Related papers: Optimal Sublinear Sampling of Spanning Trees and D…
It is known that greedy methods perform well for maximizing monotone submodular functions. At the same time, such methods perform poorly in the face of non-monotonicity. In this paper, we show - arguably, surprisingly - that invoking the…
We consider the distributional fixed-point equation: $$R \stackrel{\mathcal{D}}{=} Q \vee \left( \bigvee_{i=1}^N C_i R_i \right),$$ where the $\{R_i\}$ are i.i.d.~copies of $R$, independent of the vector $(Q, N, \{C_i\})$, where $N \in…
We present a deterministic algorithm for solving a wide range of dynamic programming problems in trees in $O(\log D)$ rounds in the massively parallel computation model (MPC), with $O(n^\delta)$ words of local memory per machine, for any…
In this work we consider the Metric Steiner Forest problem in the sublinear time model. Given a set $V$ of $n$ points in a metric space where distances are provided by means of query access to an $n\times n$ distance matrix, along with a…
Offline reinforcement learning aims to learn from pre-collected datasets without active exploration. This problem faces significant challenges, including limited data availability and distributional shifts. Existing approaches adopt a…
Due to its broad applications in practice, the minimum spanning tree problem and its all kinds of variations have been studied extensively during the last decades, for which a host of efficient exact and heuristic algorithms have been…
Given i.i.d. data from an unknown distribution, we consider the problem of predicting future items. An adaptive way to estimate the probability density is to recursively subdivide the domain to an appropriate data-dependent granularity. A…
Computing the coordinate-wise maxima of a planar point set is a classic and well-studied problem in computational geometry. We give an algorithm for this problem in the \emph{self-improving setting}. We have $n$ (unknown) independent…
We investigate the problem of sampling from posterior distributions with intractable normalizing constants in Bayesian inference. Our solution is a new generative modeling approach based on optimal transport (OT) that learns a deterministic…
The connection between the maximum spanning tree in a directed graph and the best dependency tree of a sentence has been exploited by the NLP community. However, for many dependency parsing schemes, an important detail of this approach is…
Neural ordinary differential equations (ODEs) provide expressive representations of invertible transport maps that can be used to approximate complex probability distributions, e.g., for generative modeling, density estimation, and Bayesian…
We study the density estimation problem defined as follows: given $k$ distributions $p_1, \ldots, p_k$ over a discrete domain $[n]$, as well as a collection of samples chosen from a ``query'' distribution $q$ over $[n]$, output $p_i$ that…
In this paper we present a novel probabilistic sampling-based motion planning algorithm called the Fast Marching Tree algorithm (FMT*). The algorithm is specifically aimed at solving complex motion planning problems in high-dimensional…
In this work, we address the problem of approximating the $k$-disc distribution ("frequency vector") of a bounded-degree graph in sublinear-time under the assumption of hyperfiniteness. We revisit the partition-oracle framework of Hassidim,…
We investigate approximating joint distributions of random processes with causal dependence tree distributions. Such distributions are particularly useful in providing parsimonious representation when there exists causal dynamics among…
Temporal point processes offer a powerful framework for sampling from discrete distributions, yet they remain underutilized in existing literature. We show how to construct, for any target multivariate count distribution with…
We present a new random sampling strategy for k-bandlimited signals defined on graphs, based on determinantal point processes (DPP). For small graphs, ie, in cases where the spectrum of the graph is accessible, we exhibit a DPP sampling…
We study a natural problem in graph sparsification, the Spanning Tree Congestion (\STC) problem. Informally, the \STC problem seeks a spanning tree with no tree-edge \emph{routing} too many of the original edges. The root of this problem…
Motivated by a sampling problem basic to computational statistical inference, we develop a nearly optimal algorithm for a fundamental problem in spectral graph theory and numerical analysis. Given an $n\times n$ SDDM matrix ${\bf…
A key challenge in robotics is the efficient generation of optimal robot motion with safety guarantees in cluttered environments. Recently, deterministic optimal sampling-based motion planners have been shown to achieve good performance…