Related papers: Probability Distribution on Full Rooted Trees
The random forest (RF) algorithm has become a very popular prediction method for its great flexibility and promising accuracy. In RF, it is conventional to put equal weights on all the base learners (trees) to aggregate their predictions.…
Many modern experiments, such as microarray gene expression and genome-wide association studies, present the problem of estimating a large number of parallel effects. Bayesian inference is a popular approach for analyzing such data by…
Random forest regression (RF) is an extremely popular tool for the analysis of high-dimensional data. Nonetheless, its benefits may be lessened in sparse settings due to weak predictors, and a pre-estimation dimension reduction (targeting)…
Given an ensemble of randomized regression trees, it is possible to restructure them as a collection of multilayered neural networks with particular connection weights. Following this principle, we reformulate the random forest method of…
Bayesian Markov chain Monte Carlo explores tree space slowly, in part because it frequently returns to the same tree topology. An alternative strategy would be to explore tree space systematically, and never return to the same topology. In…
We develop a new Bayesian modelling framework for the class of higher-order, variable-memory Markov chains, and introduce an associated collection of methodological tools for exact inference with discrete time series. We show that a version…
We study full Bayesian procedures for high-dimensional linear regression under sparsity constraints. The prior is a mixture of point masses at zero and continuous distributions. Under compatibility conditions on the design matrix, the…
Tree-shaped graphical models are widely used for their tractability. However, they unfortunately lack expressive power as they require committing to a particular sparse dependency structure. We propose a novel class of generative models…
Tackling simulation optimization problems with non-convex objective functions remains a fundamental challenge in operations research. In this paper, we propose a class of random search algorithms, called Regular Tree Search, which…
Current methods for learning graphical models with latent variables and a fixed structure estimate optimal values for the model parameters. Whereas this approach usually produces overfitting and suboptimal generalization performance,…
Estimating a joint Highest Posterior Density credible set for a multivariate posterior density is challenging as dimension gets larger. Credible intervals for univariate marginals are usually presented for ease of computation and…
In real-world Bayesian inference applications, prior assumptions regarding the parameters of interest may be unrepresentative of their actual values for a given dataset. In particular, if the likelihood is concentrated far out in the wings…
Tree search is a fundamental tool for planning, as many sequential decision-making problems can be framed as searching over tree-structured spaces. We propose an uncertainty-guided tree search algorithm for settings where the reward…
Modeling the diameter distribution of trees in forest stands is a common forestry task that supports key biologically and economically relevant management decisions. The choice of model used to represent the diameter distribution and how to…
We present a new method to propagate lower bounds on conditional probability distributions in conventional Bayesian networks. Our method guarantees to provide outer approximations of the exact lower bounds. A key advantage is that we can…
We advocate for a new statistical principle that combines the most desirable aspects of both parameter inference and density estimation. This leads us to the predictively oriented (PrO) posterior, which expresses uncertainty as a…
Ensembles of decision trees are a useful tool for obtaining for obtaining flexible estimates of regression functions. Examples of these methods include gradient boosted decision trees, random forests, and Bayesian CART. Two potential…
Estimation of parameters that obey specific constraints is crucial in statistics and machine learning; for example, when parameters are required to satisfy boundedness, monotonicity, or linear inequalities. Traditional approaches impose…
The Bayesian method is noted to produce spuriously high posterior probabilities for phylogenetic trees in analysis of large datasets, but the precise reasons for this over-confidence are unknown. In general, the performance of Bayesian…
Recognizing handwritten mathematics is a challenging classification problem, requiring simultaneous identification of all the symbols comprising an input as well as the complex two-dimensional relationships between symbols and…