WO2006041886A2 - System, method and computer program for successive approximation of query results - Google Patents
System, method and computer program for successive approximation of query results Download PDFInfo
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- WO2006041886A2 WO2006041886A2 PCT/US2005/035764 US2005035764W WO2006041886A2 WO 2006041886 A2 WO2006041886 A2 WO 2006041886A2 US 2005035764 W US2005035764 W US 2005035764W WO 2006041886 A2 WO2006041886 A2 WO 2006041886A2
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- WIPO (PCT)
- Prior art keywords
- recited
- query
- data elements
- result
- approximation
- Prior art date
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Classifications
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F16/00—Information retrieval; Database structures therefor; File system structures therefor
- G06F16/20—Information retrieval; Database structures therefor; File system structures therefor of structured data, e.g. relational data
- G06F16/24—Querying
- G06F16/245—Query processing
- G06F16/2458—Special types of queries, e.g. statistical queries, fuzzy queries or distributed queries
- G06F16/2462—Approximate or statistical queries
-
- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y10—TECHNICAL SUBJECTS COVERED BY FORMER USPC
- Y10S—TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y10S707/00—Data processing: database and file management or data structures
- Y10S707/99931—Database or file accessing
- Y10S707/99932—Access augmentation or optimizing
-
- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y10—TECHNICAL SUBJECTS COVERED BY FORMER USPC
- Y10S—TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y10S707/00—Data processing: database and file management or data structures
- Y10S707/99931—Database or file accessing
- Y10S707/99933—Query processing, i.e. searching
-
- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y10—TECHNICAL SUBJECTS COVERED BY FORMER USPC
- Y10S—TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y10S707/00—Data processing: database and file management or data structures
- Y10S707/99931—Database or file accessing
- Y10S707/99933—Query processing, i.e. searching
- Y10S707/99934—Query formulation, input preparation, or translation
-
- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y10—TECHNICAL SUBJECTS COVERED BY FORMER USPC
- Y10S—TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y10S707/00—Data processing: database and file management or data structures
- Y10S707/99941—Database schema or data structure
- Y10S707/99944—Object-oriented database structure
- Y10S707/99945—Object-oriented database structure processing
Definitions
- the present invention relates generally to systems and methods for analyzing and querying data. More particularly, the present invention relates to systems and methods for incrementally approximating a query result, optionally until the query result is produced exactly upon completion.
- a method for generating a succession of approximations of the result R of a query on a plurality of data elements D.
- the method includes the steps of (a) computing the result Ai of the query on a sample Sj of D; (b) computing an approximation Bi of the result R based upon at least the result A; and (c) generating a succession of approximations by performing steps (a) and (b) multiple times i with different Sj.
- a system is provided for generating a succession of approximations of the result R of a query on a plurality of data elements D stored in a data storage device.
- the system includes a processor unit configured to access the data storage device and to (a) compute the result Aj of the query on a sample S 1 of the plurality of data elements D; (b) compute an approximation Bi of the result R based upon at least the result A 1 ; and (c) generate a succession of approximations by performing (a) and (b) multiple times i with different samples Si.
- a computer program for generating a succession of approximations of the result R of a query on a plurality of data elements D stored in a data storage device.
- the computer program is stored on a computer readable medium includes a first code segment for accessing the data storage device and computing the result Ai of the query on a sample Sj of the plurality of data elements D.
- the computer program further includes a second code segment for computing an approximation Bj of the result R based upon at least the result Aj.
- the computer program also includes a third code segment for generating a succession of approximations by executing the first and second code segments multiple times i with different samples S 1 .
- a method for for generating a succession of approximations of the result R of a query on a plurality of data elements D.
- the method includes (a) steps for computing the result Aj of the query on a sample Si of D; (b) steps for computing an approximation Bj of the result R based upon at least the result A; and (c) steps for generating a succession of approximations by performing steps (a) and (b) multiple times i with different Si .
- a system is provided for generating a succession of approximations of the result R of a query on a plurality of data elements D stored in a data storage device.
- the system includes a processor means for accessing the data storage device and (a) computing the result Aj of the query on a sample Si of the plurality of data elements D; (b) computing an approximation B 1 of the result R based upon at least the result A; and (c) generating a succession of approximations by performing (a) and (b) multiple times i with different samples S 1 .
- a system for generating a succession of approximations of the result R of a query on a plurality of data elements D stored in a data storage device.
- the system includes a client user interface that is coupled with a data network and configured to build a query request and transmit the query request to a processing means via the data network.
- the client user interface receives and displays the successive approximation.
- the processing means (a) computes the result A 1 of the query on a sample S 1 of the plurality of data elements D; (b) computes an approximation Bj of the result R based upon at least the result A; (c) generates a succession of approximations by performing (a) and (b) multiple times i with different samples Si, and (d) transmits the succession of approximations to the client user interface.
- FIG. 1 is a flow chart of an exemplary SAQR method
- FIG. 2 is a block diagram of a computer processor arrangement which may be used to implement the present invention.
- FIG. 3 illustrates an exemplary display according to an embodiment of the present invention.
- Successive Approximation of Query Results is a novel method for producing successive approximations of a query result until the query is finished.
- a “query” can be expressed as a mathematical function Q from a list of data elements (data list), where each data element is a member of "domain” D, to a result that is a member of "range” R; [0020] Q : list(D) ⁇ R [0021] We refer to the application of a query function Q to a data list X as a
- a query function is considered to be a "bag function" if permuting the data list does not alter the query result.
- a query function can be "incrementally evaluated” if there is an "update function" U from a previous result (i.e., a member of R), and a data element (also a member of D), to a new result (also a member of R), such that when U is applied to the result of a query Q on a list of data elements and to a new data element, its result is equal to the result of the query Q on the list formed by appending the new data element to the list.
- U i.e., a member of R
- D data element
- new result also a member of R
- Equation function A from a result (i.e., a member of R), a sample size (which is a member of the set of natural numbers N), and a population size (also a member of N), to a new result (also a member of R), such that given a sufficiently large random or pseudo-random sample of the data, the result of A applied to query Q applied to the sample, the number of data elements in the sample, and the number of data elements in the data, is a useful approximation of the result of Q applied to the data. This is represented by the following: [0025] A : (R x N x N) ⁇ R;
- (s sample(a)) -> • A( Q(s),
- ) is a useful approximation of Q(a).
- an approximation function produces an approximation of higher expected accuracy (i.e. lower expected error with respect to Q(a)) when given the result of a query on a larger sample, and produces exactly the result of the query on the population when given the entire population (i.e. A(Q(a),
- ) Q(a)).
- a query function which is a bag function and which can be approximated from a sample can be successively approximated by the method of the present invention. The preferred embodiment described next additionally requires that the query function can be incrementally evaluated.
- a flow chart is shown of a method of querying data using SAQR according to an embodiment of the present invention.
- ; d : rpdata[count] .
- an approximation function can be applied to the result, the count, and the total number of data elements to yield an approximation of Q(data) at step S1-4.
- the approximation can be displayed at step S1-5 to a user or output to another process while the computation is in progress.
- step S 6 If further iterations are required (S1-6), then the next iteration of the query is evaluated. When all iterations are complete, the query result r is generated at step S 1-7. Since at this point, the query has been exercised for all data, the result r is exactly equal to Q(data). At this point, the query result r can be displayed to a user, stored or output to another process.
- the method of the present invention evaluates a query and generates an approximate query result on successively larger samples, thereby outputting successively better approximations until the query has considered the entire population of data.
- each sample comprises the previous sample and one additional data element, so that to proceed to the next larger sample, the update function need only be applied once. Assuming that the approximation function is efficient and disregarding the cost of the random permutation, this process will take asymptotically no longer than evaluating the query on the entire data list using the update function.
- a data list can be maintained in a random permutation when new data elements are inserted by inserting each element at a random location in the permutation.
- sorting by a deterministic pseudo-random value, or a hash of some function of a data element which yields a different value for each data element may be used to generate the permutation without affecting the quality of the approximation.
- the data elements could be divided into two or more samples, which may be concatenated. Each data elements should fall into one sample, and each data element falls into a given sample with equal and independent probability.
- the concatenation of these samples which are not necessarily in a random order internally, is not a random permutation. However, if approximations are taken only at the boundary between samples, the results will still be valid and accurate.
- a very simple embodiment of the invention is to generate a small sample of the data elements, quickly evaluate the query over the small sample to generate a first approximation, and evaluate the query over the entire data list to generate a second approximation which is the exact result.
- the present invention it is possible to terminate the query at any point in time without producing an exact query result.
- the approximation result could be output based upon the final iteration before termination.
- the query might be terminated early because, in a particular application, it can be determined based on statistical properties from the approximation function that the approximate result output is sufficiently accurate for its purposes. It might also be done because the result of the query is no longer useful due to changing circumstances.
- A( (r,s),n 1 N ) ( A R (r,n,N), A s (s,n,N) ) .
- the result domain is augmented with the results of the individual queries, even though these might not be needed in the output, so that they can be used by the individual queries' update functions.
- An implementation might not choose to evaluate F in the update function at all.
- A( (f,r,s), n, N ) ( F(A R (r,n,N), A s (s,n,N)), A R (r,n,N), A s (s,n,N) ) .
- Q(data) Concatenate
- PredA(d) ⁇ 1 if age(d) > 55, 0 otherwise ;
- PredB(d) ⁇ 1 if income(d) ⁇ $15000, 0 otherwise .
- a ((f,r,s), n, N ) (r/s, r*N/n, s*N/n).
- the data list is iterated and processed as already described above. In this example, each time a few thousand records have been processed, the approximation function is calculated and the result is formatted as a percentage and displayed (as an approximate result) to the user. The user can be given the opportunity to interrupt the process. If the process is not interrupted, an exact result is displayed when it completes.
- PredA and PredB based on the query def
- PredA(d) return float( eval(queryA, ToDictionary(d)) ) ef
- PredB(d) return float( eval(queryB, ToDictionary(d)) ) def Update( (f,r,s), d ): return ( r+PredA(d) and (r+PredA(d)*PredB(d))/(s+PredA(d)), ....
- the query was interrupted by the user.
- FIG. 2 is a block diagram of a processor arrangement on which the method of the present invention may be executed.
- Processor arrangement 200 includes a processor unit 202 coupled with a data storage device 204, an input/output (I/O) device 206, a display device 208, and a printer device 210.
- the processor unit may include CPU and may be configured to execute computer programs to implement the processes described above.
- the processor arrangement 200 may be implemented with an infinite number of hardware and software configurations, and such hardware and software can be selected according to the application.
- a SAQR engine could be written in an object oriented scripting language such as PYTHON and run on a UNIX based processor.
- Data to be queried may be stored in data storage device 204, which may be a stand alone database, data warehouse, etc. Data may be organized in flat files or any other configuration. Data may be object oriented, relational, etc. One skilled in the art will understand that random permutation may be more difficult to achieve with some data constructs than with others. [0065] One will understand that processing may be performed centrally, in a distributed fashion, or via any number of arrangements, such as a client-server or web enabled arrangement.
- the data may be displayed in any fashion via any means, such as a client user interface.
- the information can be presented using numerous presentation techniques such as benchmarks, confidence intervals, color ramp metrics, dynamically filtered dimensions, scales and legends, trellis graphics, smooth transitions, moving average and kernel smoothing for line graphs, and others.
- Figure 3 shows a basic, exemplary interface 300 that allows entry of a query 302 and displays results of the query 304.
- the results 304 may be updated as a query iterates through the data as already described above.
- a "confidence" indicator 306 can be displayed along with the approximate result to indicate how competent the approximation is.
- a simple bar graph is used to indicate how much of the data has been traversed (i.e., how large the sample is).
- a confidence indicator could be calculated using any number of statistical analysis techniques to indicate a quality of the approximation. Other characteristics of the data, such as standard deviation, could be displayed as well.
- the field of statistics provides many useful formulas and methods for the calculation of confidence intervals and other metrics of accuracy.
- One simple and efficient formula which can be used to approximate the 80% symmetric confidence interval of a count of data elements satisfying a predicate is:
- SAQR provides, inter alia, the distinct advantage that a user of the system may obtain a cascade of results that become more refined over time in response to a single user interaction with the system (i.e., based upon a single query).
- a dynamic query result is generated that may be displayable, in response to a single query request.
- the dynamic result offers a limitless set of instantaneous results, each having an increased accuracy and confidence.
Abstract
Description
Claims
Priority Applications (4)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
AU2005294416A AU2005294416A1 (en) | 2004-10-05 | 2005-10-05 | System, method and computer program for successive approximation of query results |
CA002580687A CA2580687A1 (en) | 2004-10-05 | 2005-10-05 | System, method and computer program for successive approximation of query results |
JP2007534900A JP5176012B2 (en) | 2004-10-05 | 2005-10-05 | System, method and computer program for calculating a series of approximations of query results |
EP05801975A EP1820123A4 (en) | 2004-10-05 | 2005-10-05 | System, method and computer program for successive approximation of query results |
Applications Claiming Priority (2)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
US10/957,671 US7617186B2 (en) | 2004-10-05 | 2004-10-05 | System, method and computer program for successive approximation of query results |
US10/957,671 | 2004-10-05 |
Publications (2)
Publication Number | Publication Date |
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WO2006041886A2 true WO2006041886A2 (en) | 2006-04-20 |
WO2006041886A3 WO2006041886A3 (en) | 2007-05-03 |
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PCT/US2005/035764 WO2006041886A2 (en) | 2004-10-05 | 2005-10-05 | System, method and computer program for successive approximation of query results |
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US (1) | US7617186B2 (en) |
EP (1) | EP1820123A4 (en) |
JP (1) | JP5176012B2 (en) |
AU (1) | AU2005294416A1 (en) |
CA (1) | CA2580687A1 (en) |
WO (1) | WO2006041886A2 (en) |
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US9043296B2 (en) | 2010-07-30 | 2015-05-26 | Microsoft Technology Licensing, Llc | System of providing suggestions based on accessible and contextual information |
US9111238B2 (en) * | 2010-12-17 | 2015-08-18 | Microsoft Technology Licensing, Llc | Data feed having customizable analytic and visual behavior |
US9110957B2 (en) | 2010-12-17 | 2015-08-18 | Microsoft Technology Licensing, Llc | Data mining in a business intelligence document |
US9171272B2 (en) | 2010-12-17 | 2015-10-27 | Microsoft Technology Licensing, LLP | Automated generation of analytic and visual behavior |
US9104992B2 (en) | 2010-12-17 | 2015-08-11 | Microsoft Technology Licensing, Llc | Business application publication |
US9336184B2 (en) | 2010-12-17 | 2016-05-10 | Microsoft Technology Licensing, Llc | Representation of an interactive document as a graph of entities |
US9069557B2 (en) | 2010-12-17 | 2015-06-30 | Microsoft Technology Licensing, LLP | Business intelligence document |
US9024952B2 (en) | 2010-12-17 | 2015-05-05 | Microsoft Technology Licensing, Inc. | Discovering and configuring representations of data via an insight taxonomy |
US9304672B2 (en) | 2010-12-17 | 2016-04-05 | Microsoft Technology Licensing, Llc | Representation of an interactive document as a graph of entities |
US9864966B2 (en) | 2010-12-17 | 2018-01-09 | Microsoft Technology Licensing, Llc | Data mining in a business intelligence document |
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US9607045B2 (en) | 2012-07-12 | 2017-03-28 | Microsoft Technology Licensing, Llc | Progressive query computation using streaming architectures |
US20190057097A1 (en) * | 2016-02-05 | 2019-02-21 | Nec Solution Innovators, Ltd. | Information processing device, information processing method, and computer-readable recording medium |
US10740328B2 (en) | 2016-06-24 | 2020-08-11 | Microsoft Technology Licensing, Llc | Aggregate-query database system and processing |
JP6334633B2 (en) * | 2016-09-20 | 2018-05-30 | 株式会社東芝 | Data search system and data search method |
US10552435B2 (en) * | 2017-03-08 | 2020-02-04 | Microsoft Technology Licensing, Llc | Fast approximate results and slow precise results |
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US5950189A (en) * | 1997-01-02 | 1999-09-07 | At&T Corp | Retrieval system and method |
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JP3952043B2 (en) * | 2004-06-14 | 2007-08-01 | 株式会社日立製作所 | Analysis equipment |
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2004
- 2004-10-05 US US10/957,671 patent/US7617186B2/en active Active
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2005
- 2005-10-05 WO PCT/US2005/035764 patent/WO2006041886A2/en active Application Filing
- 2005-10-05 AU AU2005294416A patent/AU2005294416A1/en not_active Abandoned
- 2005-10-05 EP EP05801975A patent/EP1820123A4/en not_active Withdrawn
- 2005-10-05 CA CA002580687A patent/CA2580687A1/en not_active Abandoned
- 2005-10-05 JP JP2007534900A patent/JP5176012B2/en active Active
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Also Published As
Publication number | Publication date |
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JP5176012B2 (en) | 2013-04-03 |
EP1820123A2 (en) | 2007-08-22 |
US20060074882A1 (en) | 2006-04-06 |
WO2006041886A3 (en) | 2007-05-03 |
AU2005294416A1 (en) | 2006-04-20 |
CA2580687A1 (en) | 2006-04-20 |
JP2008516313A (en) | 2008-05-15 |
US7617186B2 (en) | 2009-11-10 |
EP1820123A4 (en) | 2009-02-18 |
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