Approximate Functional Dependencies Research Articles

Predictive mining of multi-temporal relations

In this paper, we propose a methodology for deriving a new kind of approximate temporal functional dependencies, called Approximate Predictive Functional Dependencies (APFDs), based on a three-window framework and on a multi-temporal relational model. Different features are proposed for the Observation Window (OW), where we observe predictive data, for the Waiting Window (WW), and for the Prediction Window (PW), where the predicted event occurs. We then consider the concept of approximation for such APFDs, introduce new error measures, and discuss different strategies for deriving APFDs. We discuss the quality, i.e., the informative content, of the derived AFDs by considering their entropy and information gain. Moreover, we outline the results in deriving APFDs focusing on the Acute Kidney Injury (AKI). We use real clinical data contained in the MIMIC III dataset related to patients from Intensive Care Units to show the applicability of our approach to real-world data.

Dynamic rate analysis for low frequency operation of chemical reactors

Periodic operation of chemical reactors can enhance reactant conversion and product selectivity. It is desirable to identify reaction kinetics and networks that may benefit from non-steady state operation and to quantify the extent of that enhancement without extensive computations. In this study, we describe a simple method to establish approximate functional dependencies of isothermal point reaction enhancement on dynamic and kinetic parameters during low frequency operation. Low frequency operation permits the use of steady state as opposed to transient conservation equations to identify limits of fractional rate enhancement. By approximating local dynamic rates as square waves modulating between two steady states, an analytical function can be derived from global rate expressions. The function relates fractional rate enhancement to concentration wave amplitudes, phase shifts, cyclic averages, duty cycles and reaction orders for one or more dynamically-fed reactants. We show that the method may be applied to predict integral conversion enhancement for ideal reactors. During integral operation, nonstoichiometric concentration waves may change phase through disproportionate consumption of reactants at wave maxima and minima, hence inverting waves out-of-phase (180°) from their initial waveform. This may cause local rate enhancement to transition to rate diminishment. Three experimental examples involving catalytic oxidations are described that illustrate selected theoretical aspects of the study.

Discovering Evolving Temporal Information: Theory and Application to Clinical Databases

Functional dependencies (FDs) allow us to represent database constraints, corresponding to requirements as “patients having the same symptoms undergo the same medical tests.” Some research efforts have focused on extending such dependencies to consider also temporal constraints such as “patients having the same symptoms undergo in the next period the same medical tests.” Temporal functional dependencies are able to represent such kind of temporal constraints in relational databases. Another extension for FDs allows one to represent approximate functional dependencies (AFDs), as “patients with the same symptomsgenerallyundergo the same medical tests.” It enables data to deviate from the defined constraints according to a user-defined percentage. Approximate temporal functional dependencies (ATFDs) merge the concepts of temporal functional dependency and of approximate functional dependency. Among the different kinds of ATFD, the Approximate Pure Temporally Evolving Functional Dependencies (textit{APE}-FDs for short) allow one to detect patterns on the evolution of data in the database and to discover dependencies as “For most patients with the same initial diagnosis, the same medical test is prescribed after the occurrence of same symptom.” Mining ATFDs from large databases may be computationally expensive. In this paper, we focus on textit{APE}-FDs and prove that, unfortunately, verifying a single textit{APE}-FD over a given database instance is in general NP-complete. In order to cope with this problem, we propose a framework for mining complex textit{APE}-FDs in real-world data collections. In the framework, we designed and applied sound and advanced model-checking techniques. To prove the feasibility of our proposal, we used real-world databases from two medical domains (namely, psychiatry and pharmacovigilance) and tested the running prototype we developed on such databases.

The role of wave kinematics in turbulent flow over waves

The turbulent flow over monochromatic waves of moderate steepness is studied by means of wall resolved large eddy simulations. The simulations cover a range of wave ages and Reynolds numbers. At low wave ages the form drag is highly sensitive to Reynolds number changes, and the interaction between turbulent and wave-induced stresses increases with Reynolds number. At higher wave ages, the flow enters a quasi-laminar regime where wave-induced stresses are primarily balanced by viscous stresses, and the form drag displays a simple Reynolds number dependence. To exploit the quasi-laminar response to the wave kinematics, we split the flow field into a laminar wave-generated response and a turbulent shear flow. The former is driven by the non-homogeneous boundary conditions, whereas the latter is driven by the laminar solution as well as turbulent stresses. For high wave ages, the splitting enables approximate functional dependencies for the form drag to be formulated. In the low wave age regime, where the wave-induced stresses are tightly connected with higher harmonics in the turbulent stresses, the flow is more challenging to analyse. Nevertheless, the importance of higher harmonics in the turbulent stresses can be quantified by explicitly choosing which modes to include in the split-system forcing.

Properties of Dislocation Drag from Phonon Wind at Ambient Conditions.

It is well known that, under plastic deformation, dislocations are not only created but also move through the crystal, and their mobility is impeded by their interaction with the crystal structure. At high stress and temperature, this “drag” is dominated by phonon wind, i.e., phonons scattering off dislocations. Employing the semi-isotropic approach discussed in detail in a previous paper (J. Phys. Chem. Solids 2019, 124, 24–35), we discuss here the approximate functional dependence of dislocation drag B on dislocation velocity in various regimes between a few percent of transverse sound speed and (where is the effective average transverse sound speed of the polycrystal). In doing so, we find an effective functional form for dislocation drag for different slip systems and dislocation characters at fixed (room) temperature and low pressure.

Mining Approximate Primary Functional Dependency on Web Tables

Mining Approximate Primary Functional Dependency on Web Tables

Algebraic independence over positive characteristic: New criterion and applications to locally low-algebraic-rank circuits

The motivation for this work (Pandey et al. 2016) comes from two problems: testing algebraic independence of arithmetic circuits over a field of small characteristic and generalizing the structural property of algebraic dependence used by Kumar, Saraf, CCC’16 to arbitrary fields. It is known that in the case of zero, or large characteristic, using a classical criterion based on the Jacobian, we get a randomized poly-time algorithm to test algebraic independence. Over small characteristic, the Jacobian criterion fails and there is no subexponential time algorithm known. This problem could well be conjectured to be in RP, but the current best algorithm puts it in NP $${^{\#{\rm P}}}$$ (Mittmann, Saxena, Scheiblechner, Trans.AMS’14). Currently, even the case of two bivariate circuits over $${\mathbb{F}_2}$$ is open. We come up with a natural generalization of Jacobian criterion that works over all characteristics. The new criterion is efficient if the underlying inseparable degree is promised to be a constant. This is a modest step toward the open question of fast independence testing, over finite fields, posed in (Dvir, Gabizon, Wigderson, FOCS’07). In a set of linearly dependent polynomials, any polynomial can be written as a linear combination of the polynomials forming a basis. The analogous property for algebraic dependence is false, but a property approximately in that spirit is named as “functional dependence” in Kumar, Saraf, CCC’16 and proved for zero or large characteristics. We show that functional dependence holds for arbitrary fields, thereby answering the open questions in Kumar, Saraf, CCC’16. Following them, we use the functional dependence lemma to prove the first exponential lower bound for locally low algebraic rank circuits for arbitrary fields (a model that strongly generalizes homogeneous depth-4 circuits). We also recover their quasipoly-time hitting-set for such models, for fields of characteristic smaller than the ones known before. Our results show that approximate functional dependence is indeed a more fundamental concept than the Jacobian as it is field independent. We achieve the former by first picking a “good” transcendence basis, then translating the circuits by new variables, and finally approximating them by truncating higher degree monomials. We give a tight analysis of the “degree” of approximation needed in the criterion. To get the locally low-algebraic-rank circuit applications, we follow the known shifted partial derivative-based methods.

EXODuS: Exploratory OLAP over Document Stores

OLAP has been extensively used for a couple of decades as a data analysis approach to support decision making on enterprise structured data. Now, with the wide diffusion of NoSQL databases holding semi-structured data, there is a growing need for enabling OLAP on document stores as well, to allow non-expert users to get new insights and make better decisions. Unfortunately, due to their schemaless nature, document stores are hardly accessible via direct OLAP querying. In this paper we propose EXODuS, an interactive, schema-on-read approach to enable OLAP querying of document stores in the context of self-service BI and exploratory OLAP. To discover multidimensional hierarchies in document stores we adopt a data-driven approach based on the mining of approximate functional dependencies; to ensure good performances, we incrementally build local portions of hierarchies for the levels involved in the current user query. Users execute an analysis session by expressing well-formed multidimensional queries related by OLAP operations; these queries are then translated into the native query language of MongoDB, one of the most popular document-based DBMS. An experimental evaluation on real-world datasets shows the efficiency of our approach and its compatibility with a real-time setting.

Approximate Functional Dependencies Mining Using Association Rules Specificity Interestingness Measure

Mining Approximate Functional Dependencies (AFDs) from a database may produce valuable interesting relationships among its variables that would be beneficial in several domain applications such as marketing, financial data analysis, biological data analysi s, and intrusion detection. Mining of association rules is concerned with extracting new knowledge from dat abases in the form of patterns and associations among data items. The mining of AFDs still posing special se t of challenges such as the space and time requirements in addition to the quality of the discovered AFD s. In this paper, an approach for AFDs mining is being developed through employing the specificity interestingness measure and its monotonic property used in some association rules mining algorithms. Thi s approach has been tested on a set of test bed of datasets. The results showed an improvement in time requirements and in the number of mined AFDs.

BPMN Miner: Automated discovery of BPMN process models with hierarchical structure

Existing techniques for automated discovery of process models from event logs generally produce flat process models. Thus, they fail to exploit the notion of subprocess as well as error handling and repetition constructs provided by contemporary process modeling notations, such as the Business Process Model and Notation (BPMN). This paper presents a technique, namely BPMN Miner, for automated discovery of hierarchical BPMN models containing interrupting and non-interrupting boundary events and activity markers. The technique employs approximate functional and inclusion dependency discovery techniques in order to elicit a process–subprocess hierarchy from the event log. Given this hierarchy and the projected logs associated to each node in the hierarchy, parent process and subprocess models are discovered using existing techniques for flat process model discovery. Finally, the resulting models and logs are heuristically analyzed in order to identify boundary events and markers. By employing approximate dependency discovery techniques, BPMN Miner is able to detect and filter out noise in the event log arising for example from data entry errors, missing event records or infrequent behavior. Noise is detected during the construction of the subprocess hierarchy and filtered out via heuristics at the lowest possible level of granularity in the hierarchy. A validation with one synthetic and two real-life logs shows that process models derived by the proposed technique are more accurate and less complex than those derived with flat process discovery techniques. Meanwhile, a validation on a family of synthetically generated logs shows that the technique is resilient to varying levels of noise.

Decomposition-by-normalization (DBN): leveraging approximate functional dependencies for efficient CP and tucker decompositions

For many multi-dimensional data applications, tensor operations as well as relational operations both need to be supported throughout the data lifecycle. Tensor based representations (including two widely used tensor decompositions, CP and Tucker decompositions) are proven to be effective in multi-aspect data analysis and tensor decomposition is an important tool for capturing high-order structures in multi-dimensional data. Although tensor decomposition is shown to be effective for multi-dimensional data analysis, the cost of tensor decomposition is often very high. Since the number of modes of the tensor data is one of the main factors contributing to the costs of the tensor operations, in this paper, we focus on reducing the modality of the input tensors to tackle the computational cost of the tensor decomposition process. We propose a novel decomposition-by-normalization scheme that first normalizes the given relation into smaller tensors based on the functional dependencies of the relation, decomposes these smaller tensors, and then recombines the sub-results to obtain the overall decomposition. The decomposition and recombination steps of the decomposition-by-normalization scheme fit naturally in settings with multiple cores. This leads to a highly efficient, effective, and parallelized decomposition-by-normalization algorithm for both dense and sparse tensors for CP and Tucker decompositions. Experimental results confirm the efficiency and effectiveness of the proposed decomposition-by-normalization scheme compared to the conventional nonnegative CP decomposition and Tucker decomposition approaches.

Mining approximate temporal functional dependencies with pure temporal grouping in clinical databases

Functional dependencies (FDs) typically represent associations over facts stored by a database, such as “patients with the same symptom get the same therapy.” In more recent years, some extensions have been introduced to represent both temporal constraints (temporal functional dependencies – TFDs), as “for any given month, patients with the same symptom must have the same therapy, but their therapy may change from one month to the next one,” and approximate properties (approximate functional dependencies – AFDs), as “patients with the same symptom generally have the same therapy.” An AFD holds most of the facts stored by the database, enabling some data to deviate from the defined property: the percentage of data which violate the given property is user-defined.According to this scenario, in this paper we introduce approximate temporal functional dependencies (ATFDs) and use them to mine clinical data. Specifically, we considered the need for deriving new knowledge from psychiatric and pharmacovigilance data.ATFDs may be defined and measured either on temporal granules (e.g.grouping data by day, week, month, year) or on sliding windows (e.g.a fixed-length time interval which moves over the time axis): in this regard, we propose and discuss some specific and efficient data mining techniques for ATFDs. We also developed two running prototypes and showed the feasibility of our proposal by mining two real-world clinical data sets. The clinical interest of the dependencies derived considering the psychiatry and pharmacovigilance domains confirms the soundness and the usefulness of the proposed techniques.

Representation of approximate functional dependencies using partitions, discernibility matrix and association rules

Representation of approximate functional dependencies using partitions, discernibility matrix and association rules

Representation of approximate functional dependencies using partitions, discernibility matrix and association rules

Representation of approximate functional dependencies using partitions, discernibility matrix and association rules

Bayesian networks for supporting query processing over incomplete autonomous databases

As the information available to naive users through autonomous data sources continues to increase, mediators become important to ensure that the wealth of information available is tapped effectively. A key challenge that these information mediators need to handle is the varying levels of incompleteness in the underlying databases in terms of missing attribute values. Existing approaches such as QPIAD aim to mine and use Approximate Functional Dependencies (AFDs) to predict and retrieve relevant incomplete tuples. These approaches make independence assumptions about missing values--which critically hobbles their performance when there are tuples containing missing values for multiple correlated attributes. In this paper, we present a principled probabilistic alternative that views an incomplete tuple as defining a distribution over the complete tuples that it stands for. We learn this distribution in terms of Bayesian networks. Our approach involves mining/"learning" Bayesian networks from a sample of the database, and using it to do both imputation (predict a missing value) and query rewriting (retrieve relevant results with incompleteness on the query-constrained attributes, when the data sources are autonomous). We present empirical studies to demonstrate that (i) at higher levels of incompleteness, when multiple attribute values are missing, Bayesian networks do provide a significantly higher classification accuracy and (ii) the relevant possible answers retrieved by the queries reformulated using Bayesian networks provide higher precision and recall than AFDs while keeping query processing costs manageable.

Discovering approximate functional dependencies via the rough set approach.

Discovering approximate functional dependencies via the rough set approach.

Type 2 approximate functional dependency and the outliers with functional dependency.

Type 2 approximate functional dependency and the outliers with functional dependency.

Discover Dependencies from Data—A Review

Functional and inclusion dependency discovery is important to knowledge discovery, database semantics analysis, database design, and data quality assessment. Motivated by the importance of dependency discovery, this paper reviews the methods for functional dependency, conditional functional dependency, approximate functional dependency, and inclusion dependency discovery in relational databases and a method for discovering XML functional dependencies.

SMARTINT: using mined attribute dependencies to integrate fragmented web databases

Many web databases can be seen as providing partial and overlapping information about entities in the world. To answer queries effectively, we need to integrate the information about the individual entities that are fragmented over multiple sources. At first blush this is just the inverse of traditional database normalization problem--rather than go from a universal relation to normalized tables, we want to reconstruct the universal relation given the tables (sources). The standard way of reconstructing the entities will involve joining the tables. Unfortunately, because of the autonomous and decentralized way in which the sources are populated, they often do not have Primary Key---Foreign Key relations. While tables may share attributes, naive joins over these shared attributes can result in reconstruction of many spurious entities thus seriously compromising precision. Our system, SmartInt is aimed at addressing the problem of data integration in such scenarios. Given a query, our system uses the Approximate Functional Dependencies (AFDs) to piece together a tree of relevant tables to answer it. The result tuples produced by our system are able to strike a favorable balance between precision and recall.

Specific Features of Self-Heating in Systems with a Logarithmic Law of Deceleration

A qualitative analysis of structural types of phase trajectories and corresponding thermograms with various values of the Semenov and Todes criteria for systems with intense self-deceleration is performed. A rigorous criterion of degeneration of the thermal explosion is found. Physical mechanisms of various regimes of self-heating processes are analyzed. An approximate functional dependence of the critical value of the Semenov parameter on the self-deceleration parameter is obtained, and the limits of its applicability are determined.