In fairness audits, a standard objective is to detect whether a given algorithm performs substantially differently between subgroups. Properly powering the statistical analysis of such audits is crucial for obtaining informative fairness assessments, as it ensures a high probability of detecting unfairness when it exists. However, limited guidance is available on the amount of data necessary for a fairness audit, lacking directly applicable results concerning commonly used fairness metrics. Additionally, the consideration of unequal subgroup sample sizes is also missing. In this tutorial, we address these issues by providing guidance on how to determine the required subgroup sample sizes to maximize the statistical power of hypothesis tests for detecting unfairness. Our findings are applicable to audits of binary classification models and multiple fairness metrics derived as summaries of the confusion matrix. Furthermore, we discuss other aspects of audit study designs that can increase the reliability of audit results.
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A comprehensive understanding of the organizational principles in the human brain requires, among other factors, well-quantifiable descriptors of nerve fiber architecture. Three-dimensional polarized light imaging (3D-PLI) is a microscopic imaging technique that enables insights into the fine-grained organization of myelinated nerve fibers with high resolution. Descriptors characterizing the fiber architecture observed in 3D-PLI would enable downstream analysis tasks such as multimodal correlation studies, clustering, and mapping. However, best practices for observer-independent characterization of fiber architecture in 3D-PLI are not yet available. To this end, we propose the application of a fully data-driven approach to characterize nerve fiber architecture in 3D-PLI images using self-supervised representation learning. We introduce a 3D-Context Contrastive Learning (CL-3D) objective that utilizes the spatial neighborhood of texture examples across histological brain sections of a 3D reconstructed volume to sample positive pairs for contrastive learning. We combine this sampling strategy with specifically designed image augmentations to gain robustness to typical variations in 3D-PLI parameter maps. The approach is demonstrated for the 3D reconstructed occipital lobe of a vervet monkey brain. We show that extracted features are highly sensitive to different configurations of nerve fibers, yet robust to variations between consecutive brain sections arising from histological processing. We demonstrate their practical applicability for retrieving clusters of homogeneous fiber architecture and performing data mining for interactively selected templates of specific components of fiber architecture such as U-fibers.
Vision-based estimation of the motion of a moving target is usually formulated as a bearing-only estimation problem where the visual measurement is modeled as a bearing vector. Although the bearing-only approach has been studied for decades, a fundamental limitation of this approach is that it requires extra lateral motion of the observer to enhance the target's observability. Unfortunately, the extra lateral motion conflicts with the desired motion of the observer in many tasks. It is well-known that, once a target has been detected in an image, a bounding box that surrounds the target can be obtained. Surprisingly, this common visual measurement especially its size information has not been well explored up to now. In this paper, we propose a new bearing-angle approach to estimate the motion of a target by modeling its image bounding box as bearing-angle measurements. Both theoretical analysis and experimental results show that this approach can significantly enhance the observability without relying on additional lateral motion of the observer. The benefit of the bearing-angle approach comes with no additional cost because a bounding box is a standard output of object detection algorithms. The approach simply exploits the information that has not been fully exploited in the past. No additional sensing devices or special detection algorithms are required.
Sequential neural posterior estimation (SNPE) techniques have been recently proposed for dealing with simulation-based models with intractable likelihoods. They are devoted to learning the posterior from adaptively proposed simulations using neural network-based conditional density estimators. As a SNPE technique, the automatic posterior transformation (APT) method proposed by Greenberg et al. (2019) performs notably and scales to high dimensional data. However, the APT method bears the computation of an expectation of the logarithm of an intractable normalizing constant, i.e., a nested expectation. Although atomic APT was proposed to solve this by discretizing the normalizing constant, it remains challenging to analyze the convergence of learning. In this paper, we propose a nested APT method to estimate the involved nested expectation instead. This facilitates establishing the convergence analysis. Since the nested estimators for the loss function and its gradient are biased, we make use of unbiased multi-level Monte Carlo (MLMC) estimators for debiasing. To further reduce the excessive variance of the unbiased estimators, this paper also develops some truncated MLMC estimators by taking account of the trade-off between the bias and the average cost. Numerical experiments for approximating complex posteriors with multimodal in moderate dimensions are provided.
In hypothesis testing problems, taking samples sequentially and stopping opportunistically to make the inference greatly enhances the reliability. The design of the stopping and inference policy, however, critically relies on the knowledge of the underlying distribution of each hypothesis. When the knowledge of distributions, say, $P_0$ and $P_1$ in the binary-hypothesis case, is replaced by empirically observed statistics from the respective distributions, the gain of sequentiality is less understood when subject to universality constraints. In this work, the gap is mended by a unified study on sequentiality in the universal binary classification problem. We propose a unified framework where the universality constraints are set on the expected stopping time as well as the type-I error exponent. The type-I error exponent is required to achieve a pre-set distribution-dependent constraint $\lambda(P_0,P_1)$ for all $P_0,P_1$. The framework is employed to investigate a semi-sequential and a fully-sequential setup, so that fair comparison can be made with the fixed-length setup. The optimal type-II error exponents in different setups are characterized when the function $\lambda$ satisfies mild continuity conditions. The benefit of sequentiality is shown by comparing the semi-sequential, the fully-sequential, and the fixed-length cases in representative examples of $\lambda$. Conditions under which sequentiality eradicates the trade-off between error exponents are also derived.
The chain graph model admits both undirected and directed edges in one graph, where symmetric conditional dependencies are encoded via undirected edges and asymmetric causal relations are encoded via directed edges. Though frequently encountered in practice, the chain graph model has been largely under investigated in literature, possibly due to the lack of identifiability conditions between undirected and directed edges. In this paper, we first establish a set of novel identifiability conditions for the Gaussian chain graph model, exploiting a low rank plus sparse decomposition of the precision matrix. Further, an efficient learning algorithm is built upon the identifiability conditions to fully recover the chain graph structure. Theoretical analysis on the proposed method is conducted, assuring its asymptotic consistency in recovering the exact chain graph structure. The advantage of the proposed method is also supported by numerical experiments on both simulated examples and a real application on the Standard & Poor 500 index data.
PageRank is a popular centrality metric that assigns importance to the vertices of a graph based on its neighbors and their score. Efficient parallel algorithms for updating PageRank on dynamic graphs is crucial for various applications, especially as dataset sizes have reached substantial scales. This technical report presents our Dynamic Frontier approach. Given a batch update of edge deletion and insertions, it progressively identifies affected vertices that are likely to change their ranks with minimal overhead. On a server equipped with a 64-core AMD EPYC-7742 processor, our Dynamic Frontier PageRank outperforms Static, Naive-dynamic, and Dynamic Traversal PageRank by 7.8x, 2.9x, and 3.9x respectively - on uniformly random batch updates of size 10^-7 |E| to 10^-3 |E|. In addition, our approach improves performance at an average rate of 1.8x for every doubling of threads.
Graphs are important data representations for describing objects and their relationships, which appear in a wide diversity of real-world scenarios. As one of a critical problem in this area, graph generation considers learning the distributions of given graphs and generating more novel graphs. Owing to their wide range of applications, generative models for graphs, which have a rich history, however, are traditionally hand-crafted and only capable of modeling a few statistical properties of graphs. Recent advances in deep generative models for graph generation is an important step towards improving the fidelity of generated graphs and paves the way for new kinds of applications. This article provides an extensive overview of the literature in the field of deep generative models for graph generation. Firstly, the formal definition of deep generative models for the graph generation and the preliminary knowledge are provided. Secondly, taxonomies of deep generative models for both unconditional and conditional graph generation are proposed respectively; the existing works of each are compared and analyzed. After that, an overview of the evaluation metrics in this specific domain is provided. Finally, the applications that deep graph generation enables are summarized and five promising future research directions are highlighted.
Graph Neural Networks (GNNs) have recently become increasingly popular due to their ability to learn complex systems of relations or interactions arising in a broad spectrum of problems ranging from biology and particle physics to social networks and recommendation systems. Despite the plethora of different models for deep learning on graphs, few approaches have been proposed thus far for dealing with graphs that present some sort of dynamic nature (e.g. evolving features or connectivity over time). In this paper, we present Temporal Graph Networks (TGNs), a generic, efficient framework for deep learning on dynamic graphs represented as sequences of timed events. Thanks to a novel combination of memory modules and graph-based operators, TGNs are able to significantly outperform previous approaches being at the same time more computationally efficient. We furthermore show that several previous models for learning on dynamic graphs can be cast as specific instances of our framework. We perform a detailed ablation study of different components of our framework and devise the best configuration that achieves state-of-the-art performance on several transductive and inductive prediction tasks for dynamic graphs.
Incompleteness is a common problem for existing knowledge graphs (KGs), and the completion of KG which aims to predict links between entities is challenging. Most existing KG completion methods only consider the direct relation between nodes and ignore the relation paths which contain useful information for link prediction. Recently, a few methods take relation paths into consideration but pay less attention to the order of relations in paths which is important for reasoning. In addition, these path-based models always ignore nonlinear contributions of path features for link prediction. To solve these problems, we propose a novel KG completion method named OPTransE. Instead of embedding both entities of a relation into the same latent space as in previous methods, we project the head entity and the tail entity of each relation into different spaces to guarantee the order of relations in the path. Meanwhile, we adopt a pooling strategy to extract nonlinear and complex features of different paths to further improve the performance of link prediction. Experimental results on two benchmark datasets show that the proposed model OPTransE performs better than state-of-the-art methods.
Named entity recognition (NER) is the task to identify text spans that mention named entities, and to classify them into predefined categories such as person, location, organization etc. NER serves as the basis for a variety of natural language applications such as question answering, text summarization, and machine translation. Although early NER systems are successful in producing decent recognition accuracy, they often require much human effort in carefully designing rules or features. In recent years, deep learning, empowered by continuous real-valued vector representations and semantic composition through nonlinear processing, has been employed in NER systems, yielding stat-of-the-art performance. In this paper, we provide a comprehensive review on existing deep learning techniques for NER. We first introduce NER resources, including tagged NER corpora and off-the-shelf NER tools. Then, we systematically categorize existing works based on a taxonomy along three axes: distributed representations for input, context encoder, and tag decoder. Next, we survey the most representative methods for recent applied techniques of deep learning in new NER problem settings and applications. Finally, we present readers with the challenges faced by NER systems and outline future directions in this area.
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