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Many algorithms have been developed for enumerating various combinatorial objects in time exponentially less than the number of objects. Two common classes of algorithms are dynamic programming and the transfer matrix method. This paper…
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…
The challenge of traversability estimation is a crucial aspect of autonomous navigation in unstructured outdoor environments such as forests. It involves determining whether certain areas are passable or risky for robots, taking into…
Normal surface theory is a central tool in algorithmic three-dimensional topology, and the enumeration of vertex normal surfaces is the computational bottleneck in many important algorithms. However, it is not well understood how the number…
Identifying optimal basic feasible solutions to linear programming problems is a critical task for mixed integer programming and other applications. The crossover method, which aims at deriving an optimal extreme point from a suboptimal…
This thesis presents a number of results related to path traversal in trees and graphs. In particular, we focus on data structures which allow such traversals to be performed efficiently in the external memory setting. In addition, for…
This paper proposes a new general technique for maximal subgraph enumeration which we call proximity search, whose aim is to design efficient enumeration algorithms for problems that could not be solved by existing frameworks. To support…
In general dimension, there is no known total polynomial algorithm for either convex hull or vertex enumeration, i.e. an algorithm whose complexity depends polynomially on the input and output sizes. It is thus important to identify…
There are many classical problems in P whose time complexities have not been improved over the past decades. Recent studies of "Hardness in P" have revealed that, for several of such problems, the current fastest algorithm is the best…
Tree kernels are fundamental tools that have been leveraged in many applications, particularly those based on machine learning for Natural Language Processing tasks. In this paper, we devise a parallel implementation of the sequential…
To understand the structure of a network, it can be useful to break it down into its constituent pieces. This is the approach taken in a multitude of successful network analysis methods, such as motif analysis. These methods require one to…
A novel multiphysics-decision tree learning algorithm is presented for (1) estimating transport properties in the variably saturated subsurface governed by explicitly coupled equations for water, heat, and solute transport; and (2)…
Decision trees and their ensembles are popular in machine learning as easy-to-understand models. Several techniques have been proposed in the literature for learning tree-based classifiers, with different techniques working well for data…
Counting non-isomorphic tree-like multigraphs that include self-loops and multiple edges is an important problem in combinatorial enumeration, with applications in chemical graph theory, polymer science, and network modeling. Traditional…
We give an algorithm to enumerate the results on trees of monadic second-order (MSO) queries represented by nondeterministic tree automata. After linear time preprocessing (in the input tree), we can enumerate answers with linear delay (in…
We propose two algorithms for interpretation and boosting of tree-based ensemble methods. Both algorithms make use of mathematical programming models that are constructed with a set of rules extracted from an ensemble of decision trees. The…
Kernel density estimation (KDE) is a popular statistical technique for estimating the underlying density distribution with minimal assumptions. Although they can be shown to achieve asymptotic estimation optimality for any input…
Tree-based machine learning techniques, such as Decision Trees and Random Forests, are top performers in several domains as they do well with limited training datasets and offer improved interpretability compared to Deep Neural Networks…
In this paper, we propose an explicit, non-strict representation of search trees in constraint-logic object-oriented programming. Our search tree representation includes both the non-deterministic and deterministic behaviour during…
Given a weighted, ordered query set $Q$ and a partition of $Q$ into classes, we study the problem of computing a minimum-cost decision tree that, given any query $q$ in $Q$, uses equality tests and less-than comparisons to determine the…