Related papers: Yay for Determinants!
This article deals with the analysis of high dimensional data that come from multiple sources (experiments) and thus have different possibly correlated responses, but share the same set of predictors. The measurements of the predictors may…
Given a malfunctioning system, sequential diagnosis aims at identifying the root cause of the failure in terms of abnormally behaving system components. As initial system observations usually do not suffice to deterministically pin down…
The adaptation to situations of sequential choice under uncertainty of decision criteria which deviate from (subjective) expected utility raises the problem of ensuring the selection of a nondominated strategy. In particular, when following…
Abductive explanations (AXp's) are widely used for understanding decisions of classifiers. Existing definitions are suitable when features are independent. However, we show that ignoring constraints when they exist between features may lead…
Humans currently use arguments for explaining choices which are already made, or for evaluating potential choices. Each potential choice has usually pros and cons of various strengths. In spite of the usefulness of arguments in a decision…
The analysis of decision making under uncertainty is closely related to the analysis of probabilistic inference. Indeed, much of the research into efficient methods for probabilistic inference in expert systems has been motivated by the…
We evaluate the determinant $\det_{1\leq i,j\leq n}(\binom{x+y+j}{x-i+2j}-\binom{x+y+j}{x+i+2j})$, which gives the number of lozenge tilings of a hexagon with cut off corners. A particularly interesting feature of this evaluation is that it…
We describe AI agents as stochastic dynamical systems and frame the problem of learning to reason as in transductive inference: Rather than approximating the distribution of past data as in classical induction, the objective is to capture…
In many real-life settings, agents must navigate dynamic environments while reasoning under incomplete information and acting on a corpus of unstable, context-dependent, and often conflicting norms. We introduce a general, non-modal,…
Interpretability and explainability are among the most important challenges of modern artificial intelligence, being mentioned even in various legislative sources. In this article, we develop a method for extracting immediately human…
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…
Scientists have long aimed to discover meaningful formulae which accurately describe experimental data. A common approach is to manually create mathematical models of natural phenomena using domain knowledge, and then fit these models to…
In this paper, we give a deterministic pushdown transducer and a normal sequence of digits compressed by it. This solves positively a question left open in a previous paper by V. Becher, P. A. Heiber and the first author.
Confounder selection is perhaps the most important step in the design of observational studies. A number of criteria, often with different objectives and approaches, have been proposed, and their validity and practical value have been…
Ren et al. recently introduced a method for aggregating multiple decision trees into a strong predictor by interpreting a path taken by a sample down each tree as a binary vector and performing linear regression on top of these vectors…
Previous work on English determiners has primarily concentrated on their semantics or scoping properties rather than their complex ordering behavior. The little work that has been done on determiner ordering generally splits determiners…
We introduce a new combinatorial structure: the superselector. We show that superselectors subsume several important combinatorial structures used in the past few years to solve problems in group testing, compressed sensing, multi-channel…
As artificial intelligence and machine learning tools become more accessible, and scientists face new obstacles to data collection (e.g. rising costs, declining survey response rates), researchers increasingly use predictions from…
In over-identified models, misspecification -- the norm rather than exception -- fundamentally changes what estimators estimate. Different estimators imply different estimands rather than different efficiency for the same target. A review…
Predictive modeling is invaded by elastic, yet complex methods such as neural networks or ensembles (model stacking, boosting or bagging). Such methods are usually described by a large number of parameters or hyper parameters - a price that…