Related papers: Spanning Trees and Redistricting: New Methods for …
The reconstruction of interaction networks between random events is a critical problem arising from statistical physics and politics, sociology, biology, psychology, and beyond. The Ising model lays the foundation for this reconstruction…
Decision tree optimization is notoriously difficult from a computational perspective but essential for the field of interpretable machine learning. Despite efforts over the past 40 years, only recently have optimization breakthroughs been…
Regression trees are one of the oldest forms of AI models, and their predictions can be made without a calculator, which makes them broadly useful, particularly for high-stakes applications. Within the large literature on regression trees,…
Additive models, such as produced by gradient boosting, and full interaction models, such as classification and regression trees (CART), are widely used algorithms that have been investigated largely in isolation. We show that these models…
In the process of redistricting, one important metric is the number of competitive districts, that is, districts where both parties have a reasonable chance of winning a majority of votes. Competitive districts are important for achieving…
In many applications of supervised learning, multiple classification or regression outputs have to be predicted jointly. We consider several extensions of gradient boosting to address such problems. We first propose a straightforward…
Random forests are an ensemble method relevant for many problems, such as regression or classification. They are popular due to their good predictive performance (compared to, e.g., decision trees) requiring only minimal tuning of…
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 propose Partition Tree, a novel tree-based framework for conditional density estimation over general outcome spaces that supports both continuous and categorical variables within a unified formulation. Our approach models conditional…
The dynamical phenomena of complex networks are very difficult to predict from local information due to the rich microstructures and corresponding complex dynamics. On the other hands, it is a horrible job to compute some stochastic…
We introduce a graph partitioning problem motivated by computational topology and propose two algorithms that produce approximate solutions. Specifically, given a weighted, undirected graph $G$ and a positive integer $k$, we desire to find…
Decision trees and diffusion models are ostensibly disparate model classes, one discrete and hierarchical, the other continuous and dynamic. This work unifies the two by establishing a crisp mathematical correspondence between hierarchical…
Existing ordinal trees and random forests typically use scores that are assigned to the ordered categories, which implies that a higher scale level is used. Versions of ordinal trees are proposed that take the scale level seriously and…
Seeding then expanding is a commonly used scheme to discover overlapping communities in a network. Most seeding methods are either too complex to scale to large networks or too simple to select high-quality seeds, and the non-principled…
Gerrymandering is the perversion of an election based on manipulation of voting district boundaries, and has been a historically important yet difficult task to analytically prove. We propose a Markov Chain Monte Carlo with Simulated…
Consensus maximization is widely used for robust fitting in computer vision. However, solving it exactly, i.e., finding the globally optimal solution, is intractable. A* tree search, which has been shown to be fixed-parameter tractable, is…
Semantic segmentation aims to robustly predict coherent class labels for entire regions of an image. It is a scene understanding task that powers real-world applications (e.g., autonomous navigation). One important application, the use of…
This paper investigates one of the most fundamental computer vision problems: image segmentation. We propose a supervised hierarchical approach to object-independent image segmentation. Starting with over-segmenting superpixels, we use a…
Reverse search is a convenient method for enumerating structured objects, that can be used both to address theoretical issues and to solve data mining problems. This method has already been successfully developed to handle unordered trees.…
The topic of this paper is "gerrymandering", namely the curse of deliberate creations of district maps with highly asymmetric electoral outcomes to disenfranchise voters, and it has a long legal history. Measuring and eliminating…