Related papers: An evaluation framework for dimensionality reducti…
Dimensionality reduction (DR) plays a vital role in the visual analysis of high-dimensional data. One main aim of DR is to reveal hidden patterns that lie on intrinsic low-dimensional manifolds. However, DR often overlooks important…
Sufficient dimension reduction aims for reduction of dimensionality of a regression without loss of information by replacing the original predictor with its lower-dimensional subspace. Partial (sufficient) dimension reduction arises when…
One of the central issues of several machine learning applications on real data is the choice of the input features. Ideally, the designer should select only the relevant, non-redundant features to preserve the complete information…
Methods and algorithms that work with data on nonlinear manifolds are collectively summarized under the term `Riemannian computing'. In practice, curvature can be a key limiting factor for the performance of Riemannian computing methods.…
Developing interpretable machine learning models has become an increasingly important issue. One way in which data scientists have been able to develop interpretable models has been to use dimension reduction techniques. In this paper, we…
In this paper, we address learning problems for high dimensional data. Previously, oblivious random projection based approaches that project high dimensional features onto a random subspace have been used in practice for tackling…
In this work, we investigate Riemannian geometry based dimensionality reduction methods that respect the underlying manifold structure of the data. In particular, we focus on Principal Geodesic Analysis (PGA) as a nonlinear generalization…
By removing irrelevant and redundant features, feature selection aims to find a good representation of the original features. With the prevalence of unlabeled data, unsupervised feature selection has been proven effective in alleviating the…
In this work we are interested in the problems of supervised learning and variable selection when the input-output dependence is described by a nonlinear function depending on a few variables. Our goal is to consider a sparse nonparametric…
A novel framework is introduced to formalize identifiability in well-specified but ill-posed linear regression models. The framework is distribution-free and accommodates highly correlated features that may or may not relate to the…
Machine unlearning, an emerging research topic focusing on compliance with data privacy regulations, enables trained models to remove the information learned from specific data. While many existing methods indirectly address this issue by…
We propose a class of dimension reduction methods for right censored survival data using a counting process representation of the failure process. Semiparametric estimating equations are constructed to estimate the dimension reduction…
Most machine learning techniques are based upon statistical learning theory, often simplified for the sake of computing speed. This paper is focused on the uncertainty aspect of mathematical modeling in machine learning. Regression analysis…
Nonlinear dimensionality reduction methods provide a valuable means to visualize and interpret high-dimensional data. However, many popular methods can fail dramatically, even on simple two-dimensional manifolds, due to problems such as…
We consider partially observed multiscale diffusion models that are specified up to an unknown vector parameter. We establish for a very general class of test functions that the filter of the original model converges to a filter of reduced…
Nonparametric mean function regression with repeated measurements serves as a cornerstone for many statistical branches, such as longitudinal/panel/functional data analysis. In this work, we investigate this problem using fully connected…
Regression evaluation has been performed for decades. Some metrics have been identified to be robust against shifting and scaling of the data but considering the different distributions of data is much more difficult to address (imbalance…
The effectiveness of supervised learning techniques has made them ubiquitous in research and practice. In high-dimensional settings, supervised learning commonly relies on dimensionality reduction to improve performance and identify the…
In this paper, we consider the alignment between an upstream dimensionality reduction task of learning a low-dimensional representation of a set of high-dimensional data and a downstream optimization task of solving a stochastic program…
Few-shot learning is a relatively new technique that specializes in problems where we have little amounts of data. The goal of these methods is to classify categories that have not been seen before with just a handful of samples. Recent…