Missing values estimation for skylines in incomplete database

Incompleteness of data is a common problem in many databases including web heterogeneous databases, multi-relational databases, spatial and temporal databases and data integration. The incompleteness of data introduces challenges in processing queries as providing accurate results that best meet the query conditions over incomplete database is not a trivial task. Several techniques have been proposed to process queries in incomplete database. Some of these techniques retrieve the query results based on the existing values rather than estimating the missing values. Such techniques are undesirable in many cases as the dimensions with missing values might be the important dimensions of the user’s query. Besides, the output is incomplete and might not satisfy the user preferences. In this paper we propose an approach that estimates missing values in skylines to guide users in selecting the most appropriate skylines from the several candidate skylines. The approach utilizes the concept of mining attribute correlations to generate an Approximate Functional Dependencies (AFDs) that captured the relationships between the dimensions. Besides, identifying the strength of probability correlations to estimate the values. Then, the skylines with estimated values are ranked. By doing so, we ensure that the retrieved skylines are in the order of their estimated precision

Finding Minimal Cost Herbrand Models with Branch-Cut-and-Price

Given (1) a set of clauses $T$ in some first-order language $\cal L$ and (2) a cost function $c : B_{{\cal L}} \rightarrow \mathbb{R}_{+}$, mapping each ground atom in the Herbrand base $B_{{\cal L}}$ to a non-negative real, then the problem of finding a minimal cost Herbrand model is to either find a Herbrand model $\cal I$ of $T$ which is guaranteed to minimise the sum of the costs of true ground atoms, or establish that there is no Herbrand model for $T$. A branch-cut-and-price integer programming (IP) approach to solving this problem is presented. Since the number of ground instantiations of clauses and the size of the Herbrand base are both infinite in general, we add the corresponding IP constraints and IP variables `on the fly' via `cutting' and `pricing' respectively. In the special case of a finite Herbrand base we show that adding all IP variables and constraints from the outset can be advantageous, showing that a challenging Markov logic network MAP problem can be solved in this way if encoded appropriately

Spatio-temporal random fields: Compressible representation and distributed estimation.

Abstract Modern sensing technology allows us enhanced monitoring of dynamic activities in business, traffic, and home, just to name a few. The increasing amount of sensor measurements, however, brings us the challenge for efficient data analysis. This is especially true when sensing targets can interoperate -in such cases we need learning models that can capture the relations of sensors, possibly without collecting or exchanging all data. Generative graphical models namely the Markov random fields (MRFs) fit this purpose, which can represent complex spatial and temporal relations among sensors, producing interpretable answers in terms of probability. The only drawback will be the cost for inference, storing and optimizing a very large number of parameters -not uncommon when we apply them for real-world applications. In this paper, we investigate how we can make discrete probabilistic graphical models practical for predicting sensor states in a spatio-temporal setting. A set of new ideas allows keeping the advantages of such models while achieving scalability. We first introduce a novel alternative to represent model parameters, which enables us to compress the parameter storage by removing uninformative parameters in a systematic way. For finding the best parameters via maximal likelihood estimation, we provide a separable optimization algorithm that can be performed independently in parallel in each graph node. We illustrate that the prediction quality of our suggested methods is comparable to those of the standard MRFs and a spatio-temporal knearest neighbor method, while using much less computational resources

Evaluation of ILP-based approaches for partitioning into colorful components

The NP-hard Colorful Components problem is a graph partitioning problem on vertex-colored graphs. We identify a new application of Colorful Components in the correction of Wikipedia interlanguage links, and describe and compare three exact and two heuristic approaches. In particular, we devise two ILP formulations, one based on Hitting Set and one based on Clique Partition. Furthermore, we use the recently proposed implicit hitting set framework [Karp, JCSS 2011; Chandrasekaran et al., SODA 2011] to solve Colorful Components. Finally, we study a move-based and a merge-based heuristic for Colorful Components. We can optimally solve Colorful Components for Wikipedia link correction data; while the Clique Partition-based ILP outperforms the other two exact approaches, the implicit hitting set is a simple and competitive alternative. The merge-based heuristic is very accurate and outperforms the move-based one. The above results for Wikipedia data are confirmed by experiments with synthetic instances

Deep Data Locality on Apache Hadoop

The amount of data being collected in various areas such as social media, network, scientific instrument, mobile devices, and sensors is growing continuously, and the technology to process them is also advancing rapidly. One of the fundamental technologies to process big data is Apache Hadoop that has been adopted by many commercial products, such as InfoSphere by IBM, or Spark by Cloudera. MapReduce on Hadoop has been widely used in many data science applications. As a dominant big data processing platform, the performance of MapReduce on Hadoop system has a significant impact on the big data processing capability across multiple industries. Most of the research for improving the speed of big data analysis has been on Hadoop modules such as Hadoop common, Hadoop Distribute File System (HDFS), Hadoop Yet Another Resource Negotiator (YARN) and Hadoop MapReduce. In this research, we focused on data locality on HDFS to improve the performance of MapReduce. To reduce the amount of data transfer, MapReduce has been utilizing data locality. However, even though the majority of the processing cost occurs in the later stages, data locality has been utilized only in the early stages, which we call Shallow Data Locality (SDL). As a result, the benefit of data locality has not been fully realized. We have explored a new concept called Deep Data Locality (DDL) where the data is pre-arranged to maximize the locality in the later stages. Specifically, we introduce two implementation methods of the DDL, i.e., block-based DDL and key-based DDL. In block-based DDL, the data blocks are pre-arranged to reduce the block copying time in two ways. First the RLM blocks are eliminated. Under the conventional default block placement policy (DBPP), data blocks are randomly placed on any available slave nodes, requiring a copy of RLM (Rack-Local Map) blocks. In block-based DDL, blocks are placed to avoid RLMs to reduce the block copy time. Second, block-based DDL concentrates the blocks in a smaller number of nodes and reduces the data transfer time among them. We analyzed the block distribution status with the customer review data from TripAdvisor and measured the performances with Terasort Benchmark. Our test result shows that the execution times of Map and Shuffle have been improved by up to 25% and 31% respectively. In key-based DDL, the input data is divided into several blocks and stored in HDFS before going into the Map stage. In comparison with conventional blocks that have random keys, our blocks have a unique key. This requires a pre-sorting of the key-value pairs, which can be done during ETL process. This eliminates some data movements in map, shuffle, and reduce stages, and thereby improves the performance. In our experiments, MapReduce with key-based DDL performed 21.9% faster than default MapReduce and 13.3% faster than MapReduce with block-based DDL. Additionally, key-based DDL can be combined with other methods to further improve the performance. When key-based DDL and block-based DDL are combined, the Hadoop performance went up by 34.4%. In this research, we developed the MapReduce workflow models with a novel computational model. We developed a numerical simulator that integrates the computational models. The model faithfully predicts the Hadoop performance under various conditions

Privacy-preserving Platforms for Computation on Hybrid Clouds

Ph.DDOCTOR OF PHILOSOPH

The Graph Pattern Matching Problem through Parameterized Matching

We propose a new approach to solve graph isomorphism using parameterized matching. Parameterized matching is a string matching problem where two strings parameterized-match if there exists a bijective function, on the symbols of the alphabet, that maps one of the strings into the other. Given that parameterized matching is defined for linear structures, we define the concept of graph linearization to represent the topology of a graph as a walk on it. Then, our approach to determine whether two graphs are isomorphic consists of determining whether there exists a walk in one of the graphs that parameterized-matches a linearization of the other graph. Our solution has two main steps: linearization and matching. We develop an efficient linearization algorithm, that generates short linearizations with an approximation guarantee, and develop a graph matching algorithm. We show that this solution also works for subgraph isomorphism, which is the problem of determining whether an input graph H is isomorphic to a subgraph of another input graph G. We evaluate our approach experimentally on graphs of different types and sizes, and compare to the performance of VF2, which is a prominent algorithm for graph isomorphism. Our empirical measurements show that graph linearization finds a matching graph faster than VF2 in many cases, especially in Miyazaki-constructed graphs which are known to be one of the hardest cases for graph isomorphism algorithms. We extend this approach to query attributed graphs. An attributed graph is a graph data structure, in which nodes and edges may have identifiers, types and other attributes. Attributed graphs are used in many application domains, for example to model social networks in which nodes represent people, photos, and postings and edges represent friendship, person-tagged-in-photo and mentioned-in-post relationships. Queries are used to extract information from such graphs. Several graph queries are expressed as graph pattern matching, which is the problem of finding all instances of pattern match query P in a larger attributed graph G. A pattern match query may specify both a graph structure and predicates on the attributes of the graph elements. Clearly, this problem is associated to subgraph isomorphism. Furthermore, we define a more general class of graph queries called generalized pattern queries on attributed multigraphs. The goal of this class is to find paths and subgraphs that satisfy query reachability and predicates. The query language is expressive: It allows (i) using regular expression operators (e.g., Kleene star and union); (ii) specifying structural predicates on graph nodes and edges; and (iii) using attribute predicates on nodes and edges. Pattern match queries, reachability queries, their combination, and even more queries can be expressed through generalized pattern queries. We use our approach to solve this new type of queries. The proposed technique has two phases. First, the query is linearized, i.e., represented as a graph walk that covers all nodes and edges. There are several linearizations for a given query; we derive heuristics to produce a good linearization that is short and places selective predicates early in the linearization. Second, we search for a bijective function that maps each element of the query to an element of the attributed multigraph that satisfies the reachability requirements and the predicates. Specifically, we develop an algorithm that matches the linearization by traversing the attributed graph in a manner similar to a breadth first traversal constrained by the linearization. We evaluate our solution experimentally using a real graph (the DBLP citation network) to assess its practicality and efficiency. Our results show that our techniques and optimizations are effective in querying attributed graphs, offering several factors of reduction in query response time when graph statistics are utilized.Resumen. En esta tesis se propone un nuevo enfoque de solución para resolver el problema de isomorfismo de grafos usando búsqueda parametrizada. La búsqueda parametrizada es un problema de búsqueda de cadenas de texto en el cual dos cadenas coinciden si existe una biyección que mapee los símbolos de una cadena en los símbolos de la otra. Dado que la búsqueda parametrizada está definida para estructuras lineales, se define el concepto de linearización de grafos para representar la topología de un grafo como un camino sobre este. Entonces, la solución para determinar si dos grafos son isomorfos consiste en determinar si existe un camino en uno de los grafos que haga coincidencia parametrizada con la linearización del otro grafo. La solución propuesta tiene dos pasos: linearización y búsqueda. Se presenta un algoritmo eficiente que genera linearizaciones aproximadamente óptimas en longitud, y un algoritmo de búsqueda. Se demuestra que esta solución también resuelve el problema de isomorfismo de subgrafos, en el cual se determina si un grafo H es isomorfo a un subgrafo de otro grafo G. Se evaluó experimentalmente la solución con grafos de diferentes tipos y tamaños. Se comparó su desempeño con el de VF2, el cual es un algoritmo competitivo de isomorfismo de grafos. Los resultados experimentales muestran que la solución propuesta es más eficiente que VF2 en varios casos, en especial en grafos Miyazaki, los cuales se caracterizan por constituir uno de los casos más difíciles para los algoritmos de isomorfismo de grafos. Este enfoque de solución se extiende para resolver consultas sobre grafos semánticos. Un grafo semántico es un grafo en el cual los nodes y arcos pueden tener identificadores, tipos y otros atributos. Estos grafos tienen aplicaciones importantes en diversas áreas, como por ejemplo para modelar redes sociales en las que los nodos representan personas, fotos y publicaciones y los arcos representan relaciones de amistad, etiquetado y mención. Se usan consultas para extraer información de estos grafos. Varias de estas consultas se expresan como búsqueda de patrones, la cual consiste en encontrar las coincidencias del grafo patrón P en un grafo semántico G. El grafo patrón especifica tanto la estructura de las coincidencias a encontrar, como los predicados sobre los atributos que deben cumplir los nodos y los arcos de las mismas. Claramente, este problema está asociado al isomorfismo de subgrafos. Además, se define un tipo de consultas más general sobre grafos semánticos. Estos nuevos patrones se denominan grafos patrón generalizados. El objetivo de estos es encontrar caminos y subgrafos que satisfagan ciertos requisitos semánticos, de estructura y de alcance. Estos patrones son expresivos, pues permiten (i) usar operadores de expresiones regulares (e.g., la estrella de Kleene y la unión); (ii) especificar predicados estructurales en los nodos y arcos; y (iii) evaluar predicados sobre los atributos de los nodos y arcos. Los patrones grafo tradicionales, las consultas de alcance, la combinación de estos y más se pueden representar a través de grafos patrón generalizados. Se usa el enfoque de solución propuesto para resolver los grafos patrón generalizados. La solución tiene dos fases. Primero, el patrón es linearizado, i.e., representado como un camino que incluye todos sus nodos y arcos. Hay muchas linearizaciones para un patrón dado; se proponen heurísticas para producir linearizaciones cortas que ubican los predicados selectivos al comienzo. Segundo, se busca una función biyectiva que mapee cada nodo en el patrón a un nodo en el grafo semántico que satisfaga los requisitos de alcance y los predicados. Específicamente, se propone un algoritmo de búsqueda que recorre el grafo semántico siguiendo una búsqueda en amplitud restringida por la linearización. La solución se evaluó experimentalmente usando un grafo semántico real (la red de citaciones DBLP) para evaluar su practicidad y eficiencia. Los resultados experimentales muestran que las técnicas y optimizaciones propuestas son efectivas en consultar grafos semánticos, ofreciendo un alto factor de reducción en el tiempo de ejecución cuando se utilizan las estadísticas del grafo semántico.Doctorad

Exponential families on resource-constrained systems

This work is about the estimation of exponential family models on resource-constrained systems. Our main goal is learning probabilistic models on devices with highly restricted storage, arithmetic, and computational capabilities—so called, ultra-low-power devices. Enhancing the learning capabilities of such devices opens up opportunities for intelligent ubiquitous systems in all areas of life, from medicine, over robotics, to home automation—to mention just a few. We investigate the inherent resource consumption of exponential families, review existing techniques, and devise new methods to reduce the resource consumption. The resource consumption, however, must not be reduced at all cost. Exponential families possess several desirable properties that must be preserved: Any probabilistic model encodes a conditional independence structure—our methods keep this structure intact. Exponential family models are theoretically well-founded. Instead of merely finding new algorithms based on intuition, our models are formalized within the framework of exponential families and derived from first principles. We do not introduce new assumptions which are incompatible with the formal derivation of the base model, and our methods do not rely on properties of particular high-level applications. To reduce the memory consumption, we combine and adapt reparametrization and regularization in an innovative way that facilitates the sparse parametrization of high-dimensional non-stationary time-series. The procedure allows us to load models in memory constrained systems, which would otherwise not fit. We provide new theoretical insights and prove that the uniform distance between the data generating process and our reparametrized solution is bounded. To reduce the arithmetic complexity of the learning problem, we derive the integer exponential family, based on the very definition of sufficient statistics and maximum entropy estimation. New integer-valued inference and learning algorithms are proposed, based on variational inference, proximal optimization, and regularization. The benefit of this technique is larger, the weaker the underlying system is, e.g., the probabilistic inference on a state-of-the-art ultra-lowpower microcontroller can be accelerated by a factor of 250. While our integer inference is fast, the underlying message passing relies on the variational principle, which is inexact and has unbounded error on general graphs. Since exact inference and other existing methods with bounded error exhibit exponential computational complexity, we employ near minimax optimal polynomial approximations to yield new stochastic algorithms for approximating the partition function and the marginal probabilities. Changing the polynomial degree allows us to control the complexity and the error of our new stochastic method. We provide an error bound that is parametrized by the number of samples, the polynomial degree, and the norm of the model’s parameter vector. Moreover, important intermediate quantities can be precomputed and shared with the weak computational device to reduce the resource requirement of our method even further. All new techniques are empirically evaluated on synthetic and real-world data, and the results confirm the properties which are predicted by our theoretical derivation. Our novel techniques allow a broader range of models to be learned on resource-constrained systems and imply several new research possibilities