Related papers: Imprecise probability trees: Bridging two theories…
We study the problem of computing the tightest upper and lower bounds on the probability that the sum of $n$ dependent Bernoulli random variables exceeds an integer $k$. Under knowledge of all pairs of bivariate distributions denoted by a…
A learning algorithm is presented which given the structure of a causal tree, will estimate its link probabilities by sequential measurements on the leaves only. Internal nodes of the tree represent conceptual (hidden) variables…
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…
Several classification methods assume that the underlying distributions follow tree-structured graphical models. Indeed, trees capture statistical dependencies between pairs of variables, which may be crucial to attain low classification…
This paper advocates the usefulness of new theories of uncertainty for the purpose of modeling some facets of uncertain knowledge, especially vagueness, in AI. It can be viewed as a partial reply to Cheeseman's (among others) defense of…
In this paper, we consider one aspect of the problem of applying decision theory to the design of agents that learn how to make decisions under uncertainty. This aspect concerns how an agent can estimate probabilities for the possible…
Sparse decision trees are one of the most common forms of interpretable models. While recent advances have produced algorithms that fully optimize sparse decision trees for prediction, that work does not address policy design, because the…
Random forests are decision tree ensembles that can be used to solve a variety of machine learning problems. However, as the number of trees and their individual size can be large, their decision making process is often incomprehensible. In…
The purpose of this paper is to present a mathematical theory that can be used as a foundation for statistics that include improper priors. This theory includes improper laws in the initial axioms and has in particular Bayes theorem as a…
In statistical practice, whether a Bayesian or frequentist approach is used in inference depends not only on the availability of prior information but also on the attitude taken toward partial prior information, with frequentists tending to…
The prevailing maximum likelihood estimators for inferring power law models from rank-frequency data are biased. The source of this bias is an inappropriate likelihood function. The correct likelihood function is derived and shown to be…
We explore the interplay between random and deterministic phenomena using a representation of uncertainty based on the measure-theoretic concept of outer measure. The meaning of the analogues of different probabilistic concepts is…
This paper makes a small step towards a non-stochastic version of superhedging duality relations in the case of one traded security with a continuous price path. Namely, we prove the coincidence of game-theoretic and measure-theoretic…
Probabilistic inferences distill knowledge from graphs to aid human make important decisions. Due to the inherent uncertainty in the model and the complexity of the knowledge, it is desirable to help the end-users understand the inference…
A random set is a generalisation of a random variable, i.e. a set-valued random variable. The random set theory allows a unification of other uncertainty descriptions such as interval variable, mass belief function in Dempster-Shafer theory…
We study the fundamental question of how likely it is that two randomly chosen trees are isomorphic to each other for different models of random trees. We show that the probability decays exponentially for rooted labeled trees as well as…
We consider random walks on $\Z^8$ indexed by the infinite invariant tree, which consists of an infinite spine and finite random trees attached to it on both sides. We establish the precise order of the non-intersection probability between…
This paper introduces the Bradley-Terry Regression Trunk model, a novel probabilistic approach for the analysis of preference data expressed through paired comparison rankings. In some cases, it may be reasonable to assume that the…
We introduce Joint Probability Trees (JPT), a novel approach that makes learning of and reasoning about joint probability distributions tractable for practical applications. JPTs support both symbolic and subsymbolic variables in a single…
Besides serving as prediction models, classification trees are useful for finding important predictor variables and identifying interesting subgroups in the data. These functions can be compromised by weak split selection algorithms that…