相关论文: A first approach to learning a best basis for grav…

We introduce the receding-horizon policy gradient (RHPG) algorithm, the first PG algorithm with provable global convergence in learning the optimal linear estimator designs, i.e., the Kalman filter (KF). Notably, the RHPG algorithm does not…

Many real-world datasets can be represented in the form of a graph whose edge weights designate similarities between instances. A discrete Gaussian random field (GRF) model is a finite-dimensional Gaussian process (GP) whose prior…

Feature selection in reinforcement learning (RL), i.e. choosing basis functions such that useful approximations of the unkown value function can be obtained, is one of the main challenges in scaling RL to real-world applications. Here we…

One commonly finds in applications of smooth radial basis functions (RBFs) that scaling the kernels so they are `flat' leads to smaller discretization errors. However, the direct numerical approach for computing with flat RBFs (RBF-Direct)…

Gravitational-wave analyses depend heavily on waveforms that model the evolution of compact binary coalescences as seen by observing detectors. In many cases these waveforms are given by waveform approximants, models that approximate the…

This thesis investigates algorithms regarding their applicability for highly nonlinear model fitting on big datasets. Various mathematical methods are presented with which a model fit using the least squares criterion is possible. Special…

Geospatial technologies are becoming increasingly essential in our world for a wide range of applications, including agriculture, urban planning, and disaster response. To help improve the applicability and performance of deep learning…

We consider the problem of computing dense correspondences between non-rigid shapes with potentially significant partiality. Existing formulations tackle this problem through heavy manifold optimization in the spectral domain, given…

Spatial stochastic processes that are modeled over the entire Earth's surface require statistical approaches that directly consider the spherical domain. Here, we extend the notion of intrinsic random functions (IRF) to model non-stationary…

This paper studies a machine learning regression problem as a multivariate approximation problem using the framework of the theory of random functions. An ab initio derivation of a regression method is proposed, starting from postulates of…

A common problem in applied mathematics is to find a function in a Hilbert space with prescribed best approximations from a finite number of closed vector subspaces. In the present paper we study the question of the existence of solutions…

Astronomical observations, physical experiments as well as computer simulations often involve discrete data sets supposed to represent a fair sample of an underlying smooth and continuous field. Reconstructing the underlying fields from a…

Support Vector Machines (SVMs) are still one of the most popular and precise classifiers. The Radial Basis Function (RBF) kernel has been used in SVMs to separate among classes with considerable success. However, there is an intrinsic…

We propose a novel online learning paradigm for nonlinear-function estimation tasks based on the iterative projections in the L2 space with probability measure reflecting the stochastic property of input signals. The proposed learning…

Preliminary spacecraft trajectory optimization is a parameter dependent global search problem that aims to provide a set of solutions that are of high quality and diverse. In the case of numerical solution, it is dependent on the original…

We present new algorithms for inverse reinforcement learning (IRL, or inverse optimal control) in convex optimization settings. We argue that finite-space IRL can be posed as a convex quadratic program under a Bayesian inference framework…

We present a theoretically grounded Gaussian process framework that leverages neural feature maps to construct expressive kernels. We show that the learned feature map can be interpreted as an optimal low-rank approximation to a Gram matrix…

One of the challenges in optimization of high dimensional problems is finding appropriate solutions in a way that are as close as possible to the global optima. In this regard, one of the most common phenomena that occurs is the curse of…

While pseudospectral (PS) methods can feature very high accuracy, they tend to be severely limited in terms of geometric flexibility. Application of global radial basis functions overcomes this, however at the expense of problematic…

Gaussian processes (GPs) are powerful probabilistic models that define flexible priors over functions, offering strong interpretability and uncertainty quantification. However, GP models often rely on simple, stationary kernels which can…