Related papers: Decision list compression by mild random restricti…
As machine learning is increasingly used to help make decisions, there is a demand for these decisions to be explainable. Arguably, the most explainable machine learning models use decision rules. This paper focuses on decision sets, a type…
Given a DNF formula on n variables, the two natural size measures are the number of terms or size s(f), and the maximum width of a term w(f). It is folklore that short DNF formulas can be made narrow. We prove a converse, showing that…
We establish nearly tight bounds on the expected shrinkage of decision lists and DNF formulas under the $p$-random restriction $\mathbf R_p$ for all values of $p \in [0,1]$. For a function $f$ with domain $\{0,1\}^n$, let $\mathrm{DL}(f)$…
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…
A classifier is considered interpretable if each of its decisions has an explanation which is small enough to be easily understood by a human user. A DNF formula can be seen as a binary classifier $\kappa$ over boolean domains. The size of…
A falling rule list is a probabilistic decision list for binary classification, consisting of a series of if-then rules with antecedents in the if clauses and probabilities of the desired outcome ("1") in the then clauses. Just as in a…
Scenario decision making offers a flexible way of making decision in an uncertain environment while obtaining probabilistic guarantees on the risk of failure of the decision. The idea of this approach is to draw samples of the uncertainty…
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…
In many situations, the decision maker observes items in sequence and needs to determine whether or not to retain a particular item immediately after it is observed. Any decision rule creates a set of items that are selected. We consider…
Learning interpretable models has become a major focus of machine learning research, given the increasing prominence of machine learning in socially important decision-making. Among interpretable models, rule lists are among the best-known…
Systems of decision rules and decision trees are widely used as a means for knowledge representation, as classifiers, and as algorithms. They are among the most interpretable models for classifying and representing knowledge. The study of…
This paper presents a theory of skiplists of arbitrary height, and shows decidability of the satisfiability problem for quantifier-free formulas. A skiplist is an imperative software data structure that implements sets by maintaining…
In this paper we introduce a novel family of decision lists consisting of highly interpretable models which can be learned efficiently in a greedy manner. The defining property is that all rules are oriented in the same direction.…
We present an algorithm, NN2Rules, to convert a trained neural network into a rule list. Rule lists are more interpretable since they align better with the way humans make decisions. NN2Rules is a decompositional approach to rule…
A $c$-short program for a string $x$ is a description of $x$ of length at most $C(x) + c$, where $C(x)$ is the Kolmogorov complexity of $x$. We show that there exists a randomized algorithm that constructs a list of $n$ elements that…
A decision tree recursively splits a feature space $\mathbb{R}^{d}$ and then assigns class labels based on the resulting partition. Decision trees have been part of the basic machine-learning toolkit for decades. A large body of work treats…
The problem of selecting small groups of itemsets that represent the data well has recently gained a lot of attention. We approach the problem by searching for the itemsets that compress the data efficiently. As a compression technique we…
Random Forests are one of the most popular classifiers in machine learning. The larger they are, the more precise is the outcome of their predictions. However, this comes at a cost: their running time for classification grows linearly with…
Many researchers in artificial intelligence are beginning to explore the use of soft constraints to express a set of (possibly conflicting) problem requirements. A soft constraint is a function defined on a collection of variables which…
Large-scale supervised classification algorithms, especially those based on deep convolutional neural networks (DCNNs), require vast amounts of training data to achieve state-of-the-art performance. Decreasing this data requirement would…