Related papers: Learning High Order Feature Interactions with Fine…

High-order parametric models that include terms for feature interactions are applied to various data mining tasks, where ground truth depends on interactions of features. However, with sparse data, the high- dimensional parameters for…

Particle dynamics and multi-agent systems provide accurate dynamical models for studying and forecasting the behavior of complex interacting systems. They often take the form of a high-dimensional system of differential equations…

Many scientific problems require identifying a small set of covariates that are associated with a target response and estimating their effects. Often, these effects are nonlinear and include interactions, so linear and additive methods can…

In statistical machine learning, kernel methods allow to consider infinite dimensional feature spaces with a computational cost that only depends on the number of observations. This is usually done by solving an optimization problem…

Modeling the complex interactions of systems of particles or agents is a fundamental scientific and mathematical problem that is studied in diverse fields, ranging from physics and biology, to economics and machine learning. In this work,…

By removing irrelevant and redundant features, feature selection aims to find a good representation of the original features. With the prevalence of unlabeled data, unsupervised feature selection has been proven effective in alleviating the…

We consider stochastic systems of interacting particles or agents, with dynamics determined by an interaction kernel which only depends on pairwise distances. We study the problem of inferring this interaction kernel from observations of…

We introduce a nonparametric algorithm to learn interaction kernels of mean-field equations for 1st-order systems of interacting particles. The data consist of discrete space-time observations of the solution. By least squares with…

Deep kernel learning provides an elegant and principled framework for combining the structural properties of deep learning algorithms with the flexibility of kernel methods. By means of a deep neural network, we learn a parametrized kernel…

We propose a data-driven framework to learn interaction kernels in stochastic multi-agent systems. Our approach aims at identifying the functional form of nonlocal interaction and diffusion terms directly from trajectory data, without any a…

For supervised and unsupervised learning, positive definite kernels allow to use large and potentially infinite dimensional feature spaces with a computational cost that only depends on the number of observations. This is usually done…

In order to fully utilize "big data", it is often required to use "big models". Such models tend to grow with the complexity and size of the training data, and do not make strong parametric assumptions upfront on the nature of the…

In this paper, we investigate the data-driven identification of asymmetric interaction kernels in the Motsch-Tadmor model based on observed trajectory data. The model under consideration is governed by a class of semilinear evolution…

In complex visual recognition tasks it is typical to adopt multiple descriptors, that describe different aspects of the images, for obtaining an improved recognition performance. Descriptors that have diverse forms can be fused into a…

Nonparametric feature selection in high-dimensional data is an important and challenging problem in statistics and machine learning fields. Most of the existing methods for feature selection focus on parametric or additive models which may…

We develop a scalable algorithm for mean field control problems with kernel interactions by combining particle system simulations with random Fourier feature approximations. The method replaces the quadratic-cost kernel evaluations by…

Few-shot models aim at making predictions using a minimal number of labeled examples from a given task. The main challenge in this area is the one-shot setting where only one element represents each class. We propose HyperShot - the fusion…

Systems of interacting particles or agents have wide applications in many disciplines such as Physics, Chemistry, Biology and Economics. These systems are governed by interaction laws, which are often unknown: estimating them from…

Kernel learning methods are among the most effective learning methods and have been vigorously studied in the past decades. However, when tackling with complicated tasks, classical kernel methods are not flexible or "rich" enough to…

The macroscopic properties of materials that we observe and exploit in engineering application result from complex interactions between physics at multiple length and time scales: electronic, atomistic, defects, domains etc. Multiscale…