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Minimum spanning trees (MSTs) provide a convenient representation of datasets in numerous pattern recognition activities. Moreover, they are relatively fast to compute. In this paper, we quantify the extent to which they are meaningful in…
Computing an optimal classification tree that provably maximizes training performance within a given size limit, is NP-hard, and in practice, most state-of-the-art methods do not scale beyond computing optimal trees of depth three.…
In binary classification tasks, accurate representation of probabilistic predictions is essential for various real-world applications such as predicting payment defaults or assessing medical risks. The model must then be well-calibrated to…
Causal effects are often characterized with population summaries. These might provide an incomplete picture when there are heterogeneous treatment effects across subgroups. Since the subgroup structure is typically unknown, it is more…
Traditional decision tree algorithms are explainable but struggle with non-linear, high-dimensional data, limiting its applicability in complex decision-making. Neural networks excel at capturing complex patterns but sacrifice…
There is a large discrepancy in our understanding of uncapacitated and capacitated versions of network location problems. This is perhaps best illustrated by the classical k-center problem: there is a simple tight 2-approximation algorithm…
In an ever expanding set of research and application areas, deep neural networks (DNNs) set the bar for algorithm performance. However, depending upon additional constraints such as processing power and execution time limits, or…
The minimum spanning tree clustering algorithm is capable of detecting clusters with irregular boundaries. In this paper we propose two minimum spanning trees based clustering algorithm. The first algorithm produces k clusters with center…
Thin spanning trees lie at the intersection of graph theory, approximation algorithms, and combinatorial optimization. They are central to the long-standing \emph{thin tree conjecture}, which asks whether every $k$-edge-connected graph…
In the decision tree computation model for Boolean functions, the depth corresponds to query complexity, and size corresponds to storage space. The depth measure is the most well-studied one, and is known to be polynomially related to…
Decision Trees have remained a popular machine learning method for tabular datasets, mainly due to their interpretability. However, they lack the expressiveness needed to handle highly nonlinear or unstructured datasets. Motivated by recent…
Partially Observable Markov Decision Processes (POMDPs) are a fundamental framework for decision-making under uncertainty and partial observability. Since in general optimal policies may require infinite memory, they are hard to implement…
The domain of explainable AI is of interest in all Machine Learning fields, and it is all the more important in clustering, an unsupervised task whose result must be validated by a domain expert. We aim at finding a clustering that has high…
The best-performing models in ML are not interpretable. If we can explain why they outperform, we may be able to replicate these mechanisms and obtain both interpretability and performance. One example are decision trees and their…
We study the problem of multiclass classification with an extremely large number of classes (k), with the goal of obtaining train and test time complexity logarithmic in the number of classes. We develop top-down tree construction…
Interpretability is crucial for doctors, hospitals, pharmaceutical companies and biotechnology corporations to analyze and make decisions for high stakes problems that involve human health. Tree-based methods have been widely adopted for…
Clustering is a fundamental problem in unsupervised machine learning with many applications in data analysis. Popular clustering algorithms such as Lloyd's algorithm and $k$-means++ can take $\Omega(ndk)$ time when clustering $n$ points in…
We study a variant of classical clustering formulations in the context of algorithmic fairness, known as diversity-aware clustering. In this variant we are given a collection of facility subsets, and a solution must contain at least a…
The increasing use of machine learning in high-stakes domains -- where people's livelihoods are impacted -- creates an urgent need for interpretable, fair, and highly accurate algorithms. With these needs in mind, we propose a mixed integer…
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…