Towards modeling implicit feedback with quantum entanglement

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Transcription:

Towards modeling implicit feedback with quantum entanglement Massimo Melucci Talk by Emanuele Di Buccio Department of Information Engineering University of Padua Quantum Interaction Oxford, UK, 26th 28th March 2008

1 Information Retrieval 2 Towards a Model of Implicit Feedback 3 Decomposition 4 A Methodology for Implicit Feedback 5 Concluding Remarks

Information Retrieval Concerned with retrieving all and only the documents relevant to any information need of any user Intrinsically dependent on - the user - the task the user is performing Difficulty of obtaining queries well designed for retrieval purpose - vague information need - limited experience in the search environment

Relevance Feedback Relevance information explicitly provided by the user used to - suggest query expansion terms - retrieve new search results - dynamically reorder existing results Effective but: - high user effort - benefit not always apparent How to remove the burdens of traditional RF?

Implicit Relevance Feedback Alternative: Implicit Relevance Feedback (IRF) Using contextual features generated during user-information interaction Example of contextual features: display time, bookmarking, saving, printing, scrolling Requires a software tool which - monitors subject behavior - uses these interaction data as a source of IRF

Modeling Implicit Feedback Abstraction of the software tool to automate the feedback process Geometric Framework proposed in [1] to model Implicit Feedback - considers multiple source of evidence - personalized for each user - tailored for each search task Framework revisited with some QM concepts according to the proposal originally reported in [2] where QM was proposed for tackling the problem of IR [1] M. Melucci and R. W. White. Utilizing a geometry of context for enhanced implicit feedback. In Proceedings of the ACM Conference on Information and Knowledge Management (CIKM), pp. 273 282, Lisbon, Portugal, November 2007. [2] C.J. van Rijsbergen. The Geometry of Information Retrieval. Cambridge University Press, New York, 2004.

Towards a Model of Implicit Feedback

Towards a Model of Implicit Feedback User-document interaction Information Retrieval

Towards a Model of Implicit Feedback User-document interaction Document A Information Retrieval A visited document or the visit of the document

Towards a Model of Implicit Feedback User-document interaction Document A User B Information Retrieval A visited document or the visit of the document B user, i.e. assessment the user provides about the document

Towards a Model of Implicit Feedback User-document interaction Document A interaction User B Information Retrieval A visited document or the visit of the document B user, i.e. assessment the user provides about the document AB user document interaction as a composite system

Towards a Model of Implicit Feedback User-document interaction A B Document A interaction User B Information Retrieval A visited document or the visit of the document B user, i.e. assessment the user provides about the document AB user document interaction as a composite system relationship between A and B?

Towards a Model of Implicit Feedback User-document interaction A B Document A interaction User B Information Retrieval A visited document or the visit of the document B user, i.e. assessment the user provides about the document AB user document interaction as a composite system relationship between A and B? Quantum Mechanics

Towards a Model of Implicit Feedback User-document interaction A B Document A interaction User B φ A Information Retrieval A visited document or the visit of the document B user, i.e. assessment the user provides about the document AB user document interaction as a composite system relationship between A and B? Quantum Mechanics φ A abstraction of the visited document reduced to a vector

Towards a Model of Implicit Feedback User-document interaction A B Document A interaction User B φ A φ B Information Retrieval A visited document or the visit of the document B user, i.e. assessment the user provides about the document AB user document interaction as a composite system relationship between A and B? Quantum Mechanics φ A abstraction of the visited document reduced to a vector φ B abstraction of the user who visited the document reduced to a vector

Towards a Model of Implicit Feedback User-document interaction A B Document A interaction User B φ A φ AB φ B Information Retrieval A visited document or the visit of the document B user, i.e. assessment the user provides about the document AB user document interaction as a composite system relationship between A and B? Quantum Mechanics φ A abstraction of the visited document reduced to a vector φ B abstraction of the user who visited the document reduced to a vector φ AB interaction between A and B element of A B

Towards a Model of Implicit Feedback User-document interaction A B Document A interaction User B φ A φ AB φ B Information Retrieval A visited document or the visit of the document B user, i.e. assessment the user provides about the document AB user document interaction as a composite system relationship between A and B? Quantum Mechanics φ A abstraction of the visited document reduced to a vector φ B abstraction of the user who visited the document reduced to a vector φ AB interaction between A and B element of A B φ AB entangled or separable?

Schmidt Decomposition Bipartite System AB Bipartite pure state φ AB separable iff can be written as φ AB = φ A φ B In general φ AB is written in any orthonormal product basis { i A j B } as N A N B φ AB = C ij i A j B i=0 j=0 where C ij element of a matrix C Schmidt Decomposition Theorem There always exists a product bi-orthonormal basis { e i A ej B } where λ i nonzero singular eigenvalues of C. min{n A,N B } φ AB = λ i ea i ei B i λ i : obtained by Singular Value Decomposition of C C = BΛA λ i = {Λ} i,i Schmidt Number: number of nonzero singular eigenvalues of C

A Methodology for Implicit Feedback Possible Methodology 1 preparation of the interaction data 2 computation of a contingency matrix 3 decomposition of the contingency matrix 4 analysis of entanglement

A Methodology for Implicit Feedback Possible Methodology 1 preparation of the interaction data 2 computation of a contingency matrix 3 decomposition of the contingency matrix 4 analysis of entanglement

A Methodology for Implicit Feedback Possible Methodology 1 preparation of the interaction data 2 computation of a contingency matrix 3 decomposition of the contingency matrix 4 analysis of entanglement Interaction Data subset of the document features of the dataset

A Methodology for Implicit Feedback Possible Methodology 1 preparation of the interaction data 2 computation of a contingency matrix 3 decomposition of the contingency matrix 4 analysis of entanglement Interaction Data subset of the document features of the dataset - display time - bookmark - saving - access frequency - scrolling

A Methodology for Implicit Feedback Possible Methodology 1 preparation of the interaction data 2 computation of a contingency matrix 3 decomposition of the contingency matrix 4 analysis of entanglement Interaction Data subset of the document features of the dataset - display time - bookmark - saving - access frequency - scrolling usefulness scores assigned to each document

A Methodology for Implicit Feedback Possible Methodology 1 preparation of the interaction data 2 computation of a contingency matrix 3 decomposition of the contingency matrix 4 analysis of entanglement

A Methodology for Implicit Feedback normalization of the dataset Possible Methodology 1 preparation of the interaction data 2 computation of a contingency matrix 3 decomposition of the contingency matrix 4 analysis of entanglement

A Methodology for Implicit Feedback Possible Methodology 1 preparation of the interaction data 2 computation of a contingency matrix 3 decomposition of the contingency matrix 4 analysis of entanglement normalization of the dataset choice of a subset of subject IDs and a subset of task IDs

A Methodology for Implicit Feedback Possible Methodology 1 preparation of the interaction data 2 computation of a contingency matrix 3 decomposition of the contingency matrix 4 analysis of entanglement normalization of the dataset choice of a subset of subject IDs and a subset of task IDs selection of the five features for each subject

A Methodology for Implicit Feedback Possible Methodology 1 preparation of the interaction data 2 computation of a contingency matrix 3 decomposition of the contingency matrix 4 analysis of entanglement normalization of the dataset choice of a subset of subject IDs and a subset of task IDs selection of the five features for each subject computation of the average value of every feature from the tuples of the chosen subject and task identifiers

A Methodology for Implicit Feedback Possible Methodology 1 preparation of the interaction data 2 computation of a contingency matrix 3 decomposition of the contingency matrix 4 analysis of entanglement normalization of the dataset choice of a subset of subject IDs and a subset of task IDs selection of the five features for each subject computation of the average value of every feature from the tuples of the chosen subject and task identifiers grouping average values by usefulness score into a binary scale

A Methodology for Implicit Feedback Possible Methodology 1 preparation of the interaction data 2 computation of a contingency matrix 3 decomposition of the contingency matrix 4 analysis of entanglement normalization of the dataset choice of a subset of subject IDs and a subset of task IDs selection of the five features for each subject computation of the average value of every feature from the tuples of the chosen subject and task identifiers grouping average values by usefulness score into a binary scale normalization of the obtained 2 5 matrix

A Methodology for Implicit Feedback Possible Methodology 1 preparation of the interaction data 2 computation of a contingency matrix 3 decomposition of the contingency matrix 4 analysis of entanglement

A Methodology for Implicit Feedback Possible Methodology 1 preparation of the interaction data 2 computation of a contingency matrix 3 decomposition of the contingency matrix 4 analysis of entanglement

Example - All subjects and All tasks C = display time bookmark saving frequency scrolling 0.162 0.066 0.020 0.037 0.004 useless 0.201 0.082 0.025 0.043 0.005 useful

Example - All subjects and All tasks C = display time bookmark saving frequency scrolling 0.162 0.066 0.020 0.037 0.004 useless 0.201 0.082 0.025 0.043 0.005 useful Decomposition of the contingency matrix: SVD of C C = BΛA [ ] 0.9999 0.0000 0.0000 0.0000 0.0000 Λ = 0.0000 0.0059 0.0000 0.0000 0.0000 A = display time bookmark saving frequency scrolling 0.902 0.182 0.108 0.375 0.023 0.367 0.074 0.033 0.927 0.007...

Example - All subjects and All tasks C = display time bookmark saving frequency scrolling 0.162 0.066 0.020 0.037 0.004 useless 0.201 0.082 0.025 0.043 0.005 useful [ 0.9999 0.0000 0.0000 0.0000 0.0000 Λ = 0.0000 0.0059 0.0000 0.0000 0.0000 Analysis of the Entanglement λ 1,1 = 0.9999 1 Schmidt Decomposition φ AB 1 A 1 B all the subjects and tasks: A B is a product state vector is entanglement somehow related to the subject or to the task? ]

Example - Subject 1 and Task 1 C = display time bookmark saving frequency scrolling 0.158 0.094 0.052 0.110 0.835 useless 0.014 0.128 0.052 0.256 0.411 useful

Example - Subject 1 and Task 1 C = display time bookmark saving frequency scrolling 0.158 0.094 0.052 0.110 0.835 useless 0.014 0.128 0.052 0.256 0.411 useful Decomposition of the contingency matrix: SVD of C C = BΛA [ ] 0.94 0.00 0.00 0.00 0.00 Λ = 0.00 0.33 0.00 0.00 0.00 A = display time bookmark saving frequency scrolling 0.145 0.243 0.053 0.188 0.939 0.031 0.473 0.092 0.827 0.288...

Example - Subject 1 and Task 1 C = display time bookmark saving frequency scrolling 0.158 0.094 0.052 0.110 0.835 useless 0.014 0.128 0.052 0.256 0.411 useful Analysis of the Entanglement [ 0.94 0.00 0.00 0.00 0.00 Λ = 0.00 0.33 0.00 0.00 0.00 Second singular value is significantly greater than 0 Schmidt number is significantly greater than 1 φ AB is entangled ]

Concluding Remarks and Open Issues User-document interaction A B Document A interaction User B φ A φ AB φ B User visiting a document state of the system (A) is the pure state of the observable which describes the measurement of the style of interaction User assessing the usefulness of a document the state of the system (B) is to the pure state of the observable that describes the measurement of usefulness State of A B separable measurement of a property does not influence the state of the other observable What happens if the composite state of A B is entangled?

Open Issues When the composite state of A B is entangled - how does the state of B behave? - what pure state of B does it collapse to? When does the collapse occur, given that it occurs? Entanglement used to verify the existence of a relationship between user and information. How to use it for retrieval purpose?

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