相关论文: Algorithms for Learning Sparse Additive Models wit…

A function $f: \mathbb{R}^d \rightarrow \mathbb{R}$ is referred to as a Sparse Additive Model (SPAM), if it is of the form $f(\mathbf{x}) = \sum_{l \in \mathcal{S}}\phi_{l}(x_l)$, where $\mathcal{S} \subset [d]$, $|\mathcal{S}| \ll d$.…

We consider the problem of learning a $d$-variate function $f$ defined on the cube $[-1,1]^d\subset {\mathbb R}^d$, where the algorithm is assumed to have black box access to samples of $f$ within this domain. Denote ${\mathcal S}_r \subset…

We present a new class of methods for high-dimensional nonparametric regression and classification called sparse additive models (SpAM). Our methods combine ideas from sparse linear modeling and additive nonparametric regression. We derive…

We introduce a new algorithm, called adaptive sparse backfitting algorithm, for solving high dimensional Sparse Additive Model (SpAM) utilizing symmetric, non-negative definite smoothers. Unlike the previous sparse backfitting algorithm,…

Cross-device training is a crucial subfield of federated learning, where the number of clients can reach into the billions. Standard approaches and local methods are prone to issues such as client drift and insensitivity to data…

This paper examines a general class of noisy matrix completion tasks where the goal is to estimate a matrix from observations obtained at a subset of its entries, each of which is subject to random noise or corruption. Our specific focus is…

Sparse additive models have attracted much attention in high-dimensional data analysis due to their flexible representation and strong interpretability. However, most existing models are limited to single-level learning under the…

Signals sparse in a transformation domain can be recovered from a reduced set of randomly positioned samples by using compressive sensing algorithms. Simple re- construction algorithms are presented in the first part of the paper. The…

We consider (nonparametric) sparse (generalized) additive models (SpAM) for classification. The design of a SpAM classifier is based on minimizing the logistic loss with a sparse group Lasso/Slope-type penalties on the coefficients of…

Distributed statistical learning has become a popular technique for large-scale data analysis. Most existing work in this area focuses on dividing the observations, but we propose a new algorithm, DDAC-SpAM, which divides the features under…

The sparse modeling is an evident manifestation capturing the parsimony principle just described, and sparse models are widespread in statistics, physics, information sciences, neuroscience, computational mathematics, and so on. In…

Hypergraph is a general way of representing high-order relations on a set of objects. It is a generalization of graph, in which only pairwise relations can be represented. It finds applications in various domains where relationships of more…

Additive models enjoy the flexibility of nonlinear models while still being readily understandable to humans. By contrast, other nonlinear models, which involve interactions between features, are not only harder to fit but also…

Generalized Additive Models (GAMs) have quickly become the leading choice for inherently-interpretable machine learning. However, unlike uninterpretable methods such as DNNs, they lack expressive power and easy scalability, and are hence…

Consider a multi-variate time series $(X_t)_{t=0}^{T}$ where $X_t \in \mathbb{R}^d$ which may represent spike train responses for multiple neurons in a brain, crime event data across multiple regions, and many others. An important challenge…

We consider the problem of recovery of an unknown multivariate signal $f$ observed in a $d$-dimensional Gaussian white noise model of intensity $\varepsilon$. We assume that $f$ belongs to a class of smooth functions ${\cal F}^d\subset…

Sparse regression has recently emerged as an attractive approach for discovering models of spatiotemporally complex dynamics directly from data. In many instances, such models are in the form of nonlinear partial differential equations…

Sparse linear regression is a central problem in high-dimensional statistics. We study the correlated random design setting, where the covariates are drawn from a multivariate Gaussian $N(0,\Sigma)$, and we seek an estimator with small…

Deep learning can help uncover patterns in resting-state functional Magnetic Resonance Imaging (rs-fMRI) associated with psychiatric disorders and personal traits. Yet the problem of interpreting deep learning findings is rarely more…

In machine learning and data mining, linear models have been widely used to model the response as parametric linear functions of the predictors. To relax such stringent assumptions made by parametric linear models, additive models consider…