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In uncertainty quantification, variance-based global sensitivity analysis quantitatively determines the effect of each input random variable on the output by partitioning the total output variance into contributions from each input. However, computing conditional expectations can be prohibitively costly when working with expensive-to-evaluate models. Surrogate models can accelerate this, yet their accuracy depends on the quality and quantity of training data, which is expensive to generate (experimentally or computationally) for complex engineering systems. Thus, methods that work with limited data are desirable. We propose a diffeomorphic modulation under observable response preserving homotopy (D-MORPH) regression to train a polynomial dimensional decomposition surrogate of the output that minimizes the number of training data. The new method first computes a sparse Lasso solution and uses it to define the cost function. A subsequent D-MORPH regression minimizes the difference between the D-MORPH and Lasso solution. The resulting D-MORPH surrogate is more robust to input variations and more accurate with limited training data. We illustrate the accuracy and computational efficiency of the new surrogate for global sensitivity analysis using mathematical functions and an expensive-to-simulate model of char combustion. The new method is highly efficient, requiring only 15% of the training data compared to conventional regression.

Explainable Artificial Intelligence (XAI) has received widespread interest in recent years, and two of the most popular types of explanations are feature attributions, and counterfactual explanations. These classes of approaches have been largely studied independently and the few attempts at reconciling them have been primarily empirical. This work establishes a clear theoretical connection between game-theoretic feature attributions, focusing on but not limited to SHAP, and counterfactuals explanations. After motivating operative changes to Shapley values based feature attributions and counterfactual explanations, we prove that, under conditions, they are in fact equivalent. We then extend the equivalency result to game-theoretic solution concepts beyond Shapley values. Moreover, through the analysis of the conditions of such equivalence, we shed light on the limitations of naively using counterfactual explanations to provide feature importances. Experiments on three datasets quantitatively show the difference in explanations at every stage of the connection between the two approaches and corroborate the theoretical findings.

Analysis of high-dimensional data, where the number of covariates is larger than the sample size, is a topic of current interest. In such settings, an important goal is to estimate the signal level $\tau^2$ and noise level $\sigma^2$, i.e., to quantify how much variation in the response variable can be explained by the covariates, versus how much of the variation is left unexplained. This thesis considers the estimation of these quantities in a semi-supervised setting, where for many observations only the vector of covariates $X$ is given with no responses $Y$. Our main research question is: how can one use the unlabeled data to better estimate $\tau^2$ and $\sigma^2$? We consider two frameworks: a linear regression model and a linear projection model in which linearity is not assumed. In the first framework, while linear regression is used, no sparsity assumptions on the coefficients are made. In the second framework, the linearity assumption is also relaxed and we aim to estimate the signal and noise levels defined by the linear projection. We first propose a naive estimator which is unbiased and consistent, under some assumptions, in both frameworks. We then show how the naive estimator can be improved by using zero-estimators, where a zero-estimator is a statistic arising from the unlabeled data, whose expected value is zero. In the first framework, we calculate the optimal zero-estimator improvement and discuss ways to approximate the optimal improvement. In the second framework, such optimality does no longer hold and we suggest two zero-estimators that improve the naive estimator although not necessarily optimally. Furthermore, we show that our approach reduces the variance for general initial estimators and we present an algorithm that potentially improves any initial estimator. Lastly, we consider four datasets and study the performance of our suggested methods.

Recently, the no-box adversarial attack, in which the attacker lacks access to the model's architecture, weights, and training data, become the most practical and challenging attack setup. However, there is an unawareness of the potential and flexibility inherent in the surrogate model selection process on no-box setting. Inspired by the burgeoning interest in utilizing foundational models to address downstream tasks, this paper adopts an innovative idea that 1) recasting adversarial attack as a downstream task. Specifically, image noise generation to meet the emerging trend and 2) introducing foundational models as surrogate models. Harnessing the concept of non-robust features, we elaborate on two guiding principles for surrogate model selection to explain why the foundational model is an optimal choice for this role. However, paradoxically, we observe that these foundational models underperform. Analyzing this unexpected behavior within the feature space, we attribute the lackluster performance of foundational models (e.g., CLIP) to their significant representational capacity and, conversely, their lack of discriminative prowess. To mitigate this issue, we propose the use of a margin-based loss strategy for the fine-tuning of foundational models on target images. The experimental results verify that our approach, which employs the basic Fast Gradient Sign Method (FGSM) attack algorithm, outstrips the performance of other, more convoluted algorithms. We conclude by advocating for the research community to consider surrogate models as crucial determinants in the effectiveness of adversarial attacks in no-box settings. The implications of our work bear relevance for improving the efficacy of such adversarial attacks and the overall robustness of AI systems.

Self-supervised learning (SSL) has proven effective in solving various problems by generating internal supervisory signals. Unsupervised anomaly detection, which faces the high cost of obtaining true labels, is an area that can greatly benefit from SSL. However, recent literature suggests that tuning the hyperparameters (HP) of data augmentation functions is crucial to the success of SSL-based anomaly detection (SSAD), yet a systematic method for doing so remains unknown. In this work, we propose DSV (Discordance and Separability Validation), an unsupervised validation loss to select high-performing detection models with effective augmentation HPs. DSV captures the alignment between an augmentation function and the anomaly-generating mechanism with surrogate losses, which approximate the discordance and separability of test data, respectively. As a result, the evaluation via DSV leads to selecting an effective SSAD model exhibiting better alignment, which results in high detection accuracy. We theoretically derive the degree of approximation conducted by the surrogate losses and empirically show that DSV outperforms a wide range of baselines on 21 real-world tasks.

Automated classifiers (ACs), often built via supervised machine learning (SML), can categorize large, statistically powerful samples of data ranging from text to images and video, and have become widely popular measurement devices in communication science and related fields. Despite this popularity, even highly accurate classifiers make errors that cause misclassification bias and misleading results in downstream analyses-unless such analyses account for these errors. As we show in a systematic literature review of SML applications, communication scholars largely ignore misclassification bias. In principle, existing statistical methods can use "gold standard" validation data, such as that created by human annotators, to correct misclassification bias and produce consistent estimates. We introduce and test such methods, including a new method we design and implement in the R package misclassificationmodels, via Monte Carlo simulations designed to reveal each method's limitations, which we also release. Based on our results, we recommend our new error correction method as it is versatile and efficient. In sum, automated classifiers, even those below common accuracy standards or making systematic misclassifications, can be useful for measurement with careful study design and appropriate error correction methods.

We investigate a generalized framework for estimating latent low-rank tensors in an online setting, encompassing both linear and generalized linear models. This framework offers a flexible approach for handling continuous or categorical variables. Additionally, we investigate two specific applications: online tensor completion and online binary tensor learning. To address these challenges, we propose the online Riemannian gradient descent algorithm, which demonstrates linear convergence and the ability to recover the low-rank component under appropriate conditions in all applications. Furthermore, we establish a precise entry-wise error bound for online tensor completion. Notably, our work represents the first attempt to incorporate noise in the online low-rank tensor recovery task. Intriguingly, we observe a surprising trade-off between computational and statistical aspects in the presence of noise. Increasing the step size accelerates convergence but leads to higher statistical error, whereas a smaller step size yields a statistically optimal estimator at the expense of slower convergence. Moreover, we conduct regret analysis for online tensor regression. Under the fixed step size regime, a fascinating trilemma concerning the convergence rate, statistical error rate, and regret is observed. With an optimal choice of step size we achieve an optimal regret of $O(\sqrt{T})$. Furthermore, we extend our analysis to the adaptive setting where the horizon T is unknown. In this case, we demonstrate that by employing different step sizes, we can attain a statistically optimal error rate along with a regret of $O(\log T)$. To validate our theoretical claims, we provide numerical results that corroborate our findings and support our assertions.

We consider the classic 1-center problem: Given a set $P$ of $n$ points in a metric space find the point in $P$ that minimizes the maximum distance to the other points of $P$. We study the complexity of this problem in $d$-dimensional $\ell_p$-metrics and in edit and Ulam metrics over strings of length $d$. Our results for the 1-center problem may be classified based on $d$ as follows. $\bullet$ Small $d$: Assuming the hitting set conjecture (HSC), we show that when $d=\omega(\log n)$, no subquadratic algorithm can solve 1-center problem in any of the $\ell_p$-metrics, or in edit or Ulam metrics. $\bullet$ Large $d$: When $d=\Omega(n)$, we extend our conditional lower bound to rule out subquartic algorithms for 1-center problem in edit metric (assuming Quantified SETH). On the other hand, we give a $(1+\epsilon)$-approximation for 1-center in Ulam metric with running time $\tilde{O_{\varepsilon}}(nd+n^2\sqrt{d})$. We also strengthen some of the above lower bounds by allowing approximations or by reducing the dimension $d$, but only against a weaker class of algorithms which list all requisite solutions. Moreover, we extend one of our hardness results to rule out subquartic algorithms for the well-studied 1-median problem in the edit metric, where given a set of $n$ strings each of length $n$, the goal is to find a string in the set that minimizes the sum of the edit distances to the rest of the strings in the set.

Over the past few years, the rapid development of deep learning technologies for computer vision has greatly promoted the performance of medical image segmentation (MedISeg). However, the recent MedISeg publications usually focus on presentations of the major contributions (e.g., network architectures, training strategies, and loss functions) while unwittingly ignoring some marginal implementation details (also known as "tricks"), leading to a potential problem of the unfair experimental result comparisons. In this paper, we collect a series of MedISeg tricks for different model implementation phases (i.e., pre-training model, data pre-processing, data augmentation, model implementation, model inference, and result post-processing), and experimentally explore the effectiveness of these tricks on the consistent baseline models. Compared to paper-driven surveys that only blandly focus on the advantages and limitation analyses of segmentation models, our work provides a large number of solid experiments and is more technically operable. With the extensive experimental results on both the representative 2D and 3D medical image datasets, we explicitly clarify the effect of these tricks. Moreover, based on the surveyed tricks, we also open-sourced a strong MedISeg repository, where each of its components has the advantage of plug-and-play. We believe that this milestone work not only completes a comprehensive and complementary survey of the state-of-the-art MedISeg approaches, but also offers a practical guide for addressing the future medical image processing challenges including but not limited to small dataset learning, class imbalance learning, multi-modality learning, and domain adaptation. The code has been released at: //github.com/hust-linyi/MedISeg

With the rapid increase of large-scale, real-world datasets, it becomes critical to address the problem of long-tailed data distribution (i.e., a few classes account for most of the data, while most classes are under-represented). Existing solutions typically adopt class re-balancing strategies such as re-sampling and re-weighting based on the number of observations for each class. In this work, we argue that as the number of samples increases, the additional benefit of a newly added data point will diminish. We introduce a novel theoretical framework to measure data overlap by associating with each sample a small neighboring region rather than a single point. The effective number of samples is defined as the volume of samples and can be calculated by a simple formula $(1-\beta^{n})/(1-\beta)$, where $n$ is the number of samples and $\beta \in [0,1)$ is a hyperparameter. We design a re-weighting scheme that uses the effective number of samples for each class to re-balance the loss, thereby yielding a class-balanced loss. Comprehensive experiments are conducted on artificially induced long-tailed CIFAR datasets and large-scale datasets including ImageNet and iNaturalist. Our results show that when trained with the proposed class-balanced loss, the network is able to achieve significant performance gains on long-tailed datasets.