Private Learning Implies Online Learning: An Efficient Reduction

We study the relationship between the notions of differentially private learning and online learning in games. Several recent works have shown that differentially private learning implies online learning, but an open problem of Neel, Roth, and Wu \cite{NeelAaronRoth2018} asks whether this implication is {\it efficient}. Specifically, does an efficient differentially private learner imply an efficient online learner? In this paper we resolve this open question in the context of pure differential privacy. We derive an efficient black-box reduction from differentially private learning to online learning from expert advice

Integrity Constraints Revisited: From Exact to Approximate Implication

Integrity constraints such as functional dependencies (FD), and multi-valued dependencies (MVD) are fundamental in database schema design. Likewise, probabilistic conditional independences (CI) are crucial for reasoning about multivariate probability distributions. The implication problem studies whether a set of constraints (antecedents) implies another constraint (consequent), and has been investigated in both the database and the AI literature, under the assumption that all constraints hold exactly. However, many applications today consider constraints that hold only approximately. In this paper we define an approximate implication as a linear inequality between the degree of satisfaction of the antecedents and consequent, and we study the relaxation problem: when does an exact implication relax to an approximate implication? We use information theory to define the degree of satisfaction, and prove several results. First, we show that any implication from a set of data dependencies (MVDs+FDs) can be relaxed to a simple linear inequality with a factor at most quadratic in the number of variables; when the consequent is an FD, the factor can be reduced to 1. Second, we prove that there exists an implication between CIs that does not admit any relaxation; however, we prove that every implication between CIs relaxes "in the limit". Finally, we show that the implication problem for differential constraints in market basket analysis also admits a relaxation with a factor equal to 1. Our results recover, and sometimes extend, several previously known results about the implication problem: implication of MVDs can be checked by considering only 2-tuple relations, and the implication of differential constraints for frequent item sets can be checked by considering only databases containing a single transaction

TRACE: A Time-Relational Approximate Cubing Engine for Fast Data Insights

A large class of data questions can be modeled as identifying important slices of data driven by user defined metrics. This paper presents TRACE, a Time-Relational Approximate Cubing Engine that enables interactive analysis on such slices with a low upfront cost - both in space and computation. It does this by materializing the most important parts of the cube over time enabling interactive querying for a large class of analytical queries e.g. what part of my business has the highest revenue growth ([SubCategory=Sports Equipment, Gender=Female]), what slices are lagging in revenue per user ([State=CA, Age=20-30]). Many user defined metrics are supported including common aggregations such as SUM, COUNT, DISTINCT COUNT and more complex ones such as AVERAGE. We implemented and deployed TRACE for a variety of business use cases

Integrity Constraints Revisited: From Exact to Approximate Implication

Integrity constraints such as functional dependencies (FD), and multi-valued dependencies (MVD) are fundamental in database schema design. Likewise, probabilistic conditional independences (CI) are crucial for reasoning about multivariate probability distributions. The implication problem studies whether a set of constraints (antecedents) implies another constraint (consequent), and has been investigated in both the database and the AI literature, under the assumption that all constraints hold exactly. However, many applications today consider constraints that hold only approximately. In this paper we define an approximate implication as a linear inequality between the degree of satisfaction of the antecedents and consequent, and we study the relaxation problem: when does an exact implication relax to an approximate implication? We use information theory to define the degree of satisfaction, and prove several results. First, we show that any implication from a set of data dependencies (MVDs+FDs) can be relaxed to a simple linear inequality with a factor at most quadratic in the number of variables; when the consequent is an FD, the factor can be reduced to 1. Second, we prove that there exists an implication between CIs that does not admit any relaxation; however, we prove that every implication between CIs relaxes "in the limit". Finally, we show that the implication problem for differential constraints in market basket analysis also admits a relaxation with a factor equal to 1. Our results recover, and sometimes extend, several previously known results about the implication problem: implication of MVDs can be checked by considering only 2-tuple relations, and the implication of differential constraints for frequent item sets can be checked by considering only databases containing a single transaction

Automated Detection of Serializability Violations Under Weak Consistency

While a number of weak consistency mechanisms have been developed in recent years to improve performance and ensure availability in distributed, replicated systems, ensuring the correctness of transactional applications running on top of such systems remains a difficult and important problem. Serializability is a well-understood correctness criterion for transactional programs; understanding whether applications are serializable when executed in a weakly-consistent environment, however remains a challenging exercise. In this work, we combine a dependency graph-based characterization of serializability and leverage the framework of abstract executions to develop a fully-automated approach for statically finding bounded serializability violations under any weak consistency model. We reduce the problem of serializability to satisfiability of a formula in First-Order Logic (FOL), which allows us to harness the power of existing SMT solvers. We provide rules to automatically construct the FOL encoding from programs written in SQL (allowing loops and conditionals) and express consistency specifications as FOL formula. In addition to detecting bounded serializability violations, we also provide two orthogonal schemes to reason about unbounded executions by providing sufficient conditions (again, in the form of FOL formulae) whose satisfiability implies the absence of anomalies in any arbitrary execution. We have applied the proposed technique on TPC-C, a real-world database program with complex application logic, and were able to discover anomalies under Parallel Snapshot Isolation (PSI), and verify serializability for unbounded executions under Snapshot Isolation (SI), two consistency mechanisms substantially weaker than serializability

Gestion des données distribuées avec le langage de règles Webdamlog

Notre but est de permettre à un utilisateur du Web d organiser la gestionde ses données distribuées en place, c est à dire sans l obliger à centraliserses données chez un unique hôte. Par conséquent, notre système diffèrede Facebook et des autres systèmes centralisés, et propose une alternativepermettant aux utilisateurs de lancer leurs propres pairs sur leurs machinesgérant localement leurs données personnelles et collaborant éventuellementavec des services Web externes.Dans ma thèse, je présente Webdamlog, un langage dérivé de datalogpour la gestion de données et de connaissances distribuées. Le langage étenddatalog de plusieurs manières, principalement avec une nouvelle propriété ladélégation, autorisant les pairs à échanger non seulement des faits (les données)mais aussi des règles (la connaissance). J ai ensuite mené une étude utilisateurpour démontrer l utilisation du langage. Enfin je décris le moteur d évaluationde Webdamlog qui étend un moteur d évaluation de datalog distribué nomméBud, en ajoutant le support de la délégation et d autres innovations tellesque la possibilité d avoir des variables pour les noms de pairs et des relations.J aborde de nouvelles techniques d optimisation, notamment basées sur laprovenance des faits et des règles. Je présente des expérimentations quidémontrent que le coût du support des nouvelles propriétés de Webdamlogreste raisonnable même pour de gros volumes de données. Finalement, jeprésente l implémentation d un pair Webdamlog qui fournit l environnementpour le moteur. En particulier, certains adaptateurs permettant aux pairsWebdamlog d échanger des données avec d autres pairs sur Internet. Pourillustrer l utilisation de ces pairs, j ai implémenté une application de partagede photos dans un réseau social en Webdamlog.Our goal is to enable aWeb user to easily specify distributed data managementtasks in place, i.e. without centralizing the data to a single provider. Oursystem is therefore not a replacement for Facebook, or any centralized system,but an alternative that allows users to launch their own peers on their machinesprocessing their own local personal data, and possibly collaborating with Webservices.We introduce Webdamlog, a datalog-style language for managing distributeddata and knowledge. The language extends datalog in a numberof ways, notably with a novel feature, namely delegation, allowing peersto exchange not only facts but also rules. We present a user study thatdemonstrates the usability of the language. We describe a Webdamlog enginethat extends a distributed datalog engine, namely Bud, with the supportof delegation and of a number of other novelties of Webdamlog such as thepossibility to have variables denoting peers or relations. We mention noveloptimization techniques, notably one based on the provenance of facts andrules. We exhibit experiments that demonstrate that the rich features ofWebdamlog can be supported at reasonable cost and that the engine scales tolarge volumes of data. Finally, we discuss the implementation of a Webdamlogpeer system that provides an environment for the engine. In particular, a peersupports wrappers to exchange Webdamlog data with non-Webdamlog peers.We illustrate these peers by presenting a picture management applicationthat we used for demonstration purposes.PARIS11-SCD-Bib. électronique (914719901) / SudocSudocFranceF

On algorithms for large-scale graph and clustering problems

Gegenstand dieser Arbeit sind algorithmische Methoden der modernen Datenanalyse. Dabei werden vorwiegend zwei übergeordnete Themen behandelt: Datenstromalgorithmen mit Kompressionseigenschaften und Approximationsalgorithmen für Clusteringverfahren. Datenstromalgorithmen verarbeiten einen Datensatz sequentiell und haben das Ziel, Eigenschaften des Datensatzes (approximativ) zu bestimmen, ohne dabei den gesamten Datensatz abzuspeichern. Unter Clustering versteht man die Partitionierung eines Datensatzes in verschiedene Gruppen. Das erste dargestellte Problem betrifft Matching in Graphen. Hier besteht der Datensatz aus einer Folge von Einfüge- und Löschoperationen von Kanten. Die Aufgabe besteht darin, die Größe des so genannten Maximum Matchings so genau wie möglich zu bestimmen. Es wird ein Algorithmus vorgestellt, der, unter der Annahme, dass das Matching höchstens die Größe k hat, die exakte Größe bestimmt und dabei k² Speichereinheiten benötigt. Dieser Algorithmus lässt sich weiterhin verwenden um eine konstante Approximation der Matchinggröße in planaren Graphen zu bestimmen. Des Weiteren werden untere Schranken für den benötigten Speicherplatz bestimmt und eine Reduktion von gewichtetem Matching zu ungewichteten Matching durchgeführt. Anschließend werden Datenstromalgorithmen für die Nachbarschaftssuche betrachtet, wobei die Aufgabe darin besteht, für n gegebene Mengen die Paare mit hoher Ähnlichkeit in nahezu Linearzeit zu finden. Dabei ist der Jaccard Index |A ∩ B|/|A U B| das Ähnlichkeitsmaß für zwei Mengen A und B. In der Arbeit wird eine Datenstruktur beschrieben, die dies erstmalig in dynamischen Datenströmen mit geringem Speicherplatzverbrauch leistet. Dabei werden Zufallszahlen mit nur 2-facher Unabhängigkeit verwendet, was eine sehr effiziente Implementierung ermöglicht. Das dritte Problem befindet sich an der Schnittstelle zwischen den beiden Themen dieser Arbeit und betrifft das k-center Clustering Problem in Datenströmen mit einem Zeitfenster. Die Aufgabe besteht darin k Zentren zu finden, sodass die maximale Distanz unter allen Punkten zu dem jeweils nächsten Zentrum minimiert wird. Ergebnis sind ein 6-Approximationalgorithmus für ein beliebiges k und ein optimaler 4-Approximationsalgorithmus für k = 2. Die entwickelten Techniken lassen sich ebenfalls auf das Durchmesserproblem anwenden und ermöglichen für dieses Problem einen optimalen Algorithmus. Danach werden Clusteringprobleme bezüglich der Jaccard Distanz analysiert. Dabei sind wieder eine Menge N von Teilmengen aus einer Grundgesamtheit U sind und die Aufgabe besteht darin eine Teilmenge $C$ zu finden, die max 1-|X ∩ C|/|X U C| minimiert. Es wird gezeigt, dass zwar eine exakte Lösung des Problems NP-schwer ist, es aber gleichzeitig eine PTAS gibt. Abschließend wird die weit verbreitete lokale Suchheuristik für k-median und k-means Clustering untersucht. Obwohl es im Allgemeinen schwer ist, diese Probleme exakt oder auch nur approximativ zu lösen, gelten sie in der Praxis als relativ gut handhabbar, was andeutet, dass die Härteresultate auf pathologischen Eingaben beruhen. Auf Grund dieser Diskrepanz gab es in der Vergangenheit praxisrelevante Datensätze zu charakterisieren. Für drei der wichtigsten Charakterisierungen wird das Verhalten einer lokalen Suchheuristik untersucht mit dem Ergebnis, dass die lokale Suchheuristik in diesen Fällen optimale oder fast optimale Cluster ermittelt