Related papers: Learning Active Subspaces and Discovering Importan…

Various methods in statistical learning build on kernels considered in reproducing kernel Hilbert spaces. In applications, the kernel is often selected based on characteristics of the problem and the data. This kernel is then employed to…

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…

Non-Euclidean constraints are inherent in many kinds of data in computer vision and machine learning, typically as a result of specific invariance requirements that need to be respected during high-level inference. Often, these geometric…

We consider the active learning problem where the goal is to learn an unknown function with low prediction error under an unknown Boltzmann distribution induced by the function itself. This self-induced weighting arises naturally in…

Matrix completion and robust principal component analysis have been widely used for the recovery of data suffering from missing entries or outliers. In many real-world applications however, the data is also time-varying, and the naive…

We propose stochastic, non-parametric activation functions that are fully learnable and individual to each neuron. Complexity and the risk of overfitting are controlled by placing a Gaussian process prior over these functions. The result is…

We propose a graph spectrum-based Gaussian process for prediction of signals defined on nodes of the graph. The model is designed to capture various graph signal structures through a highly adaptive kernel that incorporates a flexible…

A grand challenge in machine learning is the development of computational algorithms that match or outperform humans in perceptual inference tasks that are complicated by nuisance variation. For instance, visual object recognition involves…

We consider the problem of jointly learning a one-dimensional projection and a univariate function in high-dimensional Gaussian models. Specifically, we study predictors of the form $f(x)=\varphi^\star(\langle w^\star, x \rangle)$, where…

Artificial neural networks show promising performance in detecting correlations within data that are associated with specific outcomes. However, the black-box nature of such models can hinder the knowledge advancement in research fields by…

We introduce a variational Bayesian neural network where the parameters are governed via a probability distribution on random matrices. Specifically, we employ a matrix variate Gaussian \cite{gupta1999matrix} parameter posterior…

Many applications in speech, robotics, finance, and biology deal with sequential data, where ordering matters and recurrent structures are common. However, this structure cannot be easily captured by standard kernel functions. To model such…

Gaussian processes are employed for non-parametric regression in a Bayesian setting. They generalize linear regression, embedding the inputs in a latent manifold inside an infinite-dimensional reproducing kernel Hilbert space. We can…

Most of existing embedding based recommendation models use embeddings (vectors) corresponding to a single fixed point in low-dimensional space, to represent users and items. Such embeddings fail to precisely represent the users/items with…

We consider the problem of active learning for global sensitivity analysis of expensive black-box functions. Our aim is to efficiently learn the importance of different input variables, e.g., in vehicle safety experimentation, we study the…

Gaussian processes are powerful, yet analytically tractable models for supervised learning. A Gaussian process is characterized by a mean function and a covariance function (kernel), which are determined by a model selection criterion. The…

Data-driven discovery of "hidden physics" -- i.e., machine learning of differential equation models underlying observed data -- has recently been approached by embedding the discovery problem into a Gaussian Process regression of spatial…

This paper investigates the nonparametric regression problem using SVMs with anisotropic Gaussian RBF kernels. Under the assumption that the target functions are resided in certain anisotropic Besov spaces, we establish the almost optimal…

In this paper, we develop an approach to exploiting kernel methods with manifold-valued data. In many computer vision problems, the data can be naturally represented as points on a Riemannian manifold. Due to the non-Euclidean geometry of…

In deep learning, a central issue is to understand how neural networks efficiently learn high-dimensional features. To this end, we explore the gradient descent learning of a general Gaussian Multi-index model…