Related papers: Density estimation using cellular binary trees and…
The density classification task is to determine which of the symbols appearing in an array has the majority. A cellular automaton solving this task is required to converge to a uniform configuration with the majority symbol at each site. It…
Large spatial datasets often represent a number of spatial point processes generated by distinct entities or classes of events. When crossed with covariates, such as discrete time buckets, this can quickly result in a data set with millions…
We study the asymptotic distribution of integers sharing the same rooted-tree structure that encodes their complete prime factorization tower. For each tree we derive an explicit density formula depending only on a pair $(m,k)$, the density…
We consider random binary trees that appear as the output of certain standard algorithms for sorting and searching if the input is random. We introduce the subtree size metric on search trees and show that the resulting metric spaces…
This study proposes a data condensation method for multivariate kernel density estimation by genetic algorithm. First, our proposed algorithm generates multiple subsamples of a given size with replacement from the original sample. The…
Random forests are an ensemble method relevant for many problems, such as regression or classification. They are popular due to their good predictive performance (compared to, e.g., decision trees) requiring only minimal tuning of…
The paper considers nonparametric kernel density/regression estimation from a stochastic optimization point of view. The estimation problem is represented through a family of stochastic optimization problems. Recursive constrained…
Let $f$ be a multivariate density and $f\_n$ be a kernel estimate of $f$ drawn from the $n$-sample $X\_1,...,X\_n$ of i.i.d. random variables with density $f$. We compute the asymptotic rate of convergence towards 0 of the volume of the…
We observe a random measure $N$ and aim at estimating its intensity $s$. This statistical framework allows to deal simultaneously with the problems of estimating a density, the marginals of a multivariate distribution, the mean of a random…
We propose a model-based clustering algorithm for a general class of functional data for which the components could be curves or images. The random functional data realizations could be measured with error at discrete, and possibly random,…
Suppose each site on a one-dimensional chain with periodic boundary condition may take on any one of the states $0,1,..., n-1$, can you find out the most frequently occurring state using cellular automaton? Here, we prove that while the…
Tree-based priors for probability distributions are usually specified using a predetermined, data-independent collection of candidate recursive partitions of the sample space. To characterize an unknown target density in detail over the…
Density ratio estimation serves as an important technique in the unsupervised machine learning toolbox. However, such ratios are difficult to estimate for complex, high-dimensional data, particularly when the densities of interest are…
A common objective in the analysis of tabular data is estimating the conditional distribution (in contrast to only producing predictions) of a set of "outcome" variables given a set of "covariates", which is sometimes referred to as the…
We consider conducting inference on the output of the Classification and Regression Tree (CART) [Breiman et al., 1984] algorithm. A naive approach to inference that does not account for the fact that the tree was estimated from the data…
The problem of estimation of the proportion of units with a given attribute in a~finite population is considered. From the population a sample is drawn due to the simple random sampling without replacement. There are limited funds for…
Rooted trees with probabilities are used to analyze properties of a variable length code. A bound is derived on the difference between the entropy rates of the code and a memoryless source. The bound is in terms of normalized informational…
Decision trees are among the most popular machine learning models and are used routinely in applications ranging from revenue management and medicine to bioinformatics. In this paper, we consider the problem of learning optimal binary…
We develop a general statistical framework for the analysis and inference of large tree-structured data, with a focus on developing asymptotic goodness-of-fit tests. We first propose a consistent statistical model for binary trees, from…
Random forests is a common non-parametric regression technique which performs well for mixed-type unordered data and irrelevant features, while being robust to monotonic variable transformations. Standard random forests, however, do not…