No Free Lunch for Noise Prediction

No-free-lunch theorems have shown that learning algorithms cannot be universally good. We show that no free funch exists for noise prediction as well. We show that when the noise is additive and the prior over target functions is uniform, a prior on the noise distribution cannot be updated, in the Bayesian sense, from any finite data set. We emphasize the importance of a prior over the target function in order to justify superior performance for learning systems

Proofs Versus Experiments: Wittgensteinian Themes Surrounding the Four-Color Theorem

The Four-Colour Theorem (4CT) proof, presented to the mathematical community in a pair of papers by Appel and Haken in the late 1970's, provoked a series of philosophical debates. Many conceptual points of these disputes still require some elucidation. After a brief presentation of the main ideas of Appel and Haken’s procedure for the proof and a reconstruction of Thomas Tymoczko’s argument for the novelty of 4CT’s proof, we shall formulate some questions regarding the connections between the points raised by Tymoczko and some Wittgensteinian topics in the philosophy of mathematics such as the importance of the surveyability as a criterion for distinguishing mathematical proofs from empirical experiments. Our aim is to show that the “characteristic Wittgensteinian invention” (Mühlhölzer 2006) – the strong distinction between proofs and experiments – can shed some light in the conceptual confusions surrounding the Four-Colour Theorem

Benchmarking in cluster analysis: A white paper

To achieve scientific progress in terms of building a cumulative body of knowledge, careful attention to benchmarking is of the utmost importance. This means that proposals of new methods of data pre-processing, new data-analytic techniques, and new methods of output post-processing, should be extensively and carefully compared with existing alternatives, and that existing methods should be subjected to neutral comparison studies. To date, benchmarking and recommendations for benchmarking have been frequently seen in the context of supervised learning. Unfortunately, there has been a dearth of guidelines for benchmarking in an unsupervised setting, with the area of clustering as an important subdomain. To address this problem, discussion is given to the theoretical conceptual underpinnings of benchmarking in the field of cluster analysis by means of simulated as well as empirical data. Subsequently, the practicalities of how to address benchmarking questions in clustering are dealt with, and foundational recommendations are made

The Relations Between Pedagogical and Scientific Explanations of Algorithms: Case Studies from the French Administration

The opacity of some recent Machine Learning (ML) techniques have raised fundamental questions on their explainability, and created a whole domain dedicated to Explainable Artificial Intelligence (XAI). However, most of the literature has been dedicated to explainability as a scientific problem dealt with typical methods of computer science, from statistics to UX. In this paper, we focus on explainability as a pedagogical problem emerging from the interaction between lay users and complex technological systems. We defend an empirical methodology based on field work, which should go beyond the in-vitro analysis of UX to examine in-vivo problems emerging in the field. Our methodology is also comparative, as it chooses to steer away from the almost exclusive focus on ML to compare its challenges with those faced by more vintage algorithms. Finally, it is also philosophical, as we defend the relevance of the philosophical literature to define the epistemic desiderata of a good explanation. This study was conducted in collaboration with Etalab, a Task Force of the French Prime Minister in charge of Open Data & Open Government Policies, dealing in particular with the enforcement of the right to an explanation. In order to illustrate and refine our methodology before going up to scale, we conduct a preliminary work of case studies on the main different types of algorithms used by the French administration: computation, matching algorithms and ML. We study the merits and drawbacks of a recent approach to explanation, which we baptize input-output black box reasoning or BBR for short. We begin by presenting a conceptual framework including the distinctions necessary to a study of pedagogical explainability. We proceed to algorithmic case studies, and draw model-specific and model-agnostic lessons and conjectures

CHARDA: Causal Hybrid Automata Recovery via Dynamic Analysis

We propose and evaluate a new technique for learning hybrid automata automatically by observing the runtime behavior of a dynamical system. Working from a sequence of continuous state values and predicates about the environment, CHARDA recovers the distinct dynamic modes, learns a model for each mode from a given set of templates, and postulates causal guard conditions which trigger transitions between modes. Our main contribution is the use of information-theoretic measures (1)~as a cost function for data segmentation and model selection to penalize over-fitting and (2)~to determine the likely causes of each transition. CHARDA is easily extended with different classes of model templates, fitting methods, or predicates. In our experiments on a complex videogame character, CHARDA successfully discovers a reasonable over-approximation of the character's true behaviors. Our results also compare favorably against recent work in automatically learning probabilistic timed automata in an aircraft domain: CHARDA exactly learns the modes of these simpler automata.Comment: 7 pages, 2 figures. Accepted for IJCAI 201