Related papers: Sparse Functional Linear Discriminant Analysis
We consider the inverse problem of recovering a continuous-domain function from a finite number of noisy linear measurements. The unknown signal is modeled as the sum of a slowly varying trend and a periodic or quasi-periodic seasonal…
Sparse principal component analysis (SPCA) addresses the poor interpretability and variable redundancy often encountered by principal component analysis (PCA) in high-dimensional data. However, SPCA typically imposes uniform penalties on…
Learned Sparse Retrieval (LSR) is an effective IR approach that exploits pre-trained language models for encoding text into a learned bag of words. Several efforts in the literature have shown that sparsity is key to enabling a good…
Regularization is widely used in statistics and machine learning to prevent overfitting and gear solution towards prior information. In general, a regularized estimation problem minimizes the sum of a loss function and a penalty term. The…
In this paper, we consider a class of sparse regression problems, whose objective function is the summation of a convex loss function and a cardinality penalty. By constructing a smoothing function for the cardinality function, we propose a…
LASSO regularized logistic regression is particularly useful for its built-in feature selection, allowing coefficients to be removed from deployment and producing sparse solutions. Differentially private versions of LASSO logistic…
In this paper, we aim at recovering an unknown signal x0 from noisy L1measurements y=Phi*x0+w, where Phi is an ill-conditioned or singular linear operator and w accounts for some noise. To regularize such an ill-posed inverse problem, we…
In this paper, we consider the optimization problem of minimizing a continuously differentiable function subject to both convex constraints and sparsity constraints. By exploiting a mixed-integer reformulation from the literature, we define…
This paper studies the role of sparse regularization in a properly chosen basis for variational data assimilation (VDA) problems. Specifically, it focuses on data assimilation of noisy and down-sampled observations while the state variable…
High dimensional sparse learning has imposed a great computational challenge to large scale data analysis. In this paper, we are interested in a broad class of sparse learning approaches formulated as linear programs parametrized by a {\em…
This work studies the theoretical rules of feature selection in linear discriminant analysis (LDA), and a new feature selection method is proposed for sparse linear discriminant analysis. An $l_1$ minimization method is used to select the…
A functional (lagged) time series regression model involves the regression of scalar response time series on a time series of regressors that consists of a sequence of random functions. In practice, the underlying regressor curve time…
Recent theoretical studies proved that deep neural network (DNN) estimators obtained by minimizing empirical risk with a certain sparsity constraint can attain optimal convergence rates for regression and classification problems. However,…
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…
Sparse optimization problems are ubiquitous in many fields such as statistics, signal/image processing and machine learning. This has led to the birth of many iterative algorithms to solve them. A powerful strategy to boost the performance…
The sparse linear regression problem is difficult to handle with usual sparse optimization models when both predictors and measurements are either quantized or represented in low-precision, due to non-convexity. In this paper, we provide a…
The observations in many applications consist of counts of discrete events, such as photons hitting a detector, which cannot be effectively modeled using an additive bounded or Gaussian noise model, and instead require a Poisson noise…
Feature selection identifies subsets of informative features and reduces dimensions in the original feature space, helping provide insights into data generation or a variety of domain problems. Existing methods mainly depend on feature…
Regression by composition provides a flexible framework for constructing conditional distributions through sequential group actions. However, when multiple flows act on the same distribution, the model becomes non-identifiable, leading to…
Deep representation learning has become one of the most widely adopted approaches for visual search, recommendation, and identification. Retrieval of such representations from a large database is however computationally challenging.…