This article studies the derivatives in models that flexibly characterize the relationship between a response variable and multiple predictors, with goals of providing both accurate estimation and inference procedures for hypothesis testing. In the setting of tensor product reproducing spaces for nonparametric multivariate functions, we propose a plug-in kernel ridge regression estimator to estimate the derivatives of the underlying multivariate regression function under the smoothing spline ANOVA model. This estimator has an analytical form, making it simple to implement in practice. We first establish $L_\infty$ and $L_2$ convergence rates of the proposed estimator under general random designs. For derivatives with some selected interesting orders, we provide an in-depth analysis establishing the minimax lower bound, which matches the $L_2$ convergence rate. Additionally, motivated by a wide range of applications, we propose a hypothesis testing procedure to examine whether a derivative is zero. Theoretical results demonstrate that the proposed testing procedure achieves the correct size under the null hypothesis and is asymptotically powerful under local alternatives. For ease of use, we also develop an associated bootstrap algorithm to construct the rejection region and calculate the p-value, and the consistency of the proposed algorithm is established. Simulation studies using synthetic data and an application to a real-world dataset confirm the effectiveness of our methods.
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This study proposes an innovative model-based modular approach (MMA) to dynamically optimize order matching and vehicle relocation in a ride-hailing platform. MMA utilizes a two-layer and modular modeling structure. The upper layer determines the spatial transfer patterns of vehicle flow within the system to maximize the total revenue of the current and future stages. With the guidance provided by the upper layer, the lower layer performs rapid vehicle-to-order matching and vehicle relocation. MMA is interpretable, and equipped with the customized and polynomial-time algorithm, which, as an online order-matching and vehicle-relocation algorithm, can scale past thousands of vehicles. We theoretically prove that the proposed algorithm can achieve the global optimum in stylized networks, while the numerical experiments based on both the toy network and realistic dataset demonstrate that MMA is capable of achieving superior systematic performance compared to batch matching and reinforcement-learning based methods. Moreover, its modular and lightweight modeling structure further enables it to achieve a high level of robustness against demand variation while maintaining a relatively low computational cost.
We present a new approach, the Topograph, which reconstructs underlying physics processes, including the intermediary particles, by leveraging underlying priors from the nature of particle physics decays and the flexibility of message passing graph neural networks. The Topograph not only solves the combinatoric assignment of observed final state objects, associating them to their original mother particles, but directly predicts the properties of intermediate particles in hard scatter processes and their subsequent decays. In comparison to standard combinatoric approaches or modern approaches using graph neural networks, which scale exponentially or quadratically, the complexity of Topographs scales linearly with the number of reconstructed objects. We apply Topographs to top quark pair production in the all hadronic decay channel, where we outperform the standard approach and match the performance of the state-of-the-art machine learning technique.
Class imbalance exists in many classification problems, and since the data is designed for accuracy, imbalance in data classes can lead to classification challenges with a few classes having higher misclassification costs. The Backblaze dataset, a widely used dataset related to hard discs, has a small amount of failure data and a large amount of health data, which exhibits a serious class imbalance. This paper provides a comprehensive overview of research in the field of imbalanced data classification. The discussion is organized into three main aspects: data-level methods, algorithmic-level methods, and hybrid methods. For each type of method, we summarize and analyze the existing problems, algorithmic ideas, strengths, and weaknesses. Additionally, the challenges of unbalanced data classification are discussed, along with strategies to address them. It is convenient for researchers to choose the appropriate method according to their needs.
Diffusion models have demonstrated compelling generation quality by optimizing the variational lower bound through a simple denoising score matching loss. In this paper, we provide theoretical evidence that the prevailing practice of using a constant loss weight strategy in diffusion models leads to biased estimation during the training phase. Simply optimizing the denoising network to predict Gaussian noise with constant weighting may hinder precise estimations of original images. To address the issue, we propose an elegant and effective weighting strategy grounded in the theoretically unbiased principle. Moreover, we conduct a comprehensive and systematic exploration to dissect the inherent bias problem deriving from constant weighting loss from the perspectives of its existence, impact and reasons. These analyses are expected to advance our understanding and demystify the inner workings of diffusion models. Through empirical evaluation, we demonstrate that our proposed debiased estimation method significantly enhances sample quality without the reliance on complex techniques, and exhibits improved efficiency compared to the baseline method both in training and sampling processes.
Understanding the impact of data set design on model training and performance can help alleviate the costs associated with generating remote sensing and overhead labeled data. This work examined the impact of training shifted window transformers using bounding boxes and segmentation labels, where the latter are more expensive to produce. We examined classification tasks by comparing models trained with both target and backgrounds against models trained with only target pixels, extracted by segmentation labels. For object detection models, we compared performance using either label type when training. We found that the models trained on only target pixels do not show performance improvement for classification tasks, appearing to conflate background pixels in the evaluation set with target pixels. For object detection, we found that models trained with either label type showed equivalent performance across testing. We found that bounding boxes appeared to be sufficient for tasks that did not require more complex labels, such as object segmentation. Continuing work to determine consistency of this result across data types and model architectures could potentially result in substantial savings in generating remote sensing data sets for deep learning.
In this article, we explore two effective means to communicate the concept of walkability - 1) visualization, and 2) descriptive statistics. We introduce the concept of walkability as measuring the quality of an urban space based on the distance needed to walk from that space to a range of different social, environmental, and economic amenities. We use Dublin city as a worked example and explore quantification and visualization of walkability of various areas of the city. We utilize the Google Map API and Tableau to visualize the less walkable areas across Dublin city and using WLS regression, we assess the effects of unwalkability on house prices in Dublin, thus quantifying the importance of walkable areas from an economic perspective.
An important aspect in developing language models that interact with humans is aligning their behavior to be useful and unharmful for their human users. This is usually achieved by tuning the model in a way that enhances desired behaviors and inhibits undesired ones, a process referred to as alignment. In this paper, we propose a theoretical approach called Behavior Expectation Bounds (BEB) which allows us to formally investigate several inherent characteristics and limitations of alignment in large language models. Importantly, we prove that within the limits of this framework, for any behavior that has a finite probability of being exhibited by the model, there exist prompts that can trigger the model into outputting this behavior, with probability that increases with the length of the prompt. This implies that any alignment process that attenuates an undesired behavior but does not remove it altogether, is not safe against adversarial prompting attacks. Furthermore, our framework hints at the mechanism by which leading alignment approaches such as reinforcement learning from human feedback make the LLM prone to being prompted into the undesired behaviors. This theoretical result is being experimentally demonstrated in large scale by the so called contemporary "chatGPT jailbreaks", where adversarial users trick the LLM into breaking its alignment guardrails by triggering it into acting as a malicious persona. Our results expose fundamental limitations in alignment of LLMs and bring to the forefront the need to devise reliable mechanisms for ensuring AI safety.
We propose a distributional framework for assessing socio-technical risks of foundation models with quantified statistical significance. Our approach hinges on a new statistical relative testing based on first and second order stochastic dominance of real random variables. We show that the second order statistics in this test are linked to mean-risk models commonly used in econometrics and mathematical finance to balance risk and utility when choosing between alternatives. Using this framework, we formally develop a risk-aware approach for foundation model selection given guardrails quantified by specified metrics. Inspired by portfolio optimization and selection theory in mathematical finance, we define a \emph{metrics portfolio} for each model as a means to aggregate a collection of metrics, and perform model selection based on the stochastic dominance of these portfolios. The statistical significance of our tests is backed theoretically by an asymptotic analysis via central limit theorems instantiated in practice via a bootstrap variance estimate. We use our framework to compare various large language models regarding risks related to drifting from instructions and outputting toxic content.
Deep neural networks have revolutionized many machine learning tasks in power systems, ranging from pattern recognition to signal processing. The data in these tasks is typically represented in Euclidean domains. Nevertheless, there is an increasing number of applications in power systems, where data are collected from non-Euclidean domains and represented as the graph-structured data with high dimensional features and interdependency among nodes. The complexity of graph-structured data has brought significant challenges to the existing deep neural networks defined in Euclidean domains. Recently, many studies on extending deep neural networks for graph-structured data in power systems have emerged. In this paper, a comprehensive overview of graph neural networks (GNNs) in power systems is proposed. Specifically, several classical paradigms of GNNs structures (e.g., graph convolutional networks, graph recurrent neural networks, graph attention networks, graph generative networks, spatial-temporal graph convolutional networks, and hybrid forms of GNNs) are summarized, and key applications in power systems such as fault diagnosis, power prediction, power flow calculation, and data generation are reviewed in detail. Furthermore, main issues and some research trends about the applications of GNNs in power systems are discussed.
Recent years have seen important advances in the quality of state-of-the-art models, but this has come at the expense of models becoming less interpretable. This survey presents an overview of the current state of Explainable AI (XAI), considered within the domain of Natural Language Processing (NLP). We discuss the main categorization of explanations, as well as the various ways explanations can be arrived at and visualized. We detail the operations and explainability techniques currently available for generating explanations for NLP model predictions, to serve as a resource for model developers in the community. Finally, we point out the current gaps and encourage directions for future work in this important research area.
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