Related papers: Theoretical Challenges in Learning for Branch-and-…
Decision trees are powerful machine learning algorithms, widely used in fields such as economics and medicine for their simplicity and interpretability. However, decision trees such as CART are prone to overfitting, especially when grown…
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 big challenge in branch and bound lies in identifying the optimal node within the search tree from which to proceed. Current state-of-the-art selectors utilize either hand-crafted ensembles that automatically switch between naive sub-node…
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…
Existing guarantees in terms of rigorous upper bounds on the generalization error for the original random forest algorithm, one of the most frequently used machine learning methods, are unsatisfying. We discuss and evaluate various…
Score-based algorithms that learn Bayesian Network (BN) structures provide solutions ranging from different levels of approximate learning to exact learning. Approximate solutions exist because exact learning is generally not applicable to…
Resource allocation in wireless networks, such as device-to-device (D2D) communications, is usually formulated as mixed integer nonlinear programming (MINLP) problems, which are generally NP-hard and difficult to get the optimal solutions.…
Tree-based models are widely recognized for their interpretability and have proven effective in various application domains, particularly in high-stakes domains. However, learning decision trees (DTs) poses a significant challenge due to…
Efficient sampling from constraint manifolds, and thereby generating a diverse set of solutions for feasibility problems, is a fundamental challenge. We consider the case where a problem is factored, that is, the underlying nonlinear…
When using machine learning for imbalanced binary classification problems, it is common to subsample the majority class to create a (more) balanced training dataset. This biases the model's predictions because the model learns from data…
Choosing appropriate step sizes is critical for reducing the computational cost of training large-scale neural network models. Mini-batch sub-sampling (MBSS) is often employed for computational tractability. However, MBSS introduces a…
Most combinatorial optimization problems can be formulated as mixed integer linear programming (MILP), in which branch-and-bound (B\&B) is a general and widely used method. Recently, learning to branch has become a hot research topic in the…
Combinatorial optimization problems are typically tackled by the branch-and-bound paradigm. We propose a new graph convolutional neural network model for learning branch-and-bound variable selection policies, which leverages the natural…
We consider the problem of computing bounds for causal queries on causal graphs with unobserved confounders and discrete valued observed variables, where identifiability does not hold. Existing non-parametric approaches for computing such…
Finding tight bounds on the optimal solution is a critical element of practical solution methods for discrete optimization problems. In the last decade, decision diagrams (DDs) have brought a new perspective on obtaining upper and lower…
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…
Recently, cutting-plane methods such as GCP-CROWN have been explored to enhance neural network verifiers and made significant advances. However, GCP-CROWN currently relies on generic cutting planes (cuts) generated from external mixed…
Mappings to structured output spaces (strings, trees, partitions, etc.) are typically learned using extensions of classification algorithms to simple graphical structures (eg., linear chains) in which search and parameter estimation can be…
The selection of branching variables is a key component of branch-and-bound algorithms for solving Mixed-Integer Programming (MIP) problems since the quality of the selection procedure is likely to have a significant effect on the size of…
Benders decomposition (BD) is a widely used solution approach for solving two-stage stochastic programs arising in real-world decision-making under uncertainty. However, it often suffers from slow convergence as the master problem grows…