to

### Learning Optimal Decision Sets and Lists with SAT

Decision sets and decision lists are two of the most easily explainable machine learning models. Given the renewed emphasis on explainable machine learning decisions, both of these machine learning models are becoming increasingly attractive, as they combine small size and clear explainability. In this paper, we define size as the total number of literals in the SAT encoding of these rule-based models as opposed to earlier work that concentrates on the number of rules. In this paper, we develop approaches to computing minimum-size "perfect" decision sets and decision lists, which are perfectly accurate on the training data, and minimal in size, making use of modern SAT solving technology. We also provide a new method for determining optimal sparse alternatives, which trade off size and accuracy. The experiments in this paper demonstrate that the optimal decision sets computed by the SAT-based approach are comparable with the best heuristic methods, but much more succinct, and thus, more explainable. We contrast the size and test accuracy of optimal decisions lists versus optimal decision sets, as well as other state-of-the-art methods for determining optimal decision lists. Finally, we examine the size of average explanations generated by decision sets and decision lists.

### Why do Decision Trees Work?

Decision trees are a type of recursive partitioning algorithm. Decision trees are built up of two types of nodes: decision nodes, and leaves. The decision tree starts with a node called the root. If the root is a leaf then the decision tree is trivial or degenerate and the same classification is made for all data. For decision nodes we examine a single variable and move to another node based on the outcome of a comparison.

### Provably robust boosted decision stumps and trees against adversarial attacks

The problem of adversarial robustness has been studied extensively for neural networks. However, for boosted decision trees and decision stumps there are almost no results, even though they are widely used in practice (e.g. We show in this paper that for boosted decision stumps the \textit{exact} min-max robust loss and test error for an $l_\infty$-attack can be computed in $O(T\log T)$ time per input, where $T$ is the number of decision stumps and the optimal update step of the ensemble can be done in $O(n 2\,T\log T)$, where $n$ is the number of data points. Moreover, the robust test error rates we achieve are competitive to the ones of provably robust convolutional networks. Papers published at the Neural Information Processing Systems Conference.

### Optimal Decision Lists using SAT

Decision lists are one of the most easily explainable machine learning models. Given the renewed emphasis on explainable machine learning decisions, this machine learning model is increasingly attractive, combining small size and clear explainability. In this paper, we show for the first time how to construct optimal "perfect" decision lists which are perfectly accurate on the training data, and minimal in size, making use of modern SAT solving technology. We also give a new method for determining optimal sparse decision lists, which trade off size and accuracy. We contrast the size and test accuracy of optimal decisions lists versus optimal decision sets, as well as other state-of-the-art methods for determining optimal decision lists. We also examine the size of average explanations generated by decision sets and decision lists.

### Getting Started with Decision Trees

Decision Tree algorithm is one of the most powerful algorithms in machine learning and data science. Decision Tree algorithm is one of the most powerful algorithms in machine learning and data science. It is very commonly used by data scientists and machine learning engineers to solve business problem and explain that to your customers easily.