-prior when the dimension and sample increase together and flat prior Bayesian logistic regression as n tends to infinity.

math.ST↗

arXiv2022

Geometric ergodicity of Gibbs samplers for Bayesian error-in-variable regression

Multivariate Bayesian error-in-variable (EIV) linear regression is considered to account for additional additive Gaussian error in the features and response. A 3-variable deterministic scan Gibbs samplers is constructed for multivariate EIV regression models using classical and Berkson errors with independent normal and inverse-Wishart priors. These Gibbs samplers are proven to always be geometrically ergodic which ensures a central limit theorem for many time averages from the Markov chains. We demonstrate the strengths and limitations of the Gibbs sampler with simulated data for large data problems, robustness to misspecification and also analyze a real-data example in astrophysics.

math.ST↗

arXiv2022

Online Malware Classification with System-Wide System Calls in Cloud IaaS

Accurately classifying malware in an environment allows the creation of better response and remediation strategies by cyber analysts. However, classifying malware in a live environment is a difficult task due to the large number of system data sources. Collecting statistics from these separate sources and processing them together in a form that can be used by a machine learning model is difficult. Fortunately, all of these resources are mediated by the operating system's kernel. User programs, malware included, interacts with system resources by making requests to the kernel with system calls. Collecting these system calls provide insight to the interaction with many system resources in a single location. Feeding these system calls into a performant model such as a random forest allows fast, accurate classification in certain situations. In this paper, we evaluate the feasibility of using system call sequences for online malware classification in both low-activity and heavy-use Cloud IaaS. We collect system calls as they are received by the kernel and take n-gram sequences of calls to use as features for tree-based machine learning models. We discuss the performance of the models on baseline systems with no extra running services and systems under heavy load and the performance gap between them.

cs.CR↗

arXiv2021

Exact Convergence Analysis for Metropolis-Hastings Independence Samplers in Wasserstein Distances

Under mild assumptions, we show the exact convergence rate in total variation is also exact in weaker Wasserstein distances for the Metropolis-Hastings independence sampler. We develop a new upper and lower bound on the worst-case Wasserstein distance when initialized from points. For an arbitrary point initialization, we show the convergence rate is the same and matches the convergence rate in total variation. We derive exact convergence expressions for more general Wasserstein distances when initialization is at a specific point. Using optimization, we construct a novel centered independent proposal to develop exact convergence rates in Bayesian quantile regression and many generalized linear model settings. We show the exact convergence rate can be upper bounded in Bayesian binary response regression (e.g. logistic and probit) when the sample size and dimension grow together.

math.ST↗