Generalized Majority-Minority Operations are Tractable

Generalized majority-minority (GMM) operations are introduced as a common generalization of near unanimity operations and Mal'tsev operations on finite sets. We show that every instance of the constraint satisfaction problem (CSP), where all constraint relations are invariant under a (fixed) GMM operation, is solvable in polynomial time. This constitutes one of the largest tractable cases of the CSP

: Méthodes d'Inférence Symbolique pour les Bases de Données

This dissertation is a summary of a line of research, that I wasactively involved in, on learning in databases from examples. Thisresearch focused on traditional as well as novel database models andlanguages for querying, transforming, and describing the schema of adatabase. In case of schemas our contributions involve proposing anoriginal languages for the emerging data models of Unordered XML andRDF. We have studied learning from examples of schemas for UnorderedXML, schemas for RDF, twig queries for XML, join queries forrelational databases, and XML transformations defined with a novelmodel of tree-to-word transducers.Investigating learnability of the proposed languages required us toexamine closely a number of their fundamental properties, often ofindependent interest, including normal forms, minimization,containment and equivalence, consistency of a set of examples, andfinite characterizability. Good understanding of these propertiesallowed us to devise learning algorithms that explore a possibly largesearch space with the help of a diligently designed set ofgeneralization operations in search of an appropriate solution.Learning (or inference) is a problem that has two parameters: theprecise class of languages we wish to infer and the type of input thatthe user can provide. We focused on the setting where the user inputconsists of positive examples i.e., elements that belong to the goallanguage, and negative examples i.e., elements that do not belong tothe goal language. In general using both negative and positiveexamples allows to learn richer classes of goal languages than usingpositive examples alone. However, using negative examples is oftendifficult because together with positive examples they may cause thesearch space to take a very complex shape and its exploration may turnout to be computationally challenging.Ce mémoire est une courte présentation d’une direction de recherche, à laquelle j’ai activementparticipé, sur l’apprentissage pour les bases de données à partir d’exemples. Cette recherches’est concentrée sur les modèles et les langages, aussi bien traditionnels qu’émergents, pourl’interrogation, la transformation et la description du schéma d’une base de données. Concernantles schémas, nos contributions consistent en plusieurs langages de schémas pour les nouveaumodèles de bases de données que sont XML non-ordonné et RDF. Nous avons ainsi étudiél’apprentissage à partir d’exemples des schémas pour XML non-ordonné, des schémas pour RDF,des requêtes twig pour XML, les requêtes de jointure pour bases de données relationnelles et lestransformations XML définies par un nouveau modèle de transducteurs arbre-à-mot.Pour explorer si les langages proposés peuvent être appris, nous avons été obligés d’examinerde près un certain nombre de leurs propriétés fondamentales, souvent souvent intéressantespar elles-mêmes, y compris les formes normales, la minimisation, l’inclusion et l’équivalence, lacohérence d’un ensemble d’exemples et la caractérisation finie. Une bonne compréhension de cespropriétés nous a permis de concevoir des algorithmes d’apprentissage qui explorent un espace derecherche potentiellement très vaste grâce à un ensemble d’opérations de généralisation adapté àla recherche d’une solution appropriée.L’apprentissage (ou l’inférence) est un problème à deux paramètres : la classe précise delangage que nous souhaitons inférer et le type d’informations que l’utilisateur peut fournir. Nousnous sommes placés dans le cas où l’utilisateur fournit des exemples positifs, c’est-à-dire deséléments qui appartiennent au langage cible, ainsi que des exemples négatifs, c’est-à-dire qui n’enfont pas partie. En général l’utilisation à la fois d’exemples positifs et négatifs permet d’apprendredes classes de langages plus riches que l’utilisation uniquement d’exemples positifs. Toutefois,l’utilisation des exemples négatifs est souvent difficile parce que les exemples positifs et négatifspeuvent rendre la forme de l’espace de recherche très complexe, et par conséquent, son explorationinfaisable

Substitutional quantification and set theory

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/43184/1/10992_2004_Article_BF00258434.pd

An update on statistical boosting in biomedicine

Statistical boosting algorithms have triggered a lot of research during the last decade. They combine a powerful machine-learning approach with classical statistical modelling, offering various practical advantages like automated variable selection and implicit regularization of effect estimates. They are extremely flexible, as the underlying base-learners (regression functions defining the type of effect for the explanatory variables) can be combined with any kind of loss function (target function to be optimized, defining the type of regression setting). In this review article, we highlight the most recent methodological developments on statistical boosting regarding variable selection, functional regression and advanced time-to-event modelling. Additionally, we provide a short overview on relevant applications of statistical boosting in biomedicine

The subpower membership problem of 2-nilpotent algebras

The subpower membership problem SMP(A) of a finite algebraic structure A asks whether a given partial function from A^k to A can be interpolated by a term operation of A, or not. While this problem can be EXPTIME-complete in general, Willard asked whether it is always solvable in polynomial time if A is a Mal'tsev algebras. In particular, this includes many important structures studied in abstract algebra, such as groups, quasigroups, rings, Boolean algebras. In this paper we give an affirmative answer to Willard's question for a big class of 2-nilpotent Mal'tsev algebras. We furthermore develop tools that might be essential in answering the question for general nilpotent Mal'tsev algebras in the future.Comment: 17 pages (including appendix

Controlling Rayleigh-B\'enard convection via Reinforcement Learning

Thermal convection is ubiquitous in nature as well as in many industrial applications. The identification of effective control strategies to, e.g., suppress or enhance the convective heat exchange under fixed external thermal gradients is an outstanding fundamental and technological issue. In this work, we explore a novel approach, based on a state-of-the-art Reinforcement Learning (RL) algorithm, which is capable of significantly reducing the heat transport in a two-dimensional Rayleigh-B\'enard system by applying small temperature fluctuations to the lower boundary of the system. By using numerical simulations, we show that our RL-based control is able to stabilize the conductive regime and bring the onset of convection up to a Rayleigh number $Ra_c \approx 3 \cdot 10^4$, whereas in the uncontrolled case it holds $Ra_{c}=1708$. Additionally, for $Ra > 3 \cdot 10^4$, our approach outperforms other state-of-the-art control algorithms reducing the heat flux by a factor of about $2.5$. In the last part of the manuscript, we address theoretical limits connected to controlling an unstable and chaotic dynamics as the one considered here. We show that controllability is hindered by observability and/or capabilities of actuating actions, which can be quantified in terms of characteristic time delays. When these delays become comparable with the Lyapunov time of the system, control becomes impossible.Comment: 24 pages, 10 figure

Algorithms and Lower Bounds in Circuit Complexity

Computational complexity theory aims to understand what problems can be efficiently solved by computation. This thesis studies computational complexity in the model of Boolean circuits. Boolean circuits provide a basic mathematical model for computation and play a central role in complexity theory, with important applications in separations of complexity classes, algorithm design, and pseudorandom constructions. In this thesis, we investigate various types of circuit models such as threshold circuits, Boolean formulas, and their extensions, focusing on obtaining complexity-theoretic lower bounds and algorithmic upper bounds for these circuits. (1) Algorithms and lower bounds for generalized threshold circuits: We extend the study of linear threshold circuits, circuits with gates computing linear threshold functions, to the more powerful model of polynomial threshold circuits where the gates can compute polynomial threshold functions. We obtain hardness and meta-algorithmic results for this circuit model, including strong average-case lower bounds, satisfiability algorithms, and derandomization algorithms for constant-depth polynomial threshold circuits with super-linear wire complexity. (2) Algorithms and lower bounds for enhanced formulas: We investigate the model of Boolean formulas whose leaf gates can compute complex functions. In particular, we study De Morgan formulas whose leaf gates are functions with "low communication complexity". Such gates can capture a broad class of functions including symmetric functions and polynomial threshold functions. We obtain new and improved results in terms of lower bounds and meta-algorithms (satisfiability, derandomization, and learning) for such enhanced formulas. (3) Circuit lower bounds for MCSP: We study circuit lower bounds for the Minimum Circuit Size Problem (MCSP), the fundamental problem of deciding whether a given function (in the form of a truth table) can be computed by small circuits. We get new and improved lower bounds for MCSP that nearly match the best-known lower bounds against several well-studied circuit models such as Boolean formulas and constant-depth circuits