Understanding how and why certain communities bear a disproportionate burden of disease is challenging due to the scarcity of data on these communities. Surveys provide a useful avenue for accessing hard-to-reach populations, as many surveys specifically oversample understudied and vulnerable populations. When survey data is used for analysis, it is important to account for the complex survey design that gave rise to the data, in order to avoid biased conclusions. The field of Bayesian survey statistics aims to account for such survey design while leveraging the advantages of Bayesian models, which can flexibly handle sparsity through borrowing of information and provide a coherent inferential framework to easily obtain variances for complex models and data types. For these reasons, Bayesian survey methods seem uniquely well-poised for health disparities research, where heterogeneity and sparsity are frequent considerations. This review discusses three main approaches found in the Bayesian survey methodology literature: 1) multilevel regression and post-stratification, 2) weighted pseudolikelihood-based methods, and 3) synthetic population generation. We discuss advantages and disadvantages of each approach, examine recent applications and extensions, and consider how these approaches may be leveraged to improve research in population health equity.
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Cryoablation is a minimally invasive and efficient therapy option for liver cancer. Liquid nitrogen was used to kill the unwanted cells via freezing. One of the challenges of cryosurgery is to destroy the complete tumor without damaging the surrounding healthy cells when the tumor is large. To overcome this challenge, multi-cryoprobes were arranged in a polygonal pattern to create a uniform cooling and optimum ablation zone in the tissue. Single, three, and four cryoprobes were placed in the center, triangle, and square patterns to analyze the temperature profile and ablation zone. The results showed that tissue will freeze quickly when cryoprobes are placed in a square pattern. After the treatment of 600 seconds, $99\%$, $96\%$, and $31\%$ of the tumor were killed using four, three, and single cryoprobes, respectively. One of the difficulties in the multi-probe technique is choosing the probe separation distance and cooling time. The volume of the ablation zone, the thermal damage to healthy cells, and the volume of tumor cells killed during the treatment for different probe separation distances of 10 mm, 15 mm, and 20 mm are analyzed. Compared to other settings, a multi-probe technique destroys the entire tumor with the least harm to healthy cells when probes are arranged in a square pattern with a 15 mm space between them.
Data assimilation is crucial in a wide range of applications, but it often faces challenges such as high computational costs due to data dimensionality and incomplete understanding of underlying mechanisms. To address these challenges, this study presents a novel assimilation framework, termed Latent Assimilation with Implicit Neural Representations (LAINR). By introducing Spherical Implicit Neural Representations (SINR) along with a data-driven uncertainty estimator of the trained neural networks, LAINR enhances efficiency in assimilation process. Experimental results indicate that LAINR holds certain advantage over existing methods based on AutoEncoders, both in terms of accuracy and efficiency.
We consider the problem of sequential change detection, where the goal is to design a scheme for detecting any changes in a parameter or functional $\theta$ of the data stream distribution that has small detection delay, but guarantees control on the frequency of false alarms in the absence of changes. In this paper, we describe a simple reduction from sequential change detection to sequential estimation using confidence sequences: we begin a new $(1-\alpha)$-confidence sequence at each time step, and proclaim a change when the intersection of all active confidence sequences becomes empty. We prove that the average run length is at least $1/\alpha$, resulting in a change detection scheme with minimal structural assumptions~(thus allowing for possibly dependent observations, and nonparametric distribution classes), but strong guarantees. Our approach bears an interesting parallel with the reduction from change detection to sequential testing of Lorden (1971) and the e-detector of Shin et al. (2022).
The notion that algorithmic systems should be "transparent" and "explainable" is common in the many statements of consensus principles developed by governments, companies, and advocacy organizations. But what exactly do policy and legal actors want from these technical concepts, and how do their desiderata compare with the explainability techniques developed in the machine learning literature? In hopes of better connecting the policy and technical communities, we provide case studies illustrating five ways in which algorithmic transparency and explainability have been used in policy settings: specific requirements for explanations; in nonbinding guidelines for internal governance of algorithms; in regulations applicable to highly regulated settings; in guidelines meant to increase the utility of legal liability for algorithms; and broad requirements for model and data transparency. The case studies span a spectrum from precise requirements for specific types of explanations to nonspecific requirements focused on broader notions of transparency, illustrating the diverse needs, constraints, and capacities of various policy actors and contexts. Drawing on these case studies, we discuss promising ways in which transparency and explanation could be used in policy, as well as common factors limiting policymakers' use of algorithmic explainability. We conclude with recommendations for researchers and policymakers.
Current physics-informed (standard or operator) neural networks still rely on accurately learning the initial conditions of the system they are solving. In contrast, standard numerical methods evolve such initial conditions without needing to learn these. In this study, we propose to improve current physics-informed deep learning strategies such that initial conditions do not need to be learned and are represented exactly in the predicted solution. Moreover, this method guarantees that when a DeepONet is applied multiple times to time step a solution, the resulting function is continuous.
Model selection aims to identify a sufficiently well performing model that is possibly simpler than the most complex model among a pool of candidates. However, the decision-making process itself can inadvertently introduce non-negligible bias when the cross-validation estimates of predictive performance are marred by excessive noise. In finite data regimes, cross-validated estimates can encourage the statistician to select one model over another when it is not actually better for future data. While this bias remains negligible in the case of few models, when the pool of candidates grows, and model selection decisions are compounded (as in forward search), the expected magnitude of selection-induced bias is likely to grow too. This paper introduces an efficient approach to estimate and correct selection-induced bias based on order statistics. Numerical experiments demonstrate the reliability of our approach in estimating both selection-induced bias and over-fitting along compounded model selection decisions, with specific application to forward search. This work represents a light-weight alternative to more computationally expensive approaches to correcting selection-induced bias, such as nested cross-validation and the bootstrap. Our approach rests on several theoretic assumptions, and we provide a diagnostic to help understand when these may not be valid and when to fall back on safer, albeit more computationally expensive approaches. The accompanying code facilitates its practical implementation and fosters further exploration in this area.
In real life, success is often contingent upon multiple critical steps that are distant in time from each other and from the final reward. These critical steps are challenging to identify with traditional reinforcement learning (RL) methods that rely on the Bellman equation for credit assignment. Here, we present a new RL algorithm that uses offline contrastive learning to hone in on critical steps. This algorithm, which we call contrastive introspection (ConSpec), can be added to any existing RL algorithm. ConSpec learns a set of prototypes for the critical steps in a task by a novel contrastive loss and delivers an intrinsic reward when the current state matches one of these prototypes. The prototypes in ConSpec provide two key benefits for credit assignment: (1) They enable rapid identification of all the critical steps. (2) They do so in a readily interpretable manner, enabling out-of-distribution generalization when sensory features are altered. Distinct from other contemporary RL approaches to credit assignment, ConSpec takes advantage of the fact that it is easier to retrospectively identify the small set of steps that success is contingent upon than it is to prospectively predict reward at every step taken in the environment. Altogether, ConSpec improves learning in a diverse set of RL tasks, including both those with explicit, discrete critical steps and those with complex, continuous critical steps.
Tens of thousands of simultaneous hypothesis tests are routinely performed in genomic studies to identify differentially expressed genes. However, due to unmeasured confounders, many standard statistical approaches may be substantially biased. This paper investigates the large-scale hypothesis testing problem for multivariate generalized linear models in the presence of confounding effects. Under arbitrary confounding mechanisms, we propose a unified statistical estimation and inference framework that harnesses orthogonal structures and integrates linear projections into three key stages. It first leverages multivariate responses to separate marginal and uncorrelated confounding effects, recovering the confounding coefficients' column space. Subsequently, latent factors and primary effects are jointly estimated, utilizing $\ell_1$-regularization for sparsity while imposing orthogonality onto confounding coefficients. Finally, we incorporate projected and weighted bias-correction steps for hypothesis testing. Theoretically, we establish various effects' identification conditions and non-asymptotic error bounds. We show effective Type-I error control of asymptotic $z$-tests as sample and response sizes approach infinity. Numerical experiments demonstrate that the proposed method controls the false discovery rate by the Benjamini-Hochberg procedure and is more powerful than alternative methods. By comparing single-cell RNA-seq counts from two groups of samples, we demonstrate the suitability of adjusting confounding effects when significant covariates are absent from the model.
Calibration is a pivotal aspect in predictive modeling, as it ensures that the predictions closely correspond with what we observe empirically. The contemporary calibration framework, however, is predominantly focused on prediction models where the outcome is a binary variable. We extend the logistic calibration framework to the generalized calibration framework which includes all members of the exponential family of distributions. We propose two different methods to estimate the calibration curve in this setting, a generalized linear model and a non-parametric smoother. In addition, we define two measures that summarize the calibration performance. The generalized calibration slope which quantifies the amount of over- or underfitting and the generalized calibration slope or calibration-in-the-large that measures the agreement between the global empirical average and the average predicted value. We provide an illustrative example using a simulated data set and hereby show how we can utilize the generalized calibration framework to assess the calibration of different types of prediction models.
We hypothesize that due to the greedy nature of learning in multi-modal deep neural networks, these models tend to rely on just one modality while under-fitting the other modalities. Such behavior is counter-intuitive and hurts the models' generalization, as we observe empirically. To estimate the model's dependence on each modality, we compute the gain on the accuracy when the model has access to it in addition to another modality. We refer to this gain as the conditional utilization rate. In the experiments, we consistently observe an imbalance in conditional utilization rates between modalities, across multiple tasks and architectures. Since conditional utilization rate cannot be computed efficiently during training, we introduce a proxy for it based on the pace at which the model learns from each modality, which we refer to as the conditional learning speed. We propose an algorithm to balance the conditional learning speeds between modalities during training and demonstrate that it indeed addresses the issue of greedy learning. The proposed algorithm improves the model's generalization on three datasets: Colored MNIST, Princeton ModelNet40, and NVIDIA Dynamic Hand Gesture.
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