Related papers: Online Kernel Sliced Inverse Regression
With the rapid development of data collection and aggregation technologies in many scientific disciplines, it is becoming increasingly ubiquitous to conduct large-scale or online regression to analyze real-world data and unveil real-world…
Many scientific problems involve data exhibiting both temporal and cross-sectional dependencies. While linear dependencies have been extensively studied, the theoretical analysis of regression estimators under nonlinear dependencies remains…
Sparse coding--that is, modelling data vectors as sparse linear combinations of basis elements--is widely used in machine learning, neuroscience, signal processing, and statistics. This paper focuses on the large-scale matrix factorization…
Nonparametric regression imputation is commonly used in missing data analysis. However, it suffers from the ``curse of dimension". The problem can be alleviated by the explosive sample size in the era of big data, while the large-scale data…
This paper addresses source component shift adaptation, aiming to update predictions adapting to source component shifts for incoming data streams based on past training data. Existing online learning methods often fail to utilize recurring…
VC-dimension and $\varepsilon$-nets are key concepts in Statistical Learning Theory. Intuitively, VC-dimension is a measure of the size of a class of sets. The famous $\varepsilon$-net theorem, a fundamental result in Discrete Geometry,…
Personalized treatment of patients based on tissue-specific cancer subtypes has strongly increased the efficacy of the chosen therapies. Even though the amount of data measured for cancer patients has increased over the last years, most…
Kernel methods are powerful and flexible approach to solve many problems in machine learning. Due to the pairwise evaluations in kernel methods, the complexity of kernel computation grows as the data size increases; thus the applicability…
Subspace clustering aims to group data points into multiple clusters of which each corresponds to one subspace. Most existing subspace clustering approaches assume that input data lie on linear subspaces. In practice, however, this…
We propose a novel sparse sliced inverse regression method based on random projections in a large $p$ small $n$ setting. Embedded in a generalized eigenvalue framework, the proposed approach finally reduces to parallel execution of…
The development and use of dimension reduction methods is prevalent in modern statistical literature. This paper reviews a class of dimension reduction techniques which aim to simultaneously select relevant predictors and find clusters…
In this paper, we propose a practical online method for solving a class of distributionally robust optimization (DRO) with non-convex objectives, which has important applications in machine learning for improving the robustness of neural…
Methodologies for multidimensionality reduction aim at discovering low-dimensional manifolds where data ranges. Principal Component Analysis (PCA) is very effective if data have linear structure. But fails in identifying a possible…
Inverse optimization is a powerful paradigm for learning preferences and restrictions that explain the behavior of a decision maker, based on a set of external signal and the corresponding decision pairs. However, most inverse optimization…
This paper carries out a large dimensional analysis of a variation of kernel ridge regression that we call \emph{centered kernel ridge regression} (CKRR), also known in the literature as kernel ridge regression with offset. This modified…
In statistical learning, high covariate dimensionality poses challenges for robust prediction and inference. To address this challenge, supervised dimension reduction is often performed, where dependence on the outcome is maximized for a…
The movement of large quantities of data during the training of a Deep Neural Network presents immense challenges for machine learning workloads. To minimize this overhead, especially on the movement and calculation of gradient information,…
We investigate nonparametric estimation of sliced inverse regression (SIR) via the $k$-nearest neighbors approach with a kernel. An estimator of the covariance matrix of the conditional expectation of the explanatory random vector given the…
Data are not only ubiquitous in society, but are increasingly complex both in size and dimensionality. Dimension reduction offers researchers and scholars the ability to make such complex, high dimensional data spaces simpler and more…
We prove minimax optimal learning rates for kernel ridge regression, resp.~support vector machines based on a data dependent partition of the input space, where the dependence of the dimension of the input space is replaced by the fractal…