12 citations · 19 across the 11 of their papers we have counts for
11 papers
Foundational theory for optimal decision tree problems. I. Algorithmic and geometric foundations
Xi He
In the first paper (part I) of this series of two, we introduce four novel definitions of the ODT problems: three for size-constrained trees and one for depth-constrained trees. Th…
Optimal hypersurface decision trees
Xi He
Optimal decision trees have attracted increasing attention in recent years, yet existing algorithms face two closely related challenges. First, the trees they construct have limite…
Functional design of efficient and parallelizable combinatorial generators using convolution
Xi He, Zhenjiang Hu, Max. A. Little
The application of program transformation and algebraic methods to the development of efficient combinatorial optimization (CO) algorithms relies on an exhaustive combinatorial gen…
Deep-ICE: the first globally optimal algorithm for minimizing 0-1 loss in two-layer ReLU and maxout networks
Xi He, Yi Miao, Max A. Little
This paper introduces the first globally optimal algorithm for the empirical risk minimization problem of two-layer maxout and ReLU networks, i.e., minimizing the number of misclas…
Proper decision trees: An axiomatic framework for solving optimal decision tree problems with arbitrary splitting rules
Xi He, Max A. Little
We present an axiomatic framework for analyzing the algorithmic properties of decision trees. This framework supports the classification of decision tree problems through structura…
EKM: An exact, polynomial-time algorithm for the -medoids problem
Xi He, Max A. Little
The -medoids problem is a challenging combinatorial clustering task, widely used in data analysis applications. While numerous algorithms have been proposed to solve this proble…
An efficient, provably optimal algorithm for the 0-1 loss linear classification problem
Xi He, Max A. Little
Algorithms for solving the linear classification problem have a long history, dating back at least to 1936 with linear discriminant analysis. For linearly separable data, many algo…
Efficient Distributed Hessian Free Algorithm for Large-scale Empirical Risk Minimization via Accumulating Sample Strategy
Majid Jahani, Xi He, Chenxin Ma +4
In this paper, we propose a Distributed Accumulated Newton Conjugate gradiEnt (DANCE) method in which sample size is gradually increasing to quickly obtain a solution whose empiric…
Dual Free Adaptive Minibatch SDCA for Empirical Risk Minimization
Xi He, Rachael Tappenden, Martin Takac
In this paper we develop an adaptive dual free Stochastic Dual Coordinate Ascent (adfSDCA) algorithm for regularized empirical risk minimization problems. This is motivated by the…
Distributed Hessian-Free Optimization for Deep Neural Network
Xi He, Dheevatsa Mudigere, Mikhail Smelyanskiy +1
Training deep neural network is a high dimensional and a highly non-convex optimization problem. Stochastic gradient descent (SGD) algorithm and it's variations are the current sta…
Dual Free Adaptive Mini-batch SDCA for Empirical Risk Minimization
Xi He, Martin Takáč
In this paper we develop dual free mini-batch SDCA with adaptive probabilities for regularized empirical risk minimization. This work is motivated by recent work of Shai Shalev-Shw…