Related papers: Solving Tree Problems with Category Theory
The main contribution of this paper is the development of a new decision tree algorithm. The proposed approach allows users to guide the algorithm through the data partitioning process. We believe this feature has many applications but in…
Recent progress in artificial intelligence (AI) has renewed interest in building systems that learn and think like people. Many advances have come from using deep neural networks trained end-to-end in tasks such as object recognition, video…
Understanding how people represent categories is a core problem in cognitive science. Decades of research have yielded a variety of formal theories of categories, but validating them with naturalistic stimuli is difficult. The challenge is…
One of the challenges artificial intelligence (AI) faces is how a collection of agents coordinate their behaviour to achieve goals that are not reachable by any single agent. In a recent article by Ozmen et al this was framed as one of six…
In this manuscript, we show that any neural network with any activation function can be represented as a decision tree. The representation is equivalence and not an approximation, thus keeping the accuracy of the neural network exactly as…
Decision trees are popular machine learning models that are simple to build and easy to interpret. Even though algorithms to learn decision trees date back to almost 50 years, key properties affecting their generalization error are still…
Tree search algorithms, such as branch-and-bound, are the most widely used tools for solving combinatorial and nonconvex problems. For example, they are the foremost method for solving (mixed) integer programs and constraint satisfaction…
Category theory provides a collective description of many arrangements in mathematics, such as topological spaces, Banach spaces and game theory. Within this collective description, the perspective from any individual member of the…
A certain amount of category theory is developed in an arbitrary finitely complete category with a factorization system on it, playing the role of the comprehensive factorization system on Cat. Those aspects related to the concepts of…
One advantage of decision tree based methods like random forests is their ability to natively handle categorical predictors without having to first transform them (e.g., by using feature engineering techniques). However, in this paper, we…
The field of AI is undergoing a fundamental transition from generative models that can produce synthetic content to artificial agents that can plan and execute complex tasks with only limited human involvement. Companies that pioneered the…
The potential lack of fairness in the outputs of machine learning algorithms has recently gained attention both within the research community as well as in society more broadly. Surprisingly, there is no prior work developing tree-induction…
The overarching problem in artificial intelligence (AI) is that we do not understand the intelligence process well enough to enable the development of adequate computational models. Much work has been done in AI over the years at lower…
We present an algorithm for classification tasks on big data. Experiments conducted as part of this study indicate that the algorithm can be as accurate as ensemble methods such as random forests or gradient boosted trees. Unlike ensemble…
The decision tree recursively partitions the input space into regions and derives axis-aligned decision boundaries from data. Despite its simplicity and interpretability, decision trees lack parameterized representation, which makes it…
We propose a tree-based algorithm for classification and regression problems in the context of functional data analysis, which allows to leverage representation learning and multiple splitting rules at the node level, reducing…
Many learning algorithms have invariances: when their training data is transformed in certain ways, the function they learn transforms in a predictable manner. Here we formalize this notion using concepts from the mathematical field of…
In the first paper (part I) of this series of two, we introduce four novel definitions of the ODT problems: three for size-constrained trees and one for depth-constrained trees. These definitions are stated unambiguously through executable…
Artificial Intelligence systems cannot yet match human abilities to apply knowledge to situations that vary from what they have been programmed for, or trained for. In visual object recognition methods of inference exploiting top-down…
We focus on generative AI for a type of data that still represent one of the most prevalent form of data: tabular data. Our paper introduces two key contributions: a new powerful class of forest-based models fit for such tasks and a simple…