Related papers: Combinatorics of least squares trees
Phylogenetic networks are a type of leaf-labelled, acyclic, directed graph used by biologists to represent the evolutionary history of species whose past includes reticulation events. A phylogenetic network is tree-child if each non-leaf…
We consider the problem of learning underlying tree structure from noisy, mixed data obtained from a linear model. To achieve this, we use the expectation maximization algorithm combined with Chow-Liu minimum spanning tree algorithm. This…
In variational assimilation, the most probable state of a dynamical system under Gaussian assumptions for the prior and likelihood can be found by solving a least-squares minimization problem . In recent years, we have seen the popularity…
This paper studies a Markov chain for phylogenetic reconstruction which uses a popular transition between tree topologies known as subtree pruning-and-regrafting (SPR). We analyze the Markov chain in the simpler setting that the generating…
Ensemble methods that average over a collection of independent predictors that are each limited to a subsampling of both the examples and features of the training data command a significant presence in machine learning, such as the…
We describe a combinatorial approach for investigating properties of rational numbers. The overall approach rests on structural bijections between rational numbers and familiar combinatorial objects, namely rooted trees. We emphasize that…
Many combinatorial optimization problems can be formulated as the search for a subgraph that satisfies certain properties and minimizes the total weight. We assume here that the vertices correspond to points in a metric space and can take…
In this paper, we present an improved numerical algorithm for computing the intersection area of multiple circles and a complex polygon efficiently. This geometric problem is fundamental to applications such as wireless sensor networks and…
Phylogenetic trees are used to model evolution: leaves are labelled to represent contemporary species ("taxa") and interior vertices represent extinct ancestors. Informally, convex characters are measurements on the contemporary species in…
Additive regression models are actively researched in the statistical field because of their usefulness in the analysis of responses determined by non-linear relationships with multivariate predictors. In this kind of statistical models,…
Weighted least squares polynomial approximation uses random samples to determine projections of functions onto spaces of polynomials. It has been shown that, using an optimal distribution of sample locations, the number of samples required…
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…
We study a popular algorithm for fitting polynomial curves to scattered data based on the least squares with gradient weights. We show that sometimes this algorithm admits a substantial reduction of complexity, and, furthermore, find…
Research in explorable uncertainty addresses combinatorial optimization problems where there is partial information about the values of numeric input parameters, and exact values of these parameters can be determined by performing costly…
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…
Finding diverse solutions in combinatorial problems recently has received considerable attention (Baste et al. 2020; Fomin et al. 2020; Hanaka et al. 2021). In this paper we study the following type of problems: given an integer $k$, the…
The algebraic properties of flattenings and subflattenings provide direct methods for identifying edges in the true phylogeny -- and by extension the complete tree -- using pattern counts from a sequence alignment. The relatively small…
In this paper we apply new geometric and combinatorial methods to the study of phylogenetic mixtures. The focus of the geometric approach is to describe the geometry of phylogenetic mixture distributions for the two state random cluster…
In phylogenetics, a central problem is to infer the evolutionary relationships between a set of species $X$; these relationships are often depicted via a phylogenetic tree -- a tree having its leaves univocally labeled by elements of $X$…
Shape-constrained convex regression problem deals with fitting a convex function to the observed data, where additional constraints are imposed, such as component-wise monotonicity and uniform Lipschitz continuity. This paper provides a…