Related papers: The Branch-and-Bound Tree Closure
Decision trees are widely used for interpretable machine learning due to their clearly structured reasoning process. However, this structure belies a challenge we refer to as predictive equivalence: a given tree's decision boundary can be…
Combinatorial optimisation problems framed as mixed integer linear programmes (MILPs) are ubiquitous across a range of real-world applications. The canonical branch-and-bound algorithm seeks to exactly solve MILPs by constructing a search…
Neural Networks and Decision Trees: two popular techniques for supervised learning that are seemingly disconnected in their formulation and optimization method, have recently been combined in a single construct. The connection pivots on…
Strict inequalities in mixed-integer linear optimization can cause difficulties in guaranteeing convergence and exactness. Utilizing that optimal vertex solutions follow a lattice structure we propose a rounding rule for strict inequalities…
A model of computation for which reasonable yet still incomplete lower bounds are known is the read-once branching program. Here variants of complexity measures successful in the study of read-once branching programs are defined and…
The (axis-parallel) stabbing number of a given set of line segments is the maximum number of segments that can be intersected by any one (axis-parallel) line. This paper deals with finding perfect matchings, spanning trees, or…
The decision tree recursively partitions the input space into regions and derives axis-aligned decision boundaries from data. Despite its simplicity and interpretability, decision trees lack parameterized representation, which makes it…
We investigate the gap between theory and practice for exact branching algorithms. In theory, branch-and-reduce algorithms currently have the best time complexity for numerous important problems. On the other hand, in practice,…
The decision tree is one of the most fundamental programming abstractions. A commonly used type of decision tree is the alphabetic binary tree, which uses (without loss of generality) ``less than'' versus ''greater than or equal to'' tests…
Stick-breaking (SB) processes are often adopted in Bayesian mixture models for generating mixing weights. When covariates influence the sizes of clusters, SB mixtures are particularly convenient as they can leverage their connection to…
We prove complex contraction for zero-free regions of counting weighted set cover problem in which an element can appear in an unbounded number of sets, thus obtaining fully polynomial-time approximation schemes(FPTAS) via Barvinok's…
The Binary Search Tree (BST) is average in computer science which supports a compact data structure in memory and oneself even conducts a row of quick algorithms, by which people often apply it in dynamical circumstance. Besides these…
The Tree Evaluation Problem was introduced by Cook et al. in 2010 as a candidate for separating P from L and NL. The most general space lower bounds known for the Tree Evaluation Problem require a semantic restriction on the branching…
Given a tree $T$ on $n$ vertices, and $k, b, s_1, \ldots, s_b \in N$, the Tree Partitioning problem asks if at most $k$ edges can be removed from $T$ so that the resulting components can be grouped into $b$ groups such that the number of…
The success of Deep Learning and its potential use in many safety-critical applications has motivated research on formal verification of Neural Network (NN) models. In this context, verification involves proving or disproving that an NN…
We revisit the Bayesian Context Trees (BCT) modelling framework for discrete time series, which was recently found to be very effective in numerous tasks including model selection, estimation and prediction. A novel representation of the…
Many network applications are based on binary-state networks, where each component has one of two states: success or failure. Efficient algorithms to evaluate binary-state network reliability are continually being developed. Reliability…
We develop a spatial branch-and-cut approach for nonconvex Quadratically Constrained Quadratic Programs with bounded complex variables (CQCQP). Linear valid inequalities are added at each node of the search tree to strengthen semidefinite…
We introduce the problem of finding a spanning tree along with a partition of the tree edges into fewest number of feasible sets, where constraints on the edges define feasibility. The motivation comes from wireless networking, where we…
This work considers a number of optimization problems and reductive relations between them. The two main problems we are interested in are the \emph{Optimal Decision Tree} and \emph{Set Cover}. We study these two fundamental tasks under…