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Bayesian Decision Trees are known for their probabilistic interpretability. However, their construction can sometimes be costly. In this article we present a general Bayesian Decision Tree algorithm applicable to both regression and…
Motivated by the properties of the descent polynomials, which enumerate permutations of $S_n$ with a fixed descent set, we define descent polynomials for labeled rooted trees. We give recursive and explicit formulas for these polynomials…
A method based on mapping a symbolic sequence into a set of patterns (strings resulting from the sequence parsing) is proposed as a tool for the reconstruction of ancestral sequences. The set union of patterns comprises all the patterns…
We use here the results on the influence graph by Boissonnat et al. to adapt them for particular cases where additional information is available. In some cases, it is possible to improve the expected randomized complexity of algorithms from…
Pairwise ordered tree alignment are combinatorial objects that appear in RNA secondary structure comparison. However, the usual representation of tree alignments as supertrees is ambiguous, i.e. two distinct supertrees may induce identical…
A class of restarted randomized surrounding methods are presented to accelerate the surrounding algorithms by restarted techniques for solving the linear equations. Theoretical analysis prove that the proposed method converges under the…
We present an unusual algorithm involving classification trees where two trees are grown in opposite directions so that they are matched at their leaves. This approach finds application in a new data mining task we formulate, called…
Highly efficient and even nearly optimal algorithms have been developed for the classical problem of univariate polynomial root-finding (see, e.g., \cite{P95}, \cite{P02}, \cite{MNP13}, and the bibliography therein), but this is still an…
Rejoinder to ``Support Vector Machines with Applications'' [math.ST/0612817]
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…
Recently we had derived a new type generalized binomials mixed recurrence for primordial sequence case . Here we report on this new type mixed V and U binomials recurrence in brief.
New differential-recurrence properties of dual Bernstein polynomials are given which follow from relations between dual Bernstein and orthogonal Hahn and Jacobi polynomials. Using these results, a fourth-order differential equation…
In this paper a general class of tree algorithms is analyzed. It is shown that, by using an appropriate probabilistic representation of the quantities of interest, the asymptotic behavior of these algorithms can be obtained quite easily…
In this paper one extends the binomial and trinomial coefficients to the concept of 'k-nomial' coefficients, and one obtains some properties of these. As an application one generalizes Pascal's triangle.
Several technological applications require the translation of a protein into a nucleic acid that codes for it (``backtranslation''). The degeneracy of the genetic code makes this translation ambiguous; moreover, not every translation is…
This paper introduces a series of methods for traversing binary decision trees using arithmetic operations. We present a suite of binary tree traversal algorithms that leverage novel representation matrices to flatten the full binary tree…
We extend the authors' previous work on Wiener-Wintner double recurrence theorem to the case of polynomials.
This article examines a recent body of work on stochastic processes indexed by a tree. Emphasis is on the application of this new framework to existing probability models. Proofs are largely omitted, with references provided.
Motivated by recent studies of large Mallows$(q)$ permutations, we propose a class of random permutations of $\mathbb{N}_{+}$ and of $\mathbb{Z}$, called regenerative permutations. Many previous results of the limiting Mallows$(q)$…
The clique tree algorithm is the standard method for doing inference in Bayesian networks. It works by manipulating clique potentials - distributions over the variables in a clique. While this approach works well for many networks, it is…