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Best subset selection in linear regression is well known to be nonconvex and computationally challenging to solve, as the number of possible subsets grows rapidly with increasing dimensionality of the problem. As a result, finding the…
Motivation: Many inference tools use the Perfect Phylogeny Model (PPM) to learn trees from noisy variant allele frequency (VAF) data. Learning in this setting is hard, and existing tools use approximate or heuristic algorithms. An…
Feature subset selection, as a special case of the general subset selection problem, has been the topic of a considerable number of studies due to the growing importance of data-mining applications. In the feature subset selection problem…
Imagine being able to ask questions to a black box model such as "Which adversarial examples exist?", "Does a specific attribute have a disproportionate effect on the model's prediction?" or "What kind of predictions could possibly be made…
This work considers a number of optimization problems and reductive relations between them. The two main problems we are interested in are the \emph{Optimal Decision Tree} and \emph{Set Cover}. We study these two fundamental tasks under…
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…
Conformal prediction provides a framework for uncertainty quantification, specifically in the forms of prediction intervals and sets with distribution-free guaranteed coverage. While recent cross-conformal techniques such as CV+ and…
The maximum common subtree isomorphism problem asks for the largest possible isomorphism between subtrees of two given input trees. This problem is a natural restriction of the maximum common subgraph problem, which is ${\sf NP}$-hard in…
In decision problems, often, utilities and probabilities are hard to determine. In such cases, one can resort to so-called choice functions. They provide a means to determine which options in a particular set are optimal, and allow…
Energy systems optimization problems are complex due to strongly non-linear system behavior and multiple competing objectives, e.g. economic gain vs. environmental impact. Moreover, a large number of input variables and different variable…
Despite their enormous predictive power, machine learning models are often unsuitable for applications in regulated industries such as finance, due to their limited capacity to provide explanations. While model-agnostic frameworks such as…
Among recent developments in time series forecasting methods, deep forecasting models have gained popularity as they can utilize hidden feature patterns in time series to improve forecasting performance. Nevertheless, the majority of…
This paper investigates the a-posteriori analysis of Branch-and-Bound~(BB) trees to extract structural information about the feasible region of mixed-binary linear programs. We introduce three novel outer approximations of the feasible…
A new stream of research was born in the last decade with the goal of mining itemsets of interest using Constraint Programming (CP). This has promoted a natural way to combine complex constraints in a highly flexible manner. Although CP…
In this paper, we introduce a method for approximating the solution to inference and optimization tasks in uncertain and deterministic reasoning. Such tasks are in general intractable for exact algorithms because of the large number of…
The interpretability of models has become a crucial issue in Machine Learning because of algorithmic decisions' growing impact on real-world applications. Tree ensemble methods, such as Random Forests or XgBoost, are powerful learning tools…
Decision trees are widely used for their low computational cost, good predictive performance, and ability to assess the importance of features. Though often used in practice for feature selection, the theoretical guarantees of these methods…
We develop and analyze methods for computing provably optimal {\em maximum a posteriori} (MAP) configurations for a subclass of Markov random fields defined on graphs with cycles. By decomposing the original distribution into a convex…
Decision trees and randomized forests are widely used in computer vision and machine learning. Standard algorithms for decision tree induction optimize the split functions one node at a time according to some splitting criteria. This greedy…
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…