Related papers: An Empirical Study of Rational Tree Unification fo…

Higher-order unification has been shown to be undecidable. Miller discovered the pattern fragment and subsequently showed that higher-order pattern unification is decidable and has most general unifiers. We extend the algorithm to…

We describe here a simple application of rational trees to the implementation of an interpreter for a procedural language written in a logic programming language. This is possible in languages designed to support rational trees (such as…

In this manuscript, we show that any neural network with any activation function can be represented as a decision tree. The representation is equivalence and not an approximation, thus keeping the accuracy of the neural network exactly as…

Search-optimization problems are plentiful in scientific and engineering domains. Artificial intelligence has long contributed to the development of search algorithms and declarative programming languages geared toward solving and modeling…

Decision trees, owing to their interpretability, are attractive as control policies for (dynamical) systems. Unfortunately, constructing, or synthesising, such policies is a challenging task. Previous approaches do so by imitating a…

Experts advising decision-makers are likely to display expertise which varies as a function of the problem instance. In practice, this may lead to sub-optimal or discriminatory decisions against minority cases. In this work we model such…

State-of-the-art clustering algorithms use heuristics to partition the feature space and provide little insight into the rationale for cluster membership, limiting their interpretability. In healthcare applications, the latter poses a…

Decision tree learning is increasingly being used for pointwise inference. Important applications include causal heterogenous treatment effects and dynamic policy decisions, as well as conditional quantile regression and design of…

Tree-structured recursive neural networks (TreeRNNs) for sentence meaning have been successful for many applications, but it remains an open question whether the fixed-length representations that they learn can support tasks as demanding as…

The kernel method is a potential approach to analyzing structured data such as sequences, trees, and graphs; however, unordered trees have not been investigated extensively. Kimura et al. (2011) proposed a kernel function for unordered…

The lack of mathematical tractability of Deep Neural Networks (DNNs) has hindered progress towards having a unified convergence analysis of training algorithms, in the general setting. We propose a unified optimization framework for…

It is well-known that freeness and linearity information positively interact with aliasing information, allowing both the precision and the efficiency of the sharing analysis of logic programs to be improved. In this paper we present a…

Despite widespread interest and practical use, the theoretical properties of random forests are still not well understood. In this paper we contribute to this understanding in two ways. We present a new theoretically tractable variant of…

Networks are ubiquitous in biology and computational approaches have been largely investigated for their inference. In particular, supervised machine learning methods can be used to complete a partially known network by integrating various…

Many kinds of data are naturally amenable to being treated as sequences. An example is text data, where a text may be seen as a sequence of words. Another example is clickstream data, where a data instance is a sequence of clicks made by a…

Regular synchronization languages can be used to define rational relations of finite words, and to characterize subclasses of rational relations, like automatic or recognizable relations. We provide a systematic study of the decidability of…

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…

We consider random binary trees that appear as the output of certain standard algorithms for sorting and searching if the input is random. We introduce the subtree size metric on search trees and show that the resulting metric spaces…

Lists, multisets, and sets are well-known data structures whose usefulness is widely recognized in various areas of Computer Science. These data structures have been analyzed from an axiomatic point of view with a parametric approach in (*)…

We consider the problem of globally minimizing the sum of many rational functions over a given compact semialgebraic set. The number of terms can be large (10 to 100), the degree of each term should be small (up to 10), and the number of…