On the exponential cardinality of FDS for the ordered p-median problem

We study finite dominating sets (FDS) for the ordered median problem. This kind of problems allows to deal simultaneously with a large number of models. We show that there is no valid polynomial size FDS for the general multifacility version of this problem even on path networks

Multifacility ordered median problems on networks: a further analysis

In this paper, we address the ordered p-median problem, which includes as special cases most of the classical multifacility location problems discussed in the literature. Finite dominating sets (FDS) are known for particular instances of this problem: p-median, p-center, and p-centdian. We find an FDS for the ordered p-median problem. This set allows us to gain a better insight into the general FDS structure of network location problems. This FDS is later used to present the first polynomial time algorithm for p-facility ordered median problems on tree networks

Contributions à l’Optimisation de Requêtes Multidimensionnelles

Analyser les données consiste à choisir un sous-ensemble des dimensions qui les décriventafin d'en extraire des informations utiles. Or, il est rare que l'on connaisse a priori les dimensions"intéressantes". L'analyse se transforme alors en une activité exploratoire où chaque passe traduit par une requête. Ainsi, il devient primordiale de proposer des solutions d'optimisationde requêtes qui ont une vision globale du processus plutôt que de chercher à optimiser chaque requêteindépendamment les unes des autres. Nous présentons nos contributions dans le cadre de cette approcheexploratoire en nous focalisant sur trois types de requêtes: (i) le calcul de bordures,(ii) les requêtes dites OLAP (On Line Analytical Processing) dans les cubes de données et (iii) les requêtesde préférence type skyline

Profiling relational data: a survey

Profiling data to determine metadata about a given dataset is an important and frequent activity of any IT professional and researcher and is necessary for various use-cases. It encompasses a vast array of methods to examine datasets and produce metadata. Among the simpler results are statistics, such as the number of null values and distinct values in a column, its data type, or the most frequent patterns of its data values. Metadata that are more difficult to compute involve multiple columns, namely correlations, unique column combinations, functional dependencies, and inclusion dependencies. Further techniques detect conditional properties of the dataset at hand. This survey provides a classification of data profiling tasks and comprehensively reviews the state of the art for each class. In addition, we review data profiling tools and systems from research and industry. We conclude with an outlook on the future of data profiling beyond traditional profiling tasks and beyond relational databases

Interpolating between k-Median and k-Center: Approximation Algorithms for Ordered k-Median

We consider a generalization of k-median and k-center, called the ordered k-median problem. In this problem, we are given a metric space (D,{c_{ij}}) with n=|D| points, and a non-increasing weight vector w in R_+^n, and the goal is to open k centers and assign each point j in D to a center so as to minimize w_1 *(largest assignment cost)+w_2 *(second-largest assignment cost)+...+w_n *(n-th largest assignment cost). We give an (18+epsilon)-approximation algorithm for this problem. Our algorithms utilize Lagrangian relaxation and the primal-dual schema, combined with an enumeration procedure of Aouad and Segev. For the special case of {0,1}-weights, which models the problem of minimizing the l largest assignment costs that is interesting in and of by itself, we provide a novel reduction to the (standard) k-median problem, showing that LP-relative guarantees for k-median translate to guarantees for the ordered k-median problem; this yields a nice and clean (8.5+epsilon)-approximation algorithm for {0,1} weights

Approximate Data Mining Techniques on Clinical Data

The past two decades have witnessed an explosion in the number of medical and healthcare datasets available to researchers and healthcare professionals. Data collection efforts are highly required, and this prompts the development of appropriate data mining techniques and tools that can automatically extract relevant information from data. Consequently, they provide insights into various clinical behaviors or processes captured by the data. Since these tools should support decision-making activities of medical experts, all the extracted information must be represented in a human-friendly way, that is, in a concise and easy-to-understand form. To this purpose, here we propose a new framework that collects different new mining techniques and tools proposed. These techniques mainly focus on two aspects: the temporal one and the predictive one. All of these techniques were then applied to clinical data and, in particular, ICU data from MIMIC III database. It showed the flexibility of the framework, which is able to retrieve different outcomes from the overall dataset. The first two techniques rely on the concept of Approximate Temporal Functional Dependencies (ATFDs). ATFDs have been proposed, with their suitable treatment of temporal information, as a methodological tool for mining clinical data. An example of the knowledge derivable through dependencies may be "within 15 days, patients with the same diagnosis and the same therapy usually receive the same daily amount of drug". However, current ATFD models are not analyzing the temporal evolution of the data, such as "For most patients with the same diagnosis, the same drug is prescribed after the same symptom". To this extent, we propose a new kind of ATFD called Approximate Pure Temporally Evolving Functional Dependencies (APEFDs). Another limitation of such kind of dependencies is that they cannot deal with quantitative data when some tolerance can be allowed for numerical values. In particular, this limitation arises in clinical data warehouses, where analysis and mining have to consider one or more measures related to quantitative data (such as lab test results and vital signs), concerning multiple dimensional (alphanumeric) attributes (such as patient, hospital, physician, diagnosis) and some time dimensions (such as the day since hospitalization and the calendar date). According to this scenario, we introduce a new kind of ATFD, named Multi-Approximate Temporal Functional Dependency (MATFD), which considers dependencies between dimensions and quantitative measures from temporal clinical data. These new dependencies may provide new knowledge as "within 15 days, patients with the same diagnosis and the same therapy receive a daily amount of drug within a fixed range". The other techniques are based on pattern mining, which has also been proposed as a methodological tool for mining clinical data. However, many methods proposed so far focus on mining of temporal rules which describe relationships between data sequences or instantaneous events, without considering the presence of more complex temporal patterns into the dataset. These patterns, such as trends of a particular vital sign, are often very relevant for clinicians. Moreover, it is really interesting to discover if some sort of event, such as a drug administration, is capable of changing these trends and how. To this extent, we propose a new kind of temporal patterns, called Trend-Event Patterns (TEPs), that focuses on events and their influence on trends that can be retrieved from some measures, such as vital signs. With TEPs we can express concepts such as "The administration of paracetamol on a patient with an increasing temperature leads to a decreasing trend in temperature after such administration occurs". We also decided to analyze another interesting pattern mining technique that includes prediction. This technique discovers a compact set of patterns that aim to describe the condition (or class) of interest. Our framework relies on a classification model that considers and combines various predictive pattern candidates and selects only those that are important to improve the overall class prediction performance. We show that our classification approach achieves a significant reduction in the number of extracted patterns, compared to the state-of-the-art methods based on minimum predictive pattern mining approach, while preserving the overall classification accuracy of the model. For each technique described above, we developed a tool to retrieve its kind of rule. All the results are obtained by pre-processing and mining clinical data and, as mentioned before, in particular ICU data from MIMIC III database

Unreliable point facility location problems on networks

In this paper we study facility location problems on graphs under the most common criteria, such as, median, center and centdian, but we incorporate in the objective function some reliability aspects. Assuming that facilities may become unavailable with a certain probability, the problem consists of locating facilities minimizing the overall or the maximum expected service cost in the long run, or a convex combination of the two. We show that the k-facility problem on general networks is NP-hard. Then, we provide efficient algorithms for these problems for the cases of k = 1, 2, both on general networks and on trees. We also explain how our methodology extends to handle a more general class of unreliable point facility location problems related to the ordered median objective function.Ministerio de Ciencia y TecnologíaJunta de Andalucí

Private Data Exploring, Sampling, and Profiling

Data analytics is being widely used not only as a business tool, which empowers organizations to drive efficiencies, glean deeper operational insights and identify new opportunities, but also for the greater good of society, as it is helping solve some of world's most pressing issues, such as developing COVID-19 vaccines, fighting poverty and climate change. Data analytics is a process involving a pipeline of tasks over the underlying datasets, such as data acquisition and cleaning, data exploration and profiling, building statistics and training machine learning models. In many cases, conducting data analytics faces two practical challenges. First, many sensitive datasets have restricted access and do not allow unfettered access; Second, data assets are often owned and stored in silos by multiple business units within an organization with different access control. Therefore, data scientists have to do analytics on private and siloed data. There is a fundamental trade-off between data privacy and the data analytics tasks. On the one hand, achieving good quality data analytics requires understanding the whole picture of the data; on the other hand, despite recent advances in designing privacy and security primitives such as differential privacy and secure computation, when naivly applied, they often significantly downgrade tasks' efficiency and accuracy, due to the expensive computations and injected noise, respectively. Moreover, those techniques are often piecemeal and they fall short in holistically integrating into end-to-end data analytics tasks. In this thesis, we approach this problem by treating privacy and utility as constraints on data analytics. First, we study each task and express its utility as data constraints; then, we select a principled data privacy and security model for each task; and finally, we develop mechanisms to combine them into end to end analytics tasks. This dissertation addresses the specific technical challenges of trading off privacy and utility in three popular analytics tasks. The first challenge is to ensure query accuracy in private data exploration. Current systems for answering queries with differential privacy place an inordinate burden on the data scientist to understand differential privacy, manage their privacy budget, and even implement new algorithms for noisy query answering. Moreover, current systems do not provide any guarantees to the data analyst on the quality they care about, namely accuracy of query answers. We propose APEx, a generic accuracy-aware privacy query engine for private data exploration. The key distinction of APEx is to allow the data scientist to explicitly specify the desired accuracy bounds to a SQL query. Using experiments with query benchmarks and a case study, we show that APEx allows high exploration quality with a reasonable privacy loss. The second challenge is to preserve the structure of the data in private data synthesis. Existing differentially private data synthesis methods aim to generate useful data based on applications, but they fail in keeping one of the most fundamental data properties of the structured data — the underlying correlations and dependencies among tuples and attributes. As a result, the synthesized data is not useful for any downstream tasks that require this structure to be preserved. We propose Kamino, a data synthesis system to ensure differential privacy and to preserve the structure and correlations present in the original dataset. We empirically show that while preserving the structure of the data, Kamino achieves comparable and even better usefulness in applications of training classification models and answering marginal queries than the state-of-the-art methods of differentially private data synthesis. The third challenge is efficient and secure private data profiling. Discovering functional dependencies (FDs) usually requires access to all data partitions to find constraints that hold on the whole dataset. Simply applying general secure multi-party computation protocols incurs high computation and communication cost. We propose SMFD to formulate the FD discovery problem in the secure multi-party scenario, and design secure and efficient cryptographic protocols to discover FDs over distributed partitions. Experimental results show that SMFD is practically efficient over non-secure distributed FD discovery, and can significantly outperform general purpose multi-party computation framework