Related papers: Decorrelated forward regression for high dimension…
Forward stagewise regression follows a very simple strategy for constructing a sequence of sparse regression estimates: it starts with all coefficients equal to zero, and iteratively updates the coefficient (by a small amount $\epsilon$) of…
Completely randomized experiment is the gold standard for causal inference. When the covariate information for each experimental candidate is available, one typical way is to include them in covariate adjustments for more accurate treatment…
We propose a new method for input variable selection in nonlinear regression. The method is embedded into a kernel regression machine that can model general nonlinear functions, not being a priori limited to additive models. This is the…
In many engineering and applied science domains, high-dimensional nonlinear filtering is still a challenging problem. Recent advances in score-based diffusion models offer a promising alternative for posterior sampling but require repeated…
Given data y(n) and p(n)covariates x(n) one problem in linear regression is to decide which if any of the covariates to include. There are many articles on this problem but all are based on a stochastic model for the data. This paper gives…
Constrained low-rank matrix approximations have been known for decades as powerful linear dimensionality reduction techniques to be able to extract the information contained in large data sets in a relevant way. However, such low-rank…
Variable selection in ultra-high dimensional regression problems has become an important issue. In such situations, penalized regression models may face computational problems and some pre screening of the variables may be necessary. A…
Identifying multivariate dependencies in high-dimensional data is an important problem in large-scale inference. This problem has motivated recent advances in mining (partial) correlations, which focus on the challenging ultra-high…
The goal of Feature Selection - comprising filter, wrapper, and embedded approaches - is to find the optimal feature subset for designated downstream tasks. Nevertheless, current feature selection methods are limited by: 1) the selection…
Continual learning is an emerging paradigm in machine learning, wherein a model is exposed in an online fashion to data from multiple different distributions (i.e. environments), and is expected to adapt to the distribution change.…
In high-dimensional prediction problems, where the number of features may greatly exceed the number of training instances, fully Bayesian approach with a sparsifying prior is known to produce good results but is computationally challenging.…
Advancements in modern science have led to the increasing availability of non-Euclidean data in metric spaces. This paper addresses the challenge of modeling relationships between non-Euclidean responses and multivariate Euclidean…
Traditional regression and prediction tasks often only provide deterministic point estimates. To estimate the distribution or uncertainty of the response variable, traditional methods either assume that the posterior distribution of samples…
Geometric model fitting is a fundamental research topic in computer vision and it aims to fit and segment multiple-structure data. In this paper, we propose a novel superpixel-guided two-view geometric model fitting method (called SDF),…
Feature selection is a prevalent data preprocessing paradigm for various learning tasks. Due to the expensive cost of acquiring supervision information, unsupervised feature selection sparks great interests recently. However, existing…
Many real-world machine learning applications are characterized by a huge number of features, leading to computational and memory issues, as well as the risk of overfitting. Ideally, only relevant and non-redundant features should be…
This paper studies high-dimensional regression with two-way structured data. To estimate the high-dimensional coefficient vector, we propose the generalized matrix decomposition regression (GMDR) to efficiently leverage any auxiliary…
Regression analysis of correlated data, where multiple correlated responses are recorded on the same unit, is ubiquitous in many scientific areas. With the advent of new technologies, in particular high-throughput omics profiling assays,…
Debiasing is a fundamental concept in high-dimensional statistics. While degrees-of-freedom adjustment is the state-of-the-art technique in high-dimensional linear regression, it is limited to i.i.d. samples and sub-Gaussian covariates.…
Generative modeling of discrete data underlies important applications spanning text-based agents like ChatGPT to the design of the very building blocks of life in protein sequences. However, application domains need to exert control over…