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Daniel Simpson

Publications and source records attributed to Daniel Simpson.

At least 19 recordsLinked to original sources

Scalable Bayesian Learning with posteriors

Although theoretically compelling, Bayesian learning with modern machine learning models is computationally challenging since it requires approximating a high dimensional posterior distribution. In this work, we (i) introduce posteriors, an easily extensible PyTorch library hosting general-purpose implementations making Bayesian learning accessible and scalable to large data and parameter regimes; (ii) present a tempered framing of stochastic gradient Markov chain Monte Carlo, as implemented in posteriors, that transitions seamlessly into optimization and unveils a minor modification to deep ensembles to ensure they are asymptotically unbiased for the Bayesian posterior, and (iii) demonstrate and compare the utility of Bayesian approximations through experiments including an investigation into the cold posterior effect and applications with large language models.

cs.LG

Explainable Deep Learning Models for Dynamic and Online Malware Classification

In recent years, there has been a significant surge in malware attacks, necessitating more advanced preventive measures and remedial strategies. While several successful AI-based malware classification approaches exist categorized into static, dynamic, or online analysis, most successful AI models lack easily interpretable decisions and explanations for their processes. Our paper aims to delve into explainable malware classification across various execution environments (such as dynamic and online), thoroughly analyzing their respective strengths, weaknesses, and commonalities. To evaluate our approach, we train Feed Forward Neural Networks (FFNN) and Convolutional Neural Networks (CNN) to classify malware based on features obtained from dynamic and online analysis environments. The feature attribution for malware classification is performed by explainability tools, SHAP, LIME and Permutation Importance. We perform a detailed evaluation of the calculated global and local explanations from the experiments, discuss limitations and, ultimately, offer recommendations for achieving a balanced approach.

cs.CR

Thermodynamic Linear Algebra

Linear algebraic primitives are at the core of many modern algorithms in engineering, science, and machine learning. Hence, accelerating these primitives with novel computing hardware would have tremendous economic impact. Quantum computing has been proposed for this purpose, although the resource requirements are far beyond current technological capabilities, so this approach remains long-term in timescale. Here we consider an alternative physics-based computing paradigm based on classical thermodynamics, to provide a near-term approach to accelerating linear algebra. At first sight, thermodynamics and linear algebra seem to be unrelated fields. In this work, we connect solving linear algebra problems to sampling from the thermodynamic equilibrium distribution of a system of coupled harmonic oscillators. We present simple thermodynamic algorithms for (1) solving linear systems of equations, (2) computing matrix inverses, (3) computing matrix determinants, and (4) solving Lyapunov equations. Under reasonable assumptions, we rigorously establish asymptotic speedups for our algorithms, relative to digital methods, that scale linearly in matrix dimension. Our algorithms exploit thermodynamic principles like ergodicity, entropy, and equilibration, highlighting the deep connection between these two seemingly distinct fields, and opening up algebraic applications for thermodynamic computing hardware.

cond-mat.stat-mech

Assessment of fiducial motion in CBCT projections of the abdominal tumor using template matching and sequential stereo triangulation

Purpose: To assess the fiducial motion in abdominal stereotactic body radiotherapy (SBRT) using the cone-beam computed tomography (CBCT) projections acquired for pre-treatment patient set-up. Materials and Methods: Pre-treatment CBCT projections and anterior-posterior (AP) and lateral (LAT) pair of fluoroscopic sequences of 7 pancreatic and 6 liver SBRT patients with implanted fiducials were analyzed for 49 treatment fractions retrospectively. A tracking algorithm based on template matching and sequential stereo triangulation algorithms was used to track the fiducials in the CBCT projections and the fluoro sequence pairs. We predicted the clinical couch adjustment from CBCT tracking and compared it with the clinical couch decision made during the patient's treatment. Results: In 3D coordinate, the fiducial motion ranges for pancreas cases were 9.90+/-3.52 mm, 10.65+/-5.91 mm, and 10.74+/-6.24 mm for CBCT, AP, and LAT fluoro, respectively, while in the liver, they were 13.93+/-3.39 mm, 11.17+/-3.75 mm, and 11.52+/-4.33 mm, respectively. Prediction of couch adjustment in LAT, SI, and AP coordinates from CBCT tracking agrees with the actual clinical couch correction within 0.92+/-0.74 mm, 1.37+/-1.26 mm, and 0.68+/-0.56 mm for pancreas cases and within 1.12+/-0.96 mm, 1.15+/-0.92 mm and 0.90+/-0.86 mm for liver cases, respectively. Conclusion: Tracking pre-treatment CBCT projections using template matching and sequential stereo triangulation is suitable for assessing fiducial motion and adjusting the patient setup for abdominal SBRT. CBCT can be used for motion modeling, potentially eliminating the need for additional fluoroscopic pair acquisition and thus reducing the imaging dose to the patient and the total treatment time.

physics.med-ph

Treatment effect estimation with Multilevel Regression and Poststratification

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.

stat.ME

Bayesian Workflow

The Bayesian approach to data analysis provides a powerful way to handle uncertainty in all observations, model parameters, and model structure using probability theory. Probabilistic programming languages make it easier to specify and fit Bayesian models, but this still leaves us with many options regarding constructing, evaluating, and using these models, along with many remaining challenges in computation. Using Bayesian inference to solve real-world problems requires not only statistical skills, subject matter knowledge, and programming, but also awareness of the decisions made in the process of data analysis. All of these aspects can be understood as part of a tangled workflow of applied Bayesian statistics. Beyond inference, the workflow also includes iterative model building, model checking, validation and troubleshooting of computational problems, model understanding, and model comparison. We review all these aspects of workflow in the context of several examples, keeping in mind that in practice we will be fitting many models for any given problem, even if only a subset of them will ultimately be relevant for our conclusions.

stat.ME

Using sex and gender in survey adjustment

Accounting for sex and gender is a challenge in social science research. While other methodology papers consider issues surrounding appropriate measurement, we consider the problem of adjustment for survey nonresponse and generalization from samples to populations in the context of the recent push toward measuring sex or gender as a non-binary construct. This is challenging not only in that response categories differ between sex and gender measurement, but also in that both these attributes are potentially multidimensional. We reflect on similarities to measuring race/ethnicity before considering the ethical and statistical implications of the options available to us. We present a simulation study to understand the statistical implications under a variety of scenarios, and demonstrate the application of the decision process with the New York City Poverty Tracker. Overall, we conclude not with a single best recommendation for all surveys but rather with an awareness of the complexity of the problem and the benefits and weaknesses of different approaches.

stat.AP

Hamiltonian Monte Carlo using an adjoint-differentiated Laplace approximation: Bayesian inference for latent Gaussian models and beyond

Gaussian latent variable models are a key class of Bayesian hierarchical models with applications in many fields. Performing Bayesian inference on such models can be challenging as Markov chain Monte Carlo algorithms struggle with the geometry of the resulting posterior distribution and can be prohibitively slow. An alternative is to use a Laplace approximation to marginalize out the latent Gaussian variables and then integrate out the remaining hyperparameters using dynamic Hamiltonian Monte Carlo, a gradient-based Markov chain Monte Carlo sampler. To implement this scheme efficiently, we derive a novel adjoint method that propagates the minimal information needed to construct the gradient of the approximate marginal likelihood. This strategy yields a scalable differentiation method that is orders of magnitude faster than state of the art differentiation techniques when the hyperparameters are high dimensional. We prototype the method in the probabilistic programming framework Stan and test the utility of the embedded Laplace approximation on several models, including one where the dimension of the hyperparameter is $\sim$6,000. Depending on the cases, the benefits can include an alleviation of the geometric pathologies that frustrate Hamiltonian Monte Carlo and a dramatic speed-up.

stat.CO

Improving multilevel regression and poststratification with structured priors

A central theme in the field of survey statistics is estimating population-level quantities through data coming from potentially non-representative samples of the population. Multilevel Regression and Poststratification (MRP), a model-based approach, is gaining traction against the traditional weighted approach for survey estimates. MRP estimates are susceptible to bias if there is an underlying structure that the methodology does not capture. This work aims to provide a new framework for specifying structured prior distributions that lead to bias reduction in MRP estimates. We use simulation studies to explore the benefit of these prior distributions and demonstrate their efficacy on non-representative US survey data. We show that structured prior distributions offer absolute bias reduction and variance reduction for posterior MRP estimates in a large variety of data regimes.

stat.ME

The Integrated Nested Laplace Approximation for fitting Dirichlet regression models

This paper introduces a Laplace approximation to Bayesian inference in Dirichlet regression models, which can be used to analyze a set of variables on a simplex exhibiting skewness and heteroscedasticity, without having to transform the data. These data, which mainly consist of proportions or percentages of disjoint categories, are widely known as compositional data and are common in areas such as ecology, geology, and psychology. We provide both the theoretical foundations and a description of how Laplace approximation can be implemented in the case of Dirichlet regression. The paper also introduces the package dirinla in the R-language that extends the R-INLA package, which can not deal directly with Dirichlet likelihoods. Simulation studies are presented to validate the good behaviour of the proposed method, while a real data case-study is used to show how this approach can be applied.

stat.CO

Data integration for high-resolution, continental-scale estimation of air pollution concentrations

Air pollution constitutes the highest environmental risk factor in relation to heath. In order to provide the evidence required for health impact analyses, to inform policy and to develop potential mitigation strategies comprehensive information is required on the state of air pollution. Information on air pollution traditionally comes from ground monitoring (GM) networks but these may not be able to provide sufficient coverage and may need to be supplemented with information from other sources (e.g. chemical transport models; CTMs). However, these may only be available on grids and may not capture micro-scale features that may be important in assessing air quality in areas of high population. We develop a model that allows calibration between multiple data sources available at different levels of support by allowing the coefficients of calibration equations to vary over space and time, enabling downscaling where the data is sufficient to support it. The model is used to produce high-resolution (1km $\times$ 1km) estimates of NO$_2$ and PM$_{2.5}$ across Western Europe for 2010-2016. Concentrations of both pollutants are decreasing during this period, however there remain large populations exposed to levels exceeding the WHO Air Quality Guidelines and thus air pollution remains a serious threat to health.

stat.AP

The experiment is just as important as the likelihood in understanding the prior: A cautionary note on robust cognitive modelling

Cognitive modelling shares many features with statistical modelling, making it seem trivial to borrow from the practices of robust Bayesian statistics to protect the practice of robust cognitive modelling. We take one aspect of statistical workflow-prior predictive checks-and explore how they might be applied to a cognitive modelling task. We find that it is not only the likelihood that is needed to interpret the priors, we also need to incorporate experiment information as well. This suggests that while cognitive modelling might borrow from statistical practices, especially workflow, care must be made to make the adaptions necessary.

stat.AP

Rank-normalization, folding, and localization: An improved $\widehat{R}$ for assessing convergence of MCMC

Markov chain Monte Carlo is a key computational tool in Bayesian statistics, but it can be challenging to monitor the convergence of an iterative stochastic algorithm. In this paper we show that the convergence diagnostic $\widehat{R}$ of Gelman and Rubin (1992) has serious flaws. Traditional $\widehat{R}$ will fail to correctly diagnose convergence failures when the chain has a heavy tail or when the variance varies across the chains. In this paper we propose an alternative rank-based diagnostic that fixes these problems. We also introduce a collection of quantile-based local efficiency measures, along with a practical approach for computing Monte Carlo error estimates for quantiles. We suggest that common trace plots should be replaced with rank plots from multiple chains. Finally, we give recommendations for how these methods should be used in practice.

stat.CO

Validating Bayesian Inference Algorithms with Simulation-Based Calibration

Verifying the correctness of Bayesian computation is challenging. This is especially true for complex models that are common in practice, as these require sophisticated model implementations and algorithms. In this paper we introduce \emph{simulation-based calibration} (SBC), a general procedure for validating inferences from Bayesian algorithms capable of generating posterior samples. This procedure not only identifies inaccurate computation and inconsistencies in model implementations but also provides graphical summaries that can indicate the nature of the problems that arise. We argue that SBC is a critical part of a robust Bayesian workflow, as well as being a useful tool for those developing computational algorithms and statistical software.

stat.ME

Spatial modelling with R-INLA: A review

Coming up with Bayesian models for spatial data is easy, but performing inference with them can be challenging. Writing fast inference code for a complex spatial model with realistically-sized datasets from scratch is time-consuming, and if changes are made to the model, there is little guarantee that the code performs well. The key advantages of R-INLA are the ease with which complex models can be created and modified, without the need to write complex code, and the speed at which inference can be done even for spatial problems with hundreds of thousands of observations. R-INLA handles latent Gaussian models, where fixed effects, structured and unstructured Gaussian random effects are combined linearly in a linear predictor, and the elements of the linear predictor are observed through one or more likelihoods. The structured random effects can be both standard areal model such as the Besag and the BYM models, and geostatistical models from a subset of the Mat\'ern Gaussian random fields. In this review, we discuss the large success of spatial modelling with R-INLA and the types of spatial models that can be fitted, we give an overview of recent developments for areal models, and we give an overview of the stochastic partial differential equation (SPDE) approach and some of the ways it can be extended beyond the assumptions of isotropy and separability. In particular, we describe how slight changes to the SPDE approach leads to straight-forward approaches for non-stationary spatial models and non-separable space-time models.

stat.ME

Yes, but Did It Work?: Evaluating Variational Inference

While it's always possible to compute a variational approximation to a posterior distribution, it can be difficult to discover problems with this approximation. We propose two diagnostic algorithms to alleviate this problem. The Pareto-smoothed importance sampling (PSIS) diagnostic gives a goodness of fit measurement for joint distributions, while simultaneously improving the error in the estimate. The variational simulation-based calibration (VSBC) assesses the average performance of point estimates.

stat.ML

Visualization in Bayesian workflow

Bayesian data analysis is about more than just computing a posterior distribution, and Bayesian visualization is about more than trace plots of Markov chains. Practical Bayesian data analysis, like all data analysis, is an iterative process of model building, inference, model checking and evaluation, and model expansion. Visualization is helpful in each of these stages of the Bayesian workflow and it is indispensable when drawing inferences from the types of modern, high-dimensional models that are used by applied researchers.

stat.ME

The prior can generally only be understood in the context of the likelihood

A key sticking point of Bayesian analysis is the choice of prior distribution, and there is a vast literature on potential defaults including uniform priors, Jeffreys' priors, reference priors, maximum entropy priors, and weakly informative priors. These methods, however, often manifest a key conceptual tension in prior modeling: a model encoding true prior information should be chosen without reference to the model of the measurement process, but almost all common prior modeling techniques are implicitly motivated by a reference likelihood. In this paper we resolve this apparent paradox by placing the choice of prior into the context of the entire Bayesian analysis, from inference to prediction to model evaluation.

stat.ME