Related papers: Hit-and-run mixing via localization schemes

We consider a random walk on a homogeneous space $G/\Lambda$ where $G$ is $\mathrm{SO}(2,1)$ or $\mathrm{SO}(3,1)$ and $\Lambda$ is a lattice. The walk is driven by a probability measure $\mu$ on $G$ whose support generates a Zariski-dense…

Let $X_1,\dots,X_n$ be i.i.d. log-concave random vectors in $\mathbb R^d$ with mean 0 and covariance matrix $\Sigma$. We study the problem of quantifying the normal approximation error for $W=n^{-1/2}\sum_{i=1}^nX_i$ with explicit…

This paper studies the optimal rate of estimation in a finite Gaussian location mixture model in high dimensions without separation conditions. We assume that the number of components $k$ is bounded and that the centers lie in a ball of…

In this paper, we investigate a continuous time version of the Stochastic Langevin Monte Carlo method, introduced in [WT11], that incorporates a stochastic sampling step inside the traditional over-damped Langevin diffusion. This method is…

We develop a technique using dual mixed-volumes to study the isotropic constants of some classes of spaces. In particular, we recover, strengthen and generalize results of Ball and Junge concerning the isotropic constants of subspaces and…

We consider the problem of sequential (online) estimation of a single change point in a piecewise linear regression model under a Gaussian setup. We demonstrate that certain CUSUM-type statistics attain the minimax optimal rates for…

Motivated by the central limit problem for convex bodies, we study normal approximation of linear functionals of high-dimensional random vectors with various types of symmetries. In particular, we obtain results for distributions which are…

As a natural analog of Urysohn's inequality in Euclidean space, Gao, Hug, and Schneider showed in 2003 that in spherical or hyperbolic space, the total measure of totally geodesic hypersurfaces meeting a given convex body K is minimized…

For distributions over discrete product spaces $\prod_{i=1}^n \Omega_i'$, Glauber dynamics is a Markov chain that at each step, resamples a random coordinate conditioned on the other coordinates. We show that $k$-Glauber dynamics, which…

Hamiltonian Monte Carlo (HMC) is a state-of-the-art Markov chain Monte Carlo sampling algorithm for drawing samples from smooth probability densities over continuous spaces. We study the variant most widely used in practice, Metropolized…

We present the first algorithm for fully dynamic $k$-centers clustering in an arbitrary metric space that maintains an optimal $2+\epsilon$ approximation in $O(k \cdot \operatorname{polylog}(n,\Delta))$ amortized update time. Here, $n$ is…

The complexity of nearest-neighbor search dominates the asymptotic running time of many sampling-based motion-planning algorithms. However, collision detection is often considered to be the computational bottleneck in practice. Examining…

We prove an $\widetilde O(n^2)$ bound for the relaxation time and the log-Sobolev time (inverse log-Sobolev constant) of the classical triangulation flip chain on a convex $(n+2)$-gon, implying a mixing time of $\widetilde O(n^2)$. The…

Clustering is a fundamental problem in unsupervised machine learning with many applications in data analysis. Popular clustering algorithms such as Lloyd's algorithm and $k$-means++ can take $\Omega(ndk)$ time when clustering $n$ points in…

In this paper, we obtain the best possible value of the absolute constant $C$ such that for every isotropic convex body $K \subseteq \mathbb{R}^n$ the following inequality (which was proved by Klartag and reduces the hyperplane conjecture…

The K-Means clustering using LLoyd's algorithm is an iterative approach to partition the given dataset into K different clusters. The algorithm assigns each point to the cluster based on the following objective function \[\ \min…

In the minimum $k$-edge-connected spanning subgraph ($k$-ECSS) problem the goal is to find the minimum weight subgraph resistant to up to $k-1$ edge failures. This is a central problem in network design, and a natural generalization of the…

This paper provides a convergence analysis for generalized Hamiltonian Monte Carlo samplers, a family of Markov Chain Monte Carlo methods based on leapfrog integration of Hamiltonian dynamics and kinetic Langevin diffusion, that encompasses…

We show that the volume of a convex body in $\mathbb{R}^{n}$ in the general membership oracle model can be computed to within relative error $\varepsilon$ using $\widetilde{O}(n^{3.5}\psi^{2} + n^3/\varepsilon^{2})$ oracle queries, where…

This article considers estimation of constant and time-varying coefficients in nonlinear ordinary differential equation (ODE) models where analytic closed-form solutions are not available. The numerical solution-based nonlinear least…