Privacy protection methods, such as differentially private mechanisms, introduce noise into resulting statistics which often results in complex and intractable sampling distributions. In this paper, we propose to use the simulation-based "repro sample" approach to produce statistically valid confidence intervals and hypothesis tests based on privatized statistics. We show that this methodology is applicable to a wide variety of private inference problems, appropriately accounts for biases introduced by privacy mechanisms (such as by clamping), and improves over other state-of-the-art inference methods such as the parametric bootstrap in terms of the coverage and type I error of the private inference. We also develop significant improvements and extensions for the repro sample methodology for general models (not necessarily related to privacy), including 1) modifying the procedure to ensure guaranteed coverage and type I errors, even accounting for Monte Carlo error, and 2) proposing efficient numerical algorithms to implement the confidence intervals and $p$-values.
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Manifolds discovered by machine learning models provide a compact representation of the underlying data. Geodesics on these manifolds define locally length-minimising curves and provide a notion of distance, which are key for reduced-order modelling, statistical inference, and interpolation. In this work, we first analyse existing methods for computing length-minimising geodesics. We find that these are not suitable for obtaining valid paths, and thus, geodesic distances. We remedy these shortcomings by leveraging numerical tools from differential geometry, which provide the means to obtain Hamiltonian-conserving geodesics. Second, we propose a model-based parameterisation for distance fields and geodesic flows on continuous manifolds. Our approach exploits a manifold-aware extension to the Eikonal equation, eliminating the need for approximations or discretisation. Finally, we develop a curvature-based training mechanism, sampling and scaling points in regions of the manifold exhibiting larger values of the Ricci scalar. This sampling and scaling approach ensures that we capture regions of the manifold subject to higher degrees of geodesic deviation. Our proposed methods provide principled means to compute valid geodesics and geodesic distances on manifolds. This work opens opportunities for latent-space interpolation, optimal control, and distance computation on differentiable manifolds.
The Horvitz-Thompson (HT), the Rao-Hartley-Cochran (RHC) and the generalized regression (GREG) estimators of the finite population mean are considered, when the observations are from an infinite dimensional space. We compare these estimators based on their asymptotic distributions under some commonly used sampling designs and some superpopulations satisfying linear regression models. We show that the GREG estimator is asymptotically at least as efficient as any of the other two estimators under different sampling designs considered in this paper. Further, we show that the use of some well known sampling designs utilizing auxiliary information may have an adverse effect on the performance of the GREG estimator, when the degree of heteroscedasticity present in linear regression models is not very large. On the other hand, the use of those sampling designs improves the performance of this estimator, when the degree of heteroscedasticity present in linear regression models is large. We develop methods for determining the degree of heteroscedasticity, which in turn determines the choice of appropriate sampling design to be used with the GREG estimator. We also investigate the consistency of the covariance operators of the above estimators. We carry out some numerical studies using real and synthetic data, and our theoretical results are supported by the results obtained from those numerical studies.
Simulation is an integral part in the process of developing autonomous vehicles and advantageous for training, validation, and verification of driving functions. Even though simulations come with a series of benefits compared to real-world experiments, various challenges still prevent virtual testing from entirely replacing physical test-drives. Our work provides an overview of these challenges with regard to different aspects and types of simulation and subsumes current trends to overcome them. We cover aspects around perception-, behavior- and content-realism as well as general hurdles in the domain of simulation. Among others, we observe a trend of data-driven, generative approaches and high-fidelity data synthesis to increasingly replace model-based simulation.
Component-based software development (CBD) is a methodology that has been embraced by the software industry to accelerate development, save costs and timelines, minimize testing requirements, and boost quality and output. Compared to the conventional software development approach, this led to the system's development being completed more quickly. By choosing components, identifying systems, and evaluating those systems, CBSE contributes significantly to the software development process. The objective of CBSE is to codify and standardize all disciplines that support CBD-related operations. Analysis of the comparison between component-based and scripting technologies reveals that, in terms of qualitative performance, component-based technologies scale more effectively. Further study and application of CBSE are directly related to the CBD approach's success. This paper explores the introductory concepts and comparative analysis related to component-based software engineering which have been around for a while, but proper adaption of CBSE are still lacking issues are also focused.
We consider a model for multivariate data with heavy-tailed marginal distributions and a Gaussian dependence structure. The different marginals in the model are allowed to have non-identical tail behavior in contrast to most popular modeling paradigms for multivariate heavy-tail analysis. Despite being a practical choice, results on parameter estimation and inference under such models remain limited. In this article, consistent estimates for both marginal tail indices and the Gaussian correlation parameters for such models are provided and asymptotic normality of these estimators are established. The efficacy of the estimation methods are exhibited using extensive simulations and then they are applied to real data sets from insurance claims, internet traffic, and, online networks.
The quality of the inferences we make from pathogen sequence data is determined by the number and composition of pathogen sequences that make up the sample used to drive that inference. However, there remains limited guidance on how to best structure and power studies when the end goal is phylogenetic inference. One question that we can attempt to answer with molecular data is whether some people are more likely to transmit a pathogen than others. Here we present an estimator to quantify differential transmission, as measured by the ratio of reproductive numbers between people with different characteristics, using transmission pairs linked by molecular data, along with a sample size calculation for this estimator. We also provide extensions to our method to correct for imperfect identification of transmission linked pairs, overdispersion in the transmission process, and group imbalance. We validate this method via simulation and provide tools to implement it in an R package, phylosamp.
Accurate and efficient estimation of rare events probabilities is of significant importance, since often the occurrences of such events have widespread impacts. The focus in this work is on precisely quantifying these probabilities, often encountered in reliability analysis of complex engineering systems, based on an introduced framework termed Approximate Sampling Target with Post-processing Adjustment (ASTPA), which herein is integrated with and supported by gradient-based Hamiltonian Markov Chain Monte Carlo (HMCMC) methods. The developed techniques in this paper are applicable from low- to high-dimensional stochastic spaces, and the basic idea is to construct a relevant target distribution by weighting the original random variable space through a one-dimensional output likelihood model, using the limit-state function. To sample from this target distribution, we exploit HMCMC algorithms, a family of MCMC methods that adopts physical system dynamics, rather than solely using a proposal probability distribution, to generate distant sequential samples, and we develop a new Quasi-Newton mass preconditioned HMCMC scheme (QNp-HMCMC), which is particularly efficient and suitable for high-dimensional spaces. To eventually compute the rare event probability, an original post-sampling step is devised using an inverse importance sampling procedure based on the already obtained samples. The statistical properties of the estimator are analyzed as well, and the performance of the proposed methodology is examined in detail and compared against Subset Simulation in a series of challenging low- and high-dimensional problems.
Decentralized learning has recently been attracting increasing attention for its applications in parallel computation and privacy preservation. Many recent studies stated that the underlying network topology with a faster consensus rate (a.k.a. spectral gap) leads to a better convergence rate and accuracy for decentralized learning. However, a topology with a fast consensus rate, e.g., the exponential graph, generally has a large maximum degree, which incurs significant communication costs. Thus, seeking topologies with both a fast consensus rate and small maximum degree is important. In this study, we propose a novel topology combining both a fast consensus rate and small maximum degree called the Base-$(k + 1)$ Graph. Unlike the existing topologies, the Base-$(k + 1)$ Graph enables all nodes to reach the exact consensus after a finite number of iterations for any number of nodes and maximum degree k. Thanks to this favorable property, the Base-$(k + 1)$ Graph endows Decentralized SGD (DSGD) with both a faster convergence rate and more communication efficiency than the exponential graph. We conducted experiments with various topologies, demonstrating that the Base-$(k + 1)$ Graph enables various decentralized learning methods to achieve higher accuracy with better communication efficiency than the existing topologies.
The aim of this work is to develop a fully-distributed algorithmic framework for training graph convolutional networks (GCNs). The proposed method is able to exploit the meaningful relational structure of the input data, which are collected by a set of agents that communicate over a sparse network topology. After formulating the centralized GCN training problem, we first show how to make inference in a distributed scenario where the underlying data graph is split among different agents. Then, we propose a distributed gradient descent procedure to solve the GCN training problem. The resulting model distributes computation along three lines: during inference, during back-propagation, and during optimization. Convergence to stationary solutions of the GCN training problem is also established under mild conditions. Finally, we propose an optimization criterion to design the communication topology between agents in order to match with the graph describing data relationships. A wide set of numerical results validate our proposal. To the best of our knowledge, this is the first work combining graph convolutional neural networks with distributed optimization.
How can we estimate the importance of nodes in a knowledge graph (KG)? A KG is a multi-relational graph that has proven valuable for many tasks including question answering and semantic search. In this paper, we present GENI, a method for tackling the problem of estimating node importance in KGs, which enables several downstream applications such as item recommendation and resource allocation. While a number of approaches have been developed to address this problem for general graphs, they do not fully utilize information available in KGs, or lack flexibility needed to model complex relationship between entities and their importance. To address these limitations, we explore supervised machine learning algorithms. In particular, building upon recent advancement of graph neural networks (GNNs), we develop GENI, a GNN-based method designed to deal with distinctive challenges involved with predicting node importance in KGs. Our method performs an aggregation of importance scores instead of aggregating node embeddings via predicate-aware attention mechanism and flexible centrality adjustment. In our evaluation of GENI and existing methods on predicting node importance in real-world KGs with different characteristics, GENI achieves 5-17% higher NDCG@100 than the state of the art.
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