Related papers: A probabilistic analysis of some tree algorithms
Binary search trees (BST) are a popular type of data structure when dealing with ordered data. Indeed, they enable one to access and modify data efficiently, with their height corresponding to the worst retrieval time. From a probabilistic…
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…
Decision trees are widely used for non-linear modeling, as they capture interactions between predictors while producing inherently interpretable models. Despite their popularity, performing inference on the non-linear fit remains largely…
We show how complexity theory can be introduced in machine learning to help bring together apparently disparate areas of current research. We show that this new approach requires less training data and is more generalizable as it shows…
Towards a future where machine learning systems will integrate into every aspect of people's lives, researching methods to interpret such systems is necessary, instead of focusing exclusively on enhancing their performance. Enriching the…
We introduce a batched lazy algorithm for supervised classification using decision trees. It avoids unnecessary visits to irrelevant nodes when it is used to make predictions with either eagerly or lazily trained decision trees. A set of…
This work addresses the problem of computing measures of recognisable sets of infinite trees. An algorithm is provided to compute the probability measure of a tree language recognisable by a weak alternating automaton, or equivalently…
Tree ensemble models like random forests and gradient boosting machines are widely used in machine learning due to their excellent predictive performance. However, a high-performance ensemble consisting of a large number of decision trees…
Tree-based methods are powerful nonparametric techniques in statistics and machine learning. However, their effectiveness, particularly in finite-sample settings, is not fully understood. Recent applications have revealed their surprising…
We consider the problem of estimating a large causal polytree from a relatively small i.i.d. sample. This is motivated by the problem of determining causal structure when the number of variables is very large compared to the sample size,…
We consider supervised learning with random decision trees, where the tree construction is completely random. The method is popularly used and works well in practice despite the simplicity of the setting, but its statistical mechanism is…
We prove asymptotic normality for the number of fringe subtrees isomorphic to any given tree in uniformly random trees with given vertex degrees. As applications, we also prove corresponding results for random labelled trees with given…
We introduce a random intersection graph process aimed at modeling sparse evolving affiliation networks that admit tunable (power law) degree distribution and assortativity and clustering coefficients. We show the asymptotic degree…
We present convincing empirical evidence for an effective and general strategy for building accurate small models. Such models are attractive for interpretability and also find use in resource-constrained environments. The strategy is to…
Let $\mathcal{T}_n$ be the set of trees with $n$ vertices. Suppose that each tree in $\mathcal{T}_n$ is equally likely. We show that the number of different rooted trees of a tree equals $(\mu_r+o(1))n$ for almost every tree of…
Graphs are used in many disciplines to model the relationships that exist between objects in a complex discrete system. Researchers may wish to compare a network of interest to a "typical" graph from a family (or ensemble) of graphs which…
Random forests remain among the most popular off-the-shelf supervised learning algorithms. Despite their well-documented empirical success, however, until recently, few theoretical results were available to describe their performance and…
Algorithms for binary classification based on adaptive tree partitioning are formulated and analyzed for both their risk performance and their friendliness to numerical implementation. The algorithms can be viewed as generating a set…
The problem of categorical data analysis in high dimensions is considered. A discussion of the fundamental difficulties of probability modeling is provided, and a solution to the derivation of high dimensional probability distributions…
The multispecies coalescent process models the genealogical relationships of genes sampled from several species, enabling useful predictions about phenomena such as the discordance between the gene tree and the species phylogeny due to…