Related papers: Quantum Algorithms for Evaluating MIN-MAX Trees
Decision trees have been a very popular class of predictive models for decades due to their interpretability and good performance on categorical features. However, they are not always robust and tend to overfit the data. Additionally, if…
We use a Bayesian approach to optimally solve problems in noisy binary search. We deal with two variants: 1. Each comparison can be erroneous with some probability $1 - p$. 2. At each stage $k$ comparisons can be performed in parallel and a…
We study quantum algorithms for testing bipartiteness and expansion of bounded-degree graphs. We give quantum algorithms that solve these problems in time O(N^(1/3)), beating the Omega(sqrt(N)) classical lower bound. For testing expansion,…
We prove that \Omega(n log(n)) comparisons are necessary for any quantum algorithm that sorts n numbers with high success probability and uses only comparisons. If no error is allowed, at least 0.110nlog_2(n) - 0.067n + O(1) comparisons…
We present a novel algorithm for the minimum-depth elimination tree problem, which is equivalent to the optimal treedepth decomposition problem. Our algorithm makes use of two cheaply-computed lower bound functions to prune the search tree,…
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…
Random forests and, more generally, (decision\nobreakdash-)tree ensembles are widely used methods for classification and regression. Recent algorithmic advances allow to compute decision trees that are optimal for various measures such as…
This thesis investigates the design of algorithms for solving min-max optimization problems, which form the mathematical foundation of many modern applications in machine learning, game theory, and optimization. This work offers new…
In this article we propose a heuristic algorithm to explore search space trees associated with instances of combinatorial optimization problems. The algorithm is based on Monte Carlo tree search, a popular algorithm in game playing that is…
Quantum amplitude amplification and estimation have shown quadratic speedups to unstructured search and estimation tasks. We show that a coherent combination of these quantum algorithms also provides a quadratic speedup to calculating the…
We show that, for any d, all but a doubly exponentially small fraction of decision trees of depth at most d require Omega(d) quantum queries to be computed with bounded error. In other words, most efficient classical algorithms in the query…
We present new and improved fixed-parameter algorithms for computing maximum agreement forests (MAFs) of pairs of rooted binary phylogenetic trees. The size of such a forest for two trees corresponds to their subtree prune-and-regraft…
The Maximum Agreement Forest problem has been extensively studied in phylogenetics. Most previous work is on two binary phylogenetic trees. In this paper, we study a generalized version of the problem: the Maximum Agreement Forest problem…
Tree search algorithms, such as branch-and-bound, are the most widely used tools for solving combinatorial and nonconvex problems. For example, they are the foremost method for solving (mixed) integer programs and constraint satisfaction…
When trying to use quantum-enhanced methods for optimization problems, the sheer number of options inhibits its adoption by industrial end users. Expert knowledge is required for the formulation and encoding of the use case, the selection…
Span program is a linear-algebraic model of computation originally proposed for studying the complexity theory. Recently, it has become a useful tool for designing quantum algorithms. In this paper, we present a time-efficient…
We present a quantum algorithm that verifies a product of two n*n matrices over any field with bounded error in worst-case time n^{5/3} and expected time n^{5/3} / min(w,sqrt(n))^{1/3}, where w is the number of wrong entries. This improves…
This extended abstract reports on on-going research on quantum algorithmic approaches to the problem of generalised tree search that may exhibit effective quantum speedup, even in the presence of non-constant branching factors. Two…
We describe a framework for maintaining forest algebra representations that are of logarithmic height for unranked trees. Such representations can be computed in O(n) time and updated in O(log(n)) time. The framework is of potential…
The main contribution of this paper is the development of a new decision tree algorithm. The proposed approach allows users to guide the algorithm through the data partitioning process. We believe this feature has many applications but in…