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In subset selection we search for the best linear predictor that involves a small subset of variables. From a computational complexity viewpoint, subset selection is NP-hard and few classes are known to be solvable in polynomial time. Using…

Tensor models play an increasingly prominent role in many fields, notably in machine learning. In several applications, such as community detection, topic modeling and Gaussian mixture learning, one must estimate a low-rank signal from a…

Modeling interactions between features improves the performance of machine learning solutions in many domains (e.g. recommender systems or sentiment analysis). In this paper, we introduce Exponential Machines (ExM), a predictor that models…

This work concerns learning probabilistic models for ranking data in a heterogeneous population. The specific problem we study is learning the parameters of a Mallows Mixture Model. Despite being widely studied, current heuristics for this…

We study the problem of learning latent variables in Gaussian graphical models. Existing methods for this problem assume that the precision matrix of the observed variables is the superposition of a sparse and a low-rank component. In this…

Kernel methods represent one of the most powerful tools in machine learning to tackle problems expressed in terms of function values and derivatives due to their capability to represent and model complex relations. While these methods show…

A new line of research for feature selection based on neural networks has recently emerged. Despite its superiority to classical methods, it requires many training iterations to converge and detect informative features. The computational…

We consider the problem of learning high dimensional polynomial transformations of Gaussians. Given samples of the form $p(x)$, where $x\sim N(0, \mathrm{Id}_r)$ is hidden and $p: \mathbb{R}^r \to \mathbb{R}^d$ is a function where every…

Face recognition is the important field in machine learning and pattern recognition research area. It has a lot of applications in military, finance, public security, to name a few. In this paper, the combination of the tensor sparse PCA…

The generalization capacity of various machine learning models exhibits different phenomena in the under- and over-parameterized regimes. In this paper, we focus on regression models such as feature regression and kernel regression and…

This paper presents a framework for computing random operator-valued feature maps for operator-valued positive definite kernels. This is a generalization of the random Fourier features for scalar-valued kernels to the operator-valued case.…

Neural networks have achieved remarkable empirical performance, while the current theoretical analysis is not adequate for understanding their success, e.g., the Neural Tangent Kernel approach fails to capture their key feature learning…

Despite their many appealing properties, kernel methods are heavily affected by the curse of dimensionality. For instance, in the case of inner product kernels in $\mathbb{R}^d$, the Reproducing Kernel Hilbert Space (RKHS) norm is often…

This paper studies an intriguing phenomenon related to the good generalization performance of estimators obtained by using large learning rates within gradient descent algorithms. First observed in the deep learning literature, we show that…

We propose a method for the approximation of high- or even infinite-dimensional feature vectors, which play an important role in supervised learning. The goal is to reduce the size of the training data, resulting in lower storage…

This work considers the problem of estimating the parameters of negative mixture models, i.e. mixture models that possibly involve negative weights. The contributions of this paper are as follows. (i) We show that every rational probability…

We establish connections between the problem of learning a two-layer neural network and tensor decomposition. We consider a model with feature vectors $\boldsymbol x \in \mathbb R^d$, $r$ hidden units with weights $\{\boldsymbol w_i\}_{1\le…

Machine learning of multi-dimensional potential energy surfaces, from purely ab initio datasets, has seen substantial progress in the past years. Gaussian processes, a popular regression method, have been very successful at producing…

Sparse Bayesian learning is a state-of-the-art supervised learning algorithm that can choose a subset of relevant samples from the input data and make reliable probabilistic predictions. However, in the presence of high-dimensional data…

Randomized iterative algorithms, such as the randomized Kaczmarz method, have gained considerable popularity due to their efficacy in solving matrix-vector and matrix-matrix regression problems. Our present work leverages the insights…