Related papers: In-and-Out: Algorithmic Diffusion for Sampling Con…
We describe a novel approach to statistical learning from particles tracked while moving in a random environment. The problem consists in inferring properties of the environment from recorded snapshots. We consider here the case of a fluid…
Advances in robot learning have enabled robots to generate skills for a variety of tasks. Yet, robot learning is typically sample inefficient, struggles to learn from data sources exhibiting varied behaviors, and does not naturally…
We study the persistent random walk of photons on a one-dimensional lattice of random transmittances. Transmittances at different sites are assumed independent, distributed according to a given probability density $f(t)$. Depending on the…
We consider the problem of sampling from a target distribution, which is \emph {not necessarily logconcave}, in the context of empirical risk minimization and stochastic optimization as presented in Raginsky et al. (2017). Non-asymptotic…
A L\'evy random medium, in a given space, is a random point process where the distances between points, a.k.a. targets, are long-tailed. Random walks visiting the targets of a L\'evy random medium have been used to model many (physical,…
The most common way to sample from a probability distribution is to use Monte-Carlo methods. For distributions on a continuous state space, one can find diffusions with the target distribution as equilibrium measure, so that the state of…
Score-based diffusion models have demonstrated remarkable empirical success in learning high-dimensional distributions, particularly those exhibiting low-dimensional and multi-modal structures. However, theoretical understanding of their…
We study a random walk infiltration (RWI) model, in homogeneous and in fractal media, with localized sources at their boundaries. The particles released at a source, which is maintained at a constant density, execute unbiased random walks…
This paper proposes and analyzes a novel clustering algorithm that combines graph-based diffusion geometry with techniques based on density and mode estimation. The proposed method is suitable for data generated from mixtures of…
This paper introduces a framework for simulating finite dimensional representations of (jump) diffusion sample paths over finite intervals, without discretisation error (exactly), in such a way that the sample path can be restored at any…
We study the expected volume of random polytopes generated by taking the convex hull of independent identically distributed points from a given distribution. We show that for log-concave distributions supported on convex bodies, we need at…
Representations based on random walks can exploit discrete data distributions for clustering and classification. We extend such representations from discrete to continuous distributions. Transition probabilities are now calculated using a…
Many machine learning applications require operating on a spatially distributed dataset. Despite technological advances, privacy considerations and communication constraints may prevent gathering the entire dataset in a central unit. In…
Graph generation addresses the problem of generating new graphs that have a data distribution similar to real-world graphs. While previous diffusion-based graph generation methods have shown promising results, they often struggle to scale…
Continuous time random walk models with decoupled waiting time density are studied. When the spatial one jump probability density belongs to the Levy distribution type and the total time transition is exponential a generalized…
We study the persistent random walk of photons on a one-dimensional lattice of random asymmetric transmittances. Each site is characterized by its intensity transmittance t (t') for photons moving to the right (left) direction.…
We study the slice-matching scheme, an efficient iterative method for distribution matching based on sliced optimal transport. We investigate convergence to the target distribution and derive quantitative non-asymptotic rates. To this end,…
Emerging applications of machine learning in numerous areas involve continuous gathering of and learning from streams of data. Real-time incorporation of streaming data into the learned models is essential for improved inference in these…
Probabilistic human motion prediction aims to forecast multiple possible future movements from past observations. While current approaches report high diversity and realism, they often generate motions with undetected limb stretching and…
We present a Hamiltonian Monte Carlo algorithm to sample from multivariate Gaussian distributions in which the target space is constrained by linear and quadratic inequalities or products thereof. The Hamiltonian equations of motion can be…