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We propose a communication-efficient distributed estimation method for sparse linear discriminant analysis (LDA) in the high dimensional regime. Our method distributes the data of size $N$ into $m$ machines, and estimates a local sparse LDA…
Multiple generalized additive models (GAMs) are a type of distributional regression wherein parameters of probability distributions depend on predictors through smooth functions, with selection of the degree of smoothness via $L_2$…
We introduce innovative inference procedures for analyzing time series data. Our methodology enables density approximation and composite hypothesis testing based on Whittle's estimator, a widely applied M-estimator in the frequency domain.…
We prove a general result implying the $L^2$ stability of Haar decompositions of $L^2({\bf R}^d)$ functions when the Haar functions are distorted by arbitrary, independent, affine changes of variable that are close to the identity. We apply…
We consider the problem of on-line evaluation of critical characteristic parameters such as the L_2-gain (L2G), input feedforward passivity index (IFP) and output feedback passivity index (OFP) of non-linear systems using their input-output…
Recent studies have made remarkable progress in histopathology classification. Based on current successes, contemporary works proposed to further upgrade the model towards a more generalizable and robust direction through incrementally…
For some special data in reality, such as the genetic data, adjacent genes may have the similar function. Thus ensuring the smoothness between adjacent genes is highly necessary. But, in this case, the standard lasso penalty just doesn't…
This article presents a general multivariate $f$-sensitivity index, rooted in the $f$-divergence between the unconditional and conditional probability measures of a stochastic response, for global sensitivity analysis. Unlike the…
Several new estimation methods have been recently proposed for the linear regression model with observation error in the design. Different assumptions on the data generating process have motivated different estimators and analysis. In…
This paper is devoted to the study of the general linear hypothesis testing (GLHT) problem of multi-sample high-dimensional mean vectors. For the GLHT problem, we introduce a test statistic based on $L^2$-norm and random integration method,…
In observational studies, exposures are often continuous rather than binary or discrete. At the same time, sensitivity analysis is an important tool that can help determine the robustness of a causal conclusion to a certain level of…
Empirical researchers are increasingly faced with rich data sets containing many controls or instrumental variables, making it essential to choose an appropriate approach to variable selection. In this paper, we provide results for valid…
As a powerful tool for longitudinal data analysis, the generalized estimating equations have been widely studied in the academic community. However, in large-scale settings, this approach faces pronounced computational and storage…
In this paper, we consider the nonparametric random regression model $Y=f_1(X_1)+f_2(X_2)+\epsilon$ and address the problem of estimating the function $f_1$. The term $f_2(X_2)$ is regarded as a nuisance term which can be considerably more…
The Hessian discretisation method (HDM) for fourth order linear elliptic equations provides a unified convergence analysis framework based on three properties namely coercivity, consistency, and limit-conformity. Some examples that fit in…
This paper studies the problem of estimation from relative measurements in a graph, in which a vector indexed over the nodes has to be reconstructed from pairwise measurements of differences between its components associated to nodes…
This paper studies the problems of identifiability and estimation in high-dimensional nonparametric latent structure models. We introduce an identifiability theorem that generalizes existing conditions, establishing a unified framework…
This paper addresses distributed parameter estimation in stochastic dynamic systems with quantized measurements, constrained by quantized communication and Markovian switching directed topologies. To enable accurate recovery of the original…
Causal discovery algorithms often perform poorly with limited samples. While integrating expert knowledge (including from LLMs) as constraints promises to improve performance, guarantees for existing methods require perfect predictions or…
Boosting is a key method in statistical learning, allowing for converting weak learners into strong ones. While well studied in the realizable case, the statistical properties of weak-to-strong learning remain less understood in the…