Related papers: Bidiagonalization with Parallel Tiled Algorithms
The minimum cut problem for an undirected edge-weighted graph asks us to divide its set of nodes into two blocks while minimizing the weight sum of the cut edges. Here, we introduce a linear-time algorithm to compute near-minimum cuts. Our…
Decision trees with binary splits are popularly constructed using Classification and Regression Trees (CART) methodology. For binary classification and regression models, this approach recursively divides the data into two near-homogenous…
Embeddings of graphs into distributions of trees that preserve distances in expectation are a cornerstone of many optimization algorithms. Unfortunately, online or dynamic algorithms which use these embeddings seem inherently randomized and…
The sampling based motion planning algorithm known as Rapidly-exploring Random Trees (RRT) has gained the attention of many researchers due to their computational efficiency and effectiveness. Recently, a variant of RRT called RRT* has been…
We discuss a simple, binary tree-based algorithm for the collective allreduce (reduction-to-all, MPI_Allreduce) operation for parallel systems consisting of $p$ suitably interconnected processors. The algorithm can be doubly pipelined to…
The algebraic properties of flattenings and subflattenings provide direct methods for identifying edges in the true phylogeny -- and by extension the complete tree -- using pattern counts from a sequence alignment. The relatively small…
We study computational aspects of the nonparametric maximum likelihood estimator (NPMLE) for the distribution function of bivariate interval censored data. The computation of the NPMLE consists of two steps: a parameter reduction step and…
Treewidth is a measure of how tree-like a graph is. It has many important algorithmic applications because many NP-hard problems on general graphs become tractable when restricted to graphs of bounded treewidth. Algorithms for problems on…
In this paper we develop optimal algorithms in the binary-forking model for a variety of fundamental problems, including sorting, semisorting, list ranking, tree contraction, range minima, and ordered set union, intersection and difference.…
We incorporate heteroskedasticity into Bayesian Additive Regression Trees (BART) by modeling the log of the error variance parameter as a linear function of prespecified covariates. Under this scheme, the Gibbs sampling procedure for the…
We give a simple, fast algorithm for hyperparameter optimization inspired by techniques from the analysis of Boolean functions. We focus on the high-dimensional regime where the canonical example is training a neural network with a large…
Decision trees are powerful tools for classification and regression that attract many researchers working in the burgeoning area of machine learning. One advantage of decision trees over other methods is their interpretability, which is…
Orthogonality constraints are ubiquitous in robust and probabilistic machine learning. Unfortunately, current optimizers are computationally expensive and do not scale to problems with hundreds or thousands of constraints. One notable…
We present a new approximation algorithm for the treewidth problem which finds an upper bound on the treewidth and constructs a corresponding tree decomposition as well. Our algorithm is a faster variation of Reed's classical algorithm. For…
This paper proposes a reduced-rank scheme for adaptive beamforming based on the constrained joint iterative optimization of filters. We employ this scheme to devise two novel reduced-rank adaptive algorithms according to the constant…
Orthogonality constraints naturally appear in many machine learning problems, from principal component analysis to robust neural network training. They are usually solved using Riemannian optimization algorithms, which minimize the…
The phase retrieval problem is a fundamental problem in many fields, which is appealing for investigation. It is to recover the signal vector $\tilde{x}\in\mathbb{C}^d$ from a set of $N$ measurements $b_n=|f^*_n\tilde{x}|^2,\ n=1,\cdots,…
A simple greedy refinement procedure for the generation of data-adapted triangulations is proposed and studied. Given a function of two variables, the algorithm produces a hierarchy of triangulations and piecewise polynomial approximations…
Bilevel optimization has been widely applied in many important machine learning applications such as hyperparameter optimization and meta-learning. Recently, several momentum-based algorithms have been proposed to solve bilevel optimization…
Rebalancing schemes for dynamic binary search trees are numerous in the literature, where the goal is to maintain trees of low height, either in the worst-case or expected sense. In this paper we study randomized rebalancing schemes for…