This work derives methods for performing nonparametric, nonasymptotic statistical inference for population means under the constraint of local differential privacy (LDP). Given bounded observations $(X_1, \dots, X_n)$ with mean $\mu^\star$ that are privatized into $(Z_1, \dots, Z_n)$, we present confidence intervals (CI) and time-uniform confidence sequences (CS) for $\mu^\star$ when only given access to the privatized data. To achieve this, we introduce a nonparametric and sequentially interactive generalization of Warner's famous ``randomized response'' mechanism, satisfying LDP for arbitrary bounded random variables, and then provide CIs and CSs for their means given access to the resulting privatized observations. For example, our results yield private analogues of Hoeffding's inequality in both fixed-time and time-uniform regimes. We extend these Hoeffding-type CSs to capture time-varying (non-stationary) means, and conclude by illustrating how these methods can be used to conduct private online A/B tests.
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We investigate error of the Euler scheme in the case when the right-hand side function of the underlying ODE satisfies nonstandard assumptions such as local one-sided Lipschitz condition and local H\"older continuity. Moreover, we assume two cases in regards to information availability: exact and noisy with respect to the right-hand side function. Optimality analysis of the Euler scheme is also provided. Finally, we present the results of some numerical experiments.
We propose an automated nonlinear model reduction and mesh adaptation framework for rapid and reliable solution of parameterized advection-dominated problems, with emphasis on compressible flows. The key features of our approach are threefold: (i) a metric-based mesh adaptation technique to generate an accurate mesh for a range of parameters, (ii) a general (i.e., independent of the underlying equations) registration procedure for the computation of a mapping $\Phi$ that tracks moving features of the solution field, and (iii) an hyper-reduced least-square Petrov-Galerkin reduced-order model for the rapid and reliable estimation of the mapped solution. We discuss a general paradigm -- which mimics the refinement loop considered in mesh adaptation -- to simultaneously construct the high-fidelity and the reduced-order approximations, and we discuss actionable strategies to accelerate the offline phase. We present extensive numerical investigations for a quasi-1D nozzle problem and for a two-dimensional inviscid flow past a Gaussian bump to display the many features of the methodology and to assess the performance for problems with discontinuous solutions.
In this work, we address parametric non-stationary fluid dynamics problems within a model order reduction setting based on domain decomposition. Starting from the domain decomposition approach, we derive an optimal control problem, for which we present the convergence analysis. The snapshots for the high-fidelity model are obtained with the Finite Element discretisation, and the model order reduction is then proposed both in terms of time and physical parameters, with a standard POD-Galerkin projection. We test the proposed methodology on two fluid dynamics benchmarks: the non-stationary backward-facing step and lid-driven cavity flow. Finally, also in view of future works, we compare the intrusive POD--Galerkin approach with a non--intrusive approach based on Neural Networks.
Interest in the network analysis of bibliographic data has increased significantly in recent years. Yet, appropriate statistical models for examining the full dynamics of scientific citation networks, connecting authors to the papers they write and papers to other papers they cite, are not available. Very few studies exist that have examined how the social network between co-authors and the citation network among the papers shape one another and co-evolve. In consequence, our understanding of scientific citation networks remains incomplete. In this paper we extend recently derived relational hyperevent models (RHEM) to the analysis of scientific networks, providing a general framework to model the multiple dependencies involved in the relation linking multiple authors to the papers they write, and papers to the multiple references they cite. We demonstrate the empirical value of our model in an analysis of publicly available data on a scientific network comprising millions of authors and papers and assess the relative strength of various effects explaining scientific production. We outline the implications of the model for the evaluation of scientific research.
We develop new matching estimators for estimating causal quantile exposure-response functions and quantile exposure effects with continuous treatments. We provide identification results for the parameters of interest and establish the asymptotic properties of the derived estimators. We introduce a two-step estimation procedure. In the first step, we construct a matched data set via generalized propensity score matching, adjusting for measured confounding. In the second step, we fit a kernel quantile regression to the matched set. We also derive a consistent estimator of the variance of the matching estimators. Using simulation studies, we compare the introduced approach with existing alternatives in various settings. We apply the proposed method to Medicare claims data for the period 2012-2014, and we estimate the causal effect of exposure to PM$_{2.5}$ on the length of hospital stay for each zip code of the contiguous United States.
We consider the degree-Rips construction from topological data analysis, which provides a density-sensitive, multiparameter hierarchical clustering algorithm. We analyze its stability to perturbations of the input data using the correspondence-interleaving distance, a metric for hierarchical clusterings that we introduce. Taking certain one-parameter slices of degree-Rips recovers well-known methods for density-based clustering, but we show that these methods are unstable. However, we prove that degree-Rips, as a multiparameter object, is stable, and we propose an alternative approach for taking slices of degree-Rips, which yields a one-parameter hierarchical clustering algorithm with better stability properties. We prove that this algorithm is consistent, using the correspondence-interleaving distance. We provide an algorithm for extracting a single clustering from one-parameter hierarchical clusterings, which is stable with respect to the correspondence-interleaving distance. And, we integrate these methods into a pipeline for density-based clustering, which we call Persistable. Adapting tools from multiparameter persistent homology, we propose visualization tools that guide the selection of all parameters of the pipeline. We demonstrate Persistable on benchmark datasets, showing that it identifies multi-scale cluster structure in data.
The development of technologies for causal inference with the privacy preservation of distributed data has attracted considerable attention in recent years. To address this issue, we propose a data collaboration quasi-experiment (DC-QE) that enables causal inference from distributed data with privacy preservation. In our method, first, local parties construct dimensionality-reduced intermediate representations from the private data. Second, they share intermediate representations, instead of private data for privacy preservation. Third, propensity scores were estimated from the shared intermediate representations. Finally, the treatment effects were estimated from propensity scores. Our method can reduce both random errors and biases, whereas existing methods can only reduce random errors in the estimation of treatment effects. Through numerical experiments on both artificial and real-world data, we confirmed that our method can lead to better estimation results than individual analyses. Dimensionality-reduction loses some of the information in the private data and causes performance degradation. However, we observed that in the experiments, sharing intermediate representations with many parties to resolve the lack of subjects and covariates, our method improved performance enough to overcome the degradation caused by dimensionality-reduction. With the spread of our method, intermediate representations can be published as open data to help researchers find causalities and accumulated as a knowledge base.
Training robust speaker verification systems without speaker labels has long been a challenging task. Previous studies observed a large performance gap between self-supervised and fully supervised methods. In this paper, we apply a non-contrastive self-supervised learning framework called DIstillation with NO labels (DINO) and propose two regularization terms applied to embeddings in DINO. One regularization term guarantees the diversity of the embeddings, while the other regularization term decorrelates the variables of each embedding. The effectiveness of various data augmentation techniques are explored, on both time and frequency domain. A range of experiments conducted on the VoxCeleb datasets demonstrate the superiority of the regularized DINO framework in speaker verification. Our method achieves the state-of-the-art speaker verification performance under a single-stage self-supervised setting on VoxCeleb. Code has been made publicly available at //github.com/alibaba-damo-academy/3D-Speaker.
Sequential fundraising in two sided online platforms enable peer to peer lending by sequentially bringing potential contributors, each of whose decisions impact other contributors in the market. However, understanding the dynamics of sequential contributions in online platforms for peer lending has been an open ended research question. The centralized investment mechanism in these platforms makes it difficult to understand the implicit competition that borrowers face from a single lender at any point in time. Matching markets are a model of pairing agents where the preferences of agents from both sides in terms of their preferred pairing for transactions can allow to decentralize the market. We study investment designs in two sided platforms using matching markets when the investors or lenders also face restrictions on the investments based on borrower preferences. This situation creates an implicit competition among the lenders in addition to the existing borrower competition, especially when the lenders are uncertain about their standing in the market and thereby the probability of their investments being accepted or the borrower loan requests for projects reaching the reserve price. We devise a technique based on sequential decision making that allows the lenders to adjust their choices based on the dynamics of uncertainty from competition over time. We simulate two sided market matchings in a sequential decision framework and show the dynamics of the lender regret amassed compared to the optimal borrower-lender matching and find that the lender regret depends on the initial preferences set by the lenders which could affect their learning over decision making steps.
Nonlinear extensions to the active subspaces method have brought remarkable results for dimension reduction in the parameter space and response surface design. We further develop a kernel-based nonlinear method. In particular we introduce it in a broader mathematical framework that contemplates also the reduction in parameter space of multivariate objective functions. The implementation is thoroughly discussed and tested on more challenging benchmarks than the ones already present in the literature, for which dimension reduction with active subspaces produces already good results. Finally, we show a whole pipeline for the design of response surfaces with the new methodology in the context of a parametric CFD application solved with the Discontinuous Galerkin method.
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