Related papers: Detection boundary in sparse regression
Statistical inferences for high-dimensional regression models have been extensively studied for their wide applications ranging from genomics, neuroscience, to economics. However, in practice, there are often potential unmeasured…
The problem of sparse linear regression is relevant in the context of linear system identification from large datasets. When data are collected from real-world experiments, measurements are always affected by perturbations or low-precision…
Gaussian processes (GPs) are non-parametric probabilistic regression models that are popular due to their flexibility, data efficiency, and well-calibrated uncertainty estimates. However, standard GP models assume homoskedastic Gaussian…
Dimensionality reduction is an effective method for learning high-dimensional data, which can provide better understanding of decision boundaries in human-readable low-dimensional subspace. Linear methods, such as principal component…
We propose a sparse regression method capable of discovering the governing partial differential equation(s) of a given system by time series measurements in the spatial domain. The regression framework relies on sparsity promoting…
Generic event boundary detection (GEBD) aims to identify natural boundaries in a video, segmenting it into distinct and meaningful chunks. Despite the inherent subjectivity of event boundaries, previous methods have focused on deterministic…
This paper presents uniform-in-time finite-sample bounds for regularized linear regression with vector-valued outputs and conditionally zero-mean subgaussian noise. By revisiting classical self-normalized martingale arguments, we obtain…
The discovery of Partial Differential Equations (PDEs) is an essential task for applied science and engineering. However, data-driven discovery of PDEs is generally challenging, primarily stemming from the sensitivity of the discovered…
The estimation of static parameters in dynamical systems and control theory has been extensively studied, with significant progress made in estimating varying parameters in specific system types. Suppose, in the general case, we have data…
We develop a fast variational approximation scheme for Gaussian process (GP) regression, where the spectrum of the covariance function is subjected to a sparse approximation. Our approach enables uncertainty in covariance function…
This paper develops a threshold regression model where an unknown relationship between two variables nonparametrically determines the threshold. We allow the observations to be cross-sectionally dependent so that the model can be applied to…
We show that density models describing multiple observables with (i) hard boundaries and (ii) dependence on external parameters may be created using an auto-regressive Gaussian mixture model. The model is designed to capture how observable…
This paper presents Sparse Partitioning, a Bayesian method for identifying predictors that either individually or in combination with others affect a response variable. The method is designed for regression problems involving binary or…
Interference detection in gaussian noise is proposed. It can be applied for easy detection and editing of interference lines in radio spectral line observations. One need not know the position of occurence or keep track of interference in…
Generalization theory has been established for sparse deep neural networks under high-dimensional regime. Beyond generalization, parameter estimation is also important since it is crucial for variable selection and interpretability of deep…
We consider the problem of estimating a deterministic sparse vector x from underdetermined measurements Ax+w, where w represents white Gaussian noise and A is a given deterministic dictionary. We analyze the performance of three sparse…
In this letter, we address the problem of estimating Gaussian noise level from the trained dictionaries in update stage. We first provide rigorous statistical analysis on the eigenvalue distributions of a sample covariance matrix. Then we…
We consider a high dimensional linear regression problem where the goal is to efficiently recover an unknown vector $\beta^*$ from $n$ noisy linear observations $Y=X\beta^*+W \in \mathbb{R}^n$, for known $X \in \mathbb{R}^{n \times p}$ and…
The detection of hidden two-dimensional Gauss-Markov random fields using sensor networks is considered. Under a conditional autoregressive model, the error exponent for the Neyman-Pearson detector satisfying a fixed level constraint is…
This paper presents an innovative approach to dimensionality reduction and feature extraction in high-dimensional datasets, with a specific application focus on wood surface defect detection. The proposed framework integrates sparse…