Related papers: Dimensional analysis in forest mensuration

We present an innovative approach to dimensional analysis, referred to as augmented dimensional analysis and based on a representation theorem for complete quantity functions with a scaling-covariant scalar representation. This new theorem,…

Many existing interpretation methods are based on Partial Dependence (PD) functions that, for a pre-trained machine learning model, capture how a subset of the features affects the predictions by averaging over the remaining features.…

In this short note, we find the number of forests of chord diagrams with a given number of trees and a given number of chords.

We present a real-time system for per-tree canopy volume estimation using mobile LiDAR data collected during routine robotic navigation. Unlike prior approaches that rely on static scans or assume uniform orchard structures, our method…

Tree congruence metrics are typically global indices that describe the similarity or dissimilarity between dendrograms. This study principally focuses on topological congruence metrics that quantify similarity between two dendrograms and…

Decision tree classifiers are a widely used tool in data stream mining. The use of confidence intervals to estimate the gain associated with each split leads to very effective methods, like the popular Hoeffding tree algorithm. From a…

We propose a procedure to build a decision tree which approximates the performance of complex machine learning models. This single approximation tree can be used to interpret and simplify the predicting pattern of random forests (RFs) and…

We consider query trees of graphs with degree bounded by a constant, $d$. We give simple proofs that the size of a query tree is constant in expectation and $2^{O(d)}\log{n}$ w.h.p.

We propose a measure of shape which is appropriate for the study of a complicated geometric structure, defined using the topology of neighborhoods of the structure. One aspect of this measure gives a new notion of fractal dimension. We…

Dealing with datasets of very high dimension is a major challenge in machine learning. In this paper, we consider the problem of feature selection in applications where the memory is not large enough to contain all features. In this…

The extraction of the CKM angle $\alpha$ from the asymmetry in $B^0 \to \pi^+\pi^-$ vs ${\bar B^0} \to \pi^+\pi^-$ suffers from a currently unknown penguin contribution. Experimentally, one can determine the magnitude and phase of the CP…

The success of QCD factorization(QCDF) in predicting branching ratios for charmless $B$ decays to light pseudoscalar and vector mesons and the small CP asymmetries measured at $BABAR$, Belle and LHCb show that the phase in these decays, as…

National Forest Inventories (NFIs) provide statistically reliable information on forest resources at national and other large spatial scales. As forest management and conservation needs become increasingly complex, NFIs are being called…

We revisit binary decision trees from the perspective of partitions of the data. We introduce the notion of partitioning function, and we relate it to the growth function and to the VC dimension. We consider three types of features:…

Given an ordered partition $\Pi =\{P_1,P_2, ...,P_t\}$ of the vertex set $V$ of a connected graph $G=(V,E)$, the \emph{partition representation} of a vertex $v\in V$ with respect to the partition $\Pi$ is the vector…

Tree ensemble methods such as random forests [Breiman, 2001] are very popular to handle high-dimensional tabular data sets, notably because of their good predictive accuracy. However, when machine learning is used for decision-making…

This work develops formal statistical inference procedures for machine learning ensemble methods. Ensemble methods based on bootstrapping, such as bagging and random forests, have improved the predictive accuracy of individual trees, but…

We study the energy minimization problem for an elastic interface in a random potential plus a quadratic well. As the position of the well is varied, the ground state undergoes jumps, called shocks or static avalanches. We introduce an…

Using the Lagrange inversion formula, $t$-ary trees are enumerated with respect to edge type (left, middle, right for ternary trees).

The tree-metric theorem provides a necessary and sufficient condition for a dissimilarity matrix to be a tree metric, and has served as the foundation for numerous distance-based reconstruction methods in phylogenetics. Our main result is…