Related papers: Sparse Robust Classification via the Kernel Mean

Sparse coding is a basic task in many fields including signal processing, neuroscience and machine learning where the goal is to learn a basis that enables a sparse representation of a given set of data, if one exists. Its standard…

In high-dimensional data, many sparse regression methods have been proposed. However, they may not be robust against outliers. Recently, the use of density power weight has been studied for robust parameter estimation and the corresponding…

Generalization performance of classifiers in deep learning has recently become a subject of intense study. Deep models, typically over-parametrized, tend to fit the training data exactly. Despite this "overfitting", they perform well on…

Kernel ridge regression, KRR, is a generalization of linear ridge regression that is non-linear in the data, but linear in the model parameters. Here, we introduce an equivalent formulation of the objective function of KRR, which opens up…

Many modern tools in machine learning and signal processing, such as sparse dictionary learning, principal component analysis (PCA), non-negative matrix factorization (NMF), $K$-means clustering, etc., rely on the factorization of a matrix…

The generalization performance of kernel methods is largely determined by the kernel, but common kernels are stationary thus input-independent and output-independent, that limits their applications on complicated tasks. In this paper, we…

The SparseStep algorithm is presented for the estimation of a sparse parameter vector in the linear regression problem. The algorithm works by adding an approximation of the exact counting norm as a constraint on the model parameters and…

In this work we are interested in the problems of supervised learning and variable selection when the input-output dependence is described by a nonlinear function depending on a few variables. Our goal is to consider a sparse nonparametric…

Although modern deep learning often relies on massive over-parameterized models, the fundamental interplay between capacity, sparsity, and robustness in low-capacity networks remains a vital area of study. We introduce a controlled…

Many of the successes of machine learning are based on minimizing an averaged loss function. However, it is well-known that this paradigm suffers from robustness issues that hinder its applicability in safety-critical domains. These issues…

Sparse linear discriminant analysis via penalized optimal scoring is a successful tool for classification in high-dimensional settings. While the variable selection consistency of sparse optimal scoring has been established, the…

As recent literature has demonstrated how classifiers often carry unintended biases toward some subgroups, deploying machine learned models to users demands careful consideration of the social consequences. How should we address this…

While K-means is known to be a standard clustering algorithm, its performance may be compromised due to the presence of outliers and high-dimensional noisy variables. This paper proposes adaptively robust and sparse K-means clustering…

We present a probabilistic viewpoint to multiple kernel learning unifying well-known regularised risk approaches and recent advances in approximate Bayesian inference relaxations. The framework proposes a general objective function suitable…

Variable selection is central to high-dimensional data analysis, and various algorithms have been developed. Ideally, a variable selection algorithm shall be flexible, scalable, and with theoretical guarantee, yet most existing algorithms…

Analysis of large-scale sequential data has been one of the most crucial tasks in areas such as bioinformatics, text, and audio mining. Existing string kernels, however, either (i) rely on local features of short substructures in the…

In many contexts, customized and weighted classification scores are designed in order to evaluate the goodness of the predictions carried out by neural networks. However, there exists a discrepancy between the maximization of such scores…

Reliable and robust evaluation methods are a necessary first step towards developing machine learning models that are themselves robust and reliable. Unfortunately, current evaluation protocols typically used to assess classifiers fail to…

The problem of robust hypothesis testing is studied, where under the null and the alternative hypotheses, the data-generating distributions are assumed to be in some uncertainty sets, and the goal is to design a test that performs well…

Sparse neural networks are highly desirable in deep learning in reducing its complexity. The goal of this paper is to study how choices of regularization parameters influence the sparsity level of learned neural networks. We first derive…