相关论文: Relative Optimality Conditions and Algorithms for …
We investigate the computation of minimum-cost spanning trees satisfying prescribed vertex degree constraints: Given a graph $G$ and a constraint function $D$, we ask for a (minimum-cost) spanning tree $T$ such that for each vertex $v$, $T$…
In this work, we investigate the performance CutFEM as a high fidelity solver as well as we construct a competent and economical reduced order solver for PDE-constrained optimization problems in parametrized domains that live in a fixed…
Regression trees are becoming increasingly popular as omnibus predicting tools and as the basis of numerous modern statistical learning ensembles. Part of their popularity is their ability to create a regression prediction without ever…
Computing an optimal classification tree that provably maximizes training performance within a given size limit, is NP-hard, and in practice, most state-of-the-art methods do not scale beyond computing optimal trees of depth three.…
Non-convex optimization with local search heuristics has been widely used in machine learning, achieving many state-of-art results. It becomes increasingly important to understand why they can work for these NP-hard problems on typical…
Phylogenetic trees are important tools in the study of evolutionary relationships between species. Measures such as the index of Sackin, Colless, and Total Cophenetic have been extensively used to quantify tree balance, one key property of…
The recursive and hierarchical structure of full rooted trees is applicable to represent statistical models in various areas, such as data compression, image processing, and machine learning. In most of these cases, the full rooted tree is…
The prototypical high-dimensional statistics problem entails finding a structured signal in noise. Many of these problems exhibit an intriguing phenomenon: the amount of data needed by all known computationally efficient algorithms far…
Random forests are among the most popular classification and regression methods used in industrial applications. To be effective, the parameters of random forests must be carefully tuned. This is usually done by choosing values that…
A new class of statistical deformable models is introduced to study high-dimensional curves or images. In addition to the standard measurement error term, these deformable models include an extra error term modeling the individual…
Decompositions of networks are useful not only for structural exploration. They also have implications and use in analysis and computational solution of processes (such as the Ising model, percolation, SIR model) running on a given network.…
Random objects are complex non-Euclidean data taking value in general metric space, possibly devoid of any underlying vector space structure. Such data are getting increasingly abundant with the rapid advancement in technology. Examples…
Energy systems optimization problems are complex due to strongly non-linear system behavior and multiple competing objectives, e.g. economic gain vs. environmental impact. Moreover, a large number of input variables and different variable…
This paper studies duality and optimality conditions for general convex stochastic optimization problems. The main result gives sufficient conditions for the absence of a duality gap and the existence of dual solutions in a locally convex…
Algorithms for binary classification based on adaptive tree partitioning are formulated and analyzed for both their risk performance and their friendliness to numerical implementation. The algorithms can be viewed as generating a set…
The challenge of taking many variables into account in optimization problems may be overcome under the hypothesis of low effective dimensionality. Then, the search of solutions can be reduced to the random embedding of a low dimensional…
Ensemble trees are a popular machine learning model which often yields high prediction performance when analysing structured data. Although individual small decision trees are deemed explainable by nature, an ensemble of large trees is…
Phylogenetic comparative methods are well established tools for using inter-species variation to analyse phenotypic evolution and adaptation. They are generally hampered, however, by predominantly univariate approaches and failure to…
We give algorithms to compute the Fr\'echet distance of trees and graphs with bounded tree width. Our algorithms run in $O(n^2)$ time for trees of bounded degree, and $O(n^2\sqrt{n \log n})$ time for trees of arbitrary degree. For graphs of…
We propose a gradient descent method for solving optimization problems arising in settings of tropical geometry - a variant of algebraic geometry that has attracted growing interest in applications such as computational biology, economics,…