Related papers: Performance Characteristics of TreePM codes
We study the problem of efficient adversarial attacks on tree based ensembles such as gradient boosting decision trees (GBDTs) and random forests (RFs). Since these models are non-continuous step functions and gradient does not exist, most…
Function approximation has been an indispensable component in modern reinforcement learning algorithms designed to tackle problems with large state spaces in high dimensions. This paper reviews recent results on error analysis for these…
As an entry for the 1999 Gordon Bell price/performance prize, we report an astrophysical N-body simulation performed with a treecode on GRAPE-5 (Gravity Pipe 5) system, a special-purpose computer for astrophysical N-body simulations. The…
We study a general class of nonlinear iterative algorithms which includes power iteration, belief propagation and approximate message passing, and many forms of gradient descent. When the input is a random matrix with i.i.d. entries, we use…
The long-wavelength coherent overdensity and tidal force, which are not direct observables for a finite-volume survey, affect time evolution of cosmic structure formation and therefore clustering observables through the mode coupling. In…
For interior-point algorithms in linear programming, it is well-known that the selection of the centering parameter is crucial for proving polynomility in theory and for efficiency in practice. However, the selection of the centering…
An important aspect of large-scale structure data analysis is the presence of non-negligible theoretical uncertainties, which become increasingly important on small scales. We show how to incorporate these uncertainties in realistic power…
We propose new methods for Support Vector Machines (SVMs) using tree architecture for multi-class classi- fication. In each node of the tree, we select an appropriate binary classifier using entropy and generalization error estimation, then…
In many domains, data measurements can naturally be associated with the leaves of a tree, expressing the relationships among these measurements. For example, companies belong to industries, which in turn belong to ever coarser divisions…
The paper surveys recent extensions of the Long-Short Term Memory networks to handle tree structures from the perspective of learning non-trivial forms of isomorph structured transductions. It provides a discussion of modern TreeLSTM…
Random forests perform bootstrap-aggregation by sampling the training samples with replacement. This enables the evaluation of out-of-bag error which serves as a internal cross-validation mechanism. Our motivation lies in using the…
We have developed a parallel Particle-Particle, Particle-Mesh (P3M) simulation code for the Cray T3E parallel supercomputer that is well suited to studying the time evolution of systems of particles interacting via gravity and gas forces in…
It is widely believed that the prediction accuracy of decision tree models is invariant under any strictly monotone transformation of the individual predictor variables. However, this statement may be false when predicting new observations…
Tree tensor networks (TTNs) are widely used in low-rank approximation and quantum many-body simulation. In this work, we present a formal analysis of the differential geometry underlying TTNs. Building on this foundation, we develop…
A classical decision tree is completely based on splitting measures, which utilize the occurrence of random events in correspondence to its class labels in order to optimally segregate datasets. However, the splitting measures are based on…
Despite achieving excellent performance on benchmarks, deep neural networks often underperform in real-world deployment due to sensitivity to minor, often imperceptible shifts in input data, known as distributional shifts. These shifts are…
Interior point methods (IPMs) are a common approach for solving linear programs (LPs) with strong theoretical guarantees and solid empirical performance. The time complexity of these methods is dominated by the cost of solving a linear…
We consider the problem of designing efficient particle filters for twisted Feynman--Kac models. Particle filters using twisted models can deliver low error approximations of statistical quantities and such twisting functions can be learnt…
We introduce the Thresholding Monte Carlo Tree Search problem, in which, given a tree $\mathcal{T}$ and a threshold $\theta$, a player must answer whether the root node value of $\mathcal{T}$ is at least $\theta$ or not. In the given tree,…
In this paper, we propose new learning algorithms for approximating high-dimensional functions using tree tensor networks in a least-squares setting. Given a dimension tree or architecture of the tensor network, we provide an algorithm that…