Related papers: Operator-free Equilibrium on the Sphere
We consider decentralized gradient-free optimization of minimizing Lipschitz continuous functions that satisfy neither smoothness nor convexity assumption. We propose two novel gradient-free algorithms, the Decentralized Gradient-Free…
In this paper, we study the problem of finding the Euclidean distance to a convex cone generated by a set of discrete points in $\mathbb{R}^n_+$. In particular, we are interested in problems where the discrete points are the set of feasible…
In this work, we study optimization specified only through a comparison oracle: given two points, it reports which one is preferred. We call it function-free optimization because we do not assume access to, nor the existence of, a canonical…
Latent space models have been widely adopted in modeling network data. Developing statistical inference for estimated model parameters enables quantifying associated uncertainty and is pivotal for downstream tasks. Despite recent progress…
A natural Monte Carlo method to approximate conditional expectations in a probabilistic framework is justified by a general result inspired on the Besicovitch covering theorem on differentiation of measures. The method is specially useful…
This work studies minimization problems with zero-order noisy oracle information under the assumption that the objective function is highly smooth and possibly satisfies additional properties. We consider two kinds of zero-order projected…
A judicious application of the Berry-Esseen theorem via suitable Augustin information measures is demonstrated to be sufficient for deriving the sphere packing bound with a prefactor that is…
We present a method for the approximate propagation of mean and covariance of a probability distribution through ordinary differential equations (ODE) with discontinous right-hand side. For piecewise affine systems, a normalization of the…
In this paper, we extend the class of kernel methods, the so-called diffusion maps (DM) and ghost point diffusion maps (GPDM), to solve the time-dependent advection-diffusion PDE on unknown smooth manifolds without and with boundaries. The…
A discrete divergence-free weak Galerkin finite element method is developed for the Stokes equations based on a weak Galerkin (WG) method introduced in the reference [15]. Discrete divergence-free bases are constructed explicitly for the…
We consider the Dirichlet Laplacian in unbounded strips on ruled surfaces in any space dimension. We locate the essential spectrum under the condition that the strip is asymptotically flat. If the Gauss curvature of the strip equals zero,…
The variance conjecture in Asymptotic Convex Geometry stipulates that the Euclidean norm of a random vector uniformly distributed in a (properly normalised) high-dimensional convex body $K\subset {\mathbb R}^n$ satisfies a Poincar\'e-type…
Partial differential equation is a powerful tool to characterize various physics systems. In practice, measurement errors are often present and probability models are employed to account for such uncertainties. In this paper, we present a…
We study statistical inference for small-noise-perturbed multiscale dynamical systems. We prove consistency, asymptotic normality, and convergence of all scaled moments of an appropriately-constructed maximum likelihood estimator (MLE) for…
We introduce an interpolation--regression operator for polynomial approximation on the unit sphere $\mathbb{S}^2$ from discrete samples. The approximant is a spherical polynomial of degree $r$ which interpolates the data on a prescribed…
Discretization of the uniform norm of functions from a given finite dimensional subspace of continuous functions is studied. Previous known results show that for any $N$-dimensional subspace of the space of continuous functions it is…
The $k$ principal points of a random vector $\mathbf{X}$ are defined as a set of points which minimize the expected squared distance between $\mathbf{X}$ and the nearest point in the set. They are thoroughly studied in Flury (1990, 1993),…
Within the framework of generalized noncontextuality, we introduce a general technique for systematically deriving noncontextuality inequalities for any experiment involving finitely many preparations and finitely many measurements, each of…
In this paper, we extend the Generalized Finite Difference Method (GFDM) on unknown compact submanifolds of the Euclidean domain, identified by randomly sampled data that (almost surely) lie on the interior of the manifolds. Theoretically,…
We describe a new algorithm for trajectory optimization of mechanical systems. Our method combines pseudo-spectral methods for function approximation with variational discretization schemes that exactly preserve conserved mechanical…