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Explicitly or implicitly, most of dimensionality reduction methods need to determine which samples are neighbors and the similarity between the neighbors in the original highdimensional space. The projection matrix is then learned on the…
Sufficient dimension reduction (SDR) in regression, which reduces the dimension by replacing original predictors with a minimal set of their linear combinations without loss of information, is very helpful when the number of predictors is…
Approximate Bayesian computation (ABC) and other likelihood-free inference methods have gained popularity in the last decade, as they allow rigorous statistical inference for complex models without analytically tractable likelihood…
Stochastic differential equations (SDEs) are increasingly used in longitudinal data analysis, compartmental models, growth modelling, and other applications in a number of disciplines. Parameter estimation, however, currently requires…
Dimensionality reduction is a fundamental task in modern data science. Several projection methods specifically tailored to take into account the non-linearity of the data via local embeddings have been proposed. Such methods are often based…
Many algorithms in machine learning and computational geometry require, as input, the intrinsic dimension of the manifold that supports the probability distribution of the data. This parameter is rarely known and therefore has to be…
Missing data is a common problem in clinical data collection, which causes difficulty in the statistical analysis of such data. To overcome problems caused by incomplete data, we propose a new imputation method called projective resampling…
With the development of feature extraction technique, one sample always can be represented by multiple features which locate in high-dimensional space. Multiple features can re ect various perspectives of one same sample, so there must be…
The growing number of dimensionality reduction methods available for data visualization has recently inspired the development of quality assessment measures, in order to evaluate the resulting low-dimensional representation independently…
When estimating the treatment effect in an observational study, we use a semiparametric locally efficient dimension reduction approach to assess both the treatment assignment mechanism and the average responses in both treated and…
In this work, we explore the theoretical properties of conditional deep generative models under the statistical framework of distribution regression where the response variable lies in a high-dimensional ambient space but concentrates…
Our research proposes a novel method for reducing the dimensionality of functional data, specifically for the case where the response is a scalar and the predictor is a random function. Our method utilizes distance covariance, and has…
Linear dimensionality reduction methods are a cornerstone of analyzing high dimensional data, due to their simple geometric interpretations and typically attractive computational properties. These methods capture many data features of…
We consider the problem of distributed mean estimation (DME), in which $n$ machines are each given a local $d$-dimensional vector $x_v \in \mathbb{R}^d$, and must cooperate to estimate the mean of their inputs $\mu = \frac 1n\sum_{v = 1}^n…
Identifying a low-dimensional informed parameter subspace offers a viable path to alleviating the dimensionality challenge in the sampled-based solution to large-scale Bayesian inverse problems. This paper introduces a novel gradient-based…
This paper introduces Memory-limited Online Subspace Estimation Scheme (MOSES) for both estimating the principal components of streaming data and reducing its dimension. More specifically, in various applications such as sensor networks,…
We introduce a new framework for dimension reduction in the context of high-dimensional regression. Our proposal is to aggregate an ensemble of random projections, which have been carefully chosen based on the empirical regression…
Learning an individualized dose rule in personalized medicine is a challenging statistical problem. Existing methods often suffer from the curse of dimensionality, especially when the decision function is estimated nonparametrically. To…
We consider the problem of reducing the dimensions of parameters and data in non-Gaussian Bayesian inference problems. Our goal is to identify an "informed" subspace of the parameters and an "informative" subspace of the data so that a…
Reducing the variance of the gradient estimator is known to improve the convergence rate of stochastic gradient-based optimization and sampling algorithms. One way of achieving variance reduction is to design importance sampling strategies.…