A hybrid quantum-classical recommender system. Andrea Skolik

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Mikołaj Stachowiak
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1 A hybrid quantum-classical recommender system Andrea Skolik

A recommender system built on matrix factorization got inspired by nonnegative/binary matrix factorization at Qubits 2018 [1] Q: where can we apply NBMF on D-Wave in a Volkswagen context?

2 A recommender system built on matrix factorization got inspired by nonnegative/binary matrix factorization at Qubits 2018 [1] Q: where can we apply NBMF on D-Wave in a Volkswagen context? A: recommendations for users of the VW configurator [1] O Malley D, Vesselinov VV, Alexandrov BS, Alexandrov LB (2018) Nonnegative/Binary matrix factorization with a D-Wave quantum annealer. PLoS ONE 13(12): e

3 SEAT configurator data data of car purchases data includes color packages, accessories, one-hot encoded categorical features turned them into user ratings 0: no purchase, 5: purchase

4 V<latexit sha1_base64="vhmoshlrlaeh741qcsochs+lhde=">aaab6hicbzc7swnbembn4ivgv9tszjeivuhorhsxagozghlacos9zvyyzm/v2n0twhgwt7fqxnz/xt7o/8bno9dedxz+fn8moznbirg2rvvt5fzw19y38pufre2d3b3i/kfdx6liwgexifurobofl1g33ahsjqppfahsbsobsd58qkv5lo/mkee/on3jq86osvat0s2w3li7fvkgbw6lq8/c5smavlvfr04vzmme0jbbtw57bml8jcrdmcbxoznqtcgb0j62luoaofaz6abjcmkdhgljzz80zor+7shoppuocmxlrm1al2yt87+snzrwws+4tfkdks0+clnbtewmw5mev8imgfmgthe7k2edqigz9jyfewrvcevlajyvpbfs1dxs5rpmysmrhmmpehaofbifktsbacitvmcrc+88o2/o+6w058x7dugpni8filioow==</latexit> <latexit sha1_base64="nxheu69umqddkpok5y7okjtntnk=">aaab6hicbzc7sgnbfibpeo3rlwppmxgeq7bro40ytlfmwfwgcwf2cjyzmzu7zmwkyckt2fgoyqspy28jvo2ts6gjpwx8/p85zdknsatxxvo+naxlldw19dygu7m1vbob39uv6thvdkssfrfqbfsj4bkrhhubjuqhjqkb9wbwpc7r96g0j+wtgsbyjmhp8pazaqxvqxxyba/otuqwwz9b4fldvujev9xyj//z6sysjvaajqjwtd9ltdujynamcos2uo0jzqpaw6zfsspu7wwy6igcw6dlwljzjw2zul87mhpppywcwxlr09fz2dj8l2umjjxvz1wmquhjph+fqsamjuotszcrzeymlvcmuj2vsd5vlbl7g9cewz9ferfqp0xfk/ovr1c6gqlycahhcai+neejbqamvwca8abp8ozcoy/oi/m6lv1yzj0h8efo2w8sr5ax</latexit> <latexit sha1_base64="nxheu69umqddkpok5y7okjtntnk=">aaab6hicbzc7sgnbfibpeo3rlwppmxgeq7bro40ytlfmwfwgcwf2cjyzmzu7zmwkyckt2fgoyqspy28jvo2ts6gjpwx8/p85zdknsatxxvo+naxlldw19dygu7m1vbob39uv6thvdkssfrfqbfsj4bkrhhubjuqhjqkb9wbwpc7r96g0j+wtgsbyjmhp8pazaqxvqxxyba/otuqwwz9b4fldvujev9xyj//z6sysjvaajqjwtd9ltdujynamcos2uo0jzqpaw6zfsspu7wwy6igcw6dlwljzjw2zul87mhpppywcwxlr09fz2dj8l2umjjxvz1wmquhjph+fqsamjuotszcrzeymlvcmuj2vsd5vlbl7g9cewz9ferfqp0xfk/ovr1c6gqlycahhcai+neejbqamvwca8abp8ozcoy/oi/m6lv1yzj0h8efo2w8sr5ax</latexit> <latexit sha1_base64="bk4aozpvsnjfgdmb/oozznvig0w=">aaab6hicbvbnt8jaej3if+ix6thlrmliibre9ej04hescytqko0yhzxtttndmpcgx+dfg8z49sd589+4qa8kvmssl/dmmjmvtaxxxnw/ndlg5tb2tnm3srd/chhupt5p6yrtdh2wier1q6prcim+4uzgn1vi41bgj5zczf3oeyrne/lgpikgmr1jhnfgjzva7ug15tbdbcg68qpsgwlnqfwrp0xyfqm0tfcte56bmicnynamcfbpzxptyiz0hd1ljy1rb/ni0bm5smqqrimyjq1zql8nchprpy1d2xltm9ar3lz8z+tljrojci7tzkbky0vrjohjypxrmuqkmrftsyht3n5k2jgqyoznpmjd8fzfxiftq7rn1r2ww2vcfngu4qzo4ri8uiyg3emtfgca8ayv8oy8oi/ou/oxbc05xcwp/ihz+qoxcyzw</latexit> Nonnegative matrix factorization minimise error = V (W H)

5 Nonnegative matrix factorization size determined by tunable parameter relates features to customers relates features to products

6 How are ratings inferred? We don t only want to reconstruct, but also predict values. Regularisation don t want to learn exact representation of the training data regularisation terms blur the original data Biases some customers buy only the minimum in accessories, others like to configure every detail some features are especially popular, others bought only rarely incorporate these biases in the data into predictions Koren, Yehuda, Robert Bell, and Chris Volinsky. "Matrix factorization techniques for recommender systems." Computer 8 (2009):

7 Regularisation Add a regularisation term to the update rule: non-zero entries of controls extent of regularisation Koren, Yehuda, Robert Bell, and Chris Volinsky. "Matrix factorization techniques for recommender systems." Computer 8 (2009):

Biases Add aspects that are independent of any interaction between customers and products: global bias, mean of all values in training data Learn additional value for each customer and

8 Biases Add aspects that are independent of any interaction between customers and products: global bias, mean of all values in training data Learn additional value for each customer and for each product: approximation error of prediction Koren, Yehuda, Robert Bell, and Chris Volinsky. "Matrix factorization techniques for recommender systems." Computer 8 (2009):

9 V<latexit sha1_base64="vhmoshlrlaeh741qcsochs+lhde=">aaab6hicbzc7swnbembn4ivgv9tszjeivuhorhsxagozghlacos9zvyyzm/v2n0twhgwt7fqxnz/xt7o/8bno9dedxz+fn8moznbirg2rvvt5fzw19y38pufre2d3b3i/kfdx6liwgexifurobofl1g33ahsjqppfahsbsobsd58qkv5lo/mkee/on3jq86osvat0s2w3li7fvkgbw6lq8/c5smavlvfr04vzmme0jbbtw57bml8jcrdmcbxoznqtcgb0j62luoaofaz6abjcmkdhgljzz80zor+7shoppuocmxlrm1al2yt87+snzrwws+4tfkdks0+clnbtewmw5mev8imgfmgthe7k2edqigz9jyfewrvcevlajyvpbfs1dxs5rpmysmrhmmpehaofbifktsbacitvmcrc+88o2/o+6w058x7dugpni8filioow==</latexit> <latexit sha1_base64="nxheu69umqddkpok5y7okjtntnk=">aaab6hicbzc7sgnbfibpeo3rlwppmxgeq7bro40ytlfmwfwgcwf2cjyzmzu7zmwkyckt2fgoyqspy28jvo2ts6gjpwx8/p85zdknsatxxvo+naxlldw19dygu7m1vbob39uv6thvdkssfrfqbfsj4bkrhhubjuqhjqkb9wbwpc7r96g0j+wtgsbyjmhp8pazaqxvqxxyba/otuqwwz9b4fldvujev9xyj//z6sysjvaajqjwtd9ltdujynamcos2uo0jzqpaw6zfsspu7wwy6igcw6dlwljzjw2zul87mhpppywcwxlr09fz2dj8l2umjjxvz1wmquhjph+fqsamjuotszcrzeymlvcmuj2vsd5vlbl7g9cewz9ferfqp0xfk/ovr1c6gqlycahhcai+neejbqamvwca8abp8ozcoy/oi/m6lv1yzj0h8efo2w8sr5ax</latexit> <latexit sha1_base64="nxheu69umqddkpok5y7okjtntnk=">aaab6hicbzc7sgnbfibpeo3rlwppmxgeq7bro40ytlfmwfwgcwf2cjyzmzu7zmwkyckt2fgoyqspy28jvo2ts6gjpwx8/p85zdknsatxxvo+naxlldw19dygu7m1vbob39uv6thvdkssfrfqbfsj4bkrhhubjuqhjqkb9wbwpc7r96g0j+wtgsbyjmhp8pazaqxvqxxyba/otuqwwz9b4fldvujev9xyj//z6sysjvaajqjwtd9ltdujynamcos2uo0jzqpaw6zfsspu7wwy6igcw6dlwljzjw2zul87mhpppywcwxlr09fz2dj8l2umjjxvz1wmquhjph+fqsamjuotszcrzeymlvcmuj2vsd5vlbl7g9cewz9ferfqp0xfk/ovr1c6gqlycahhcai+neejbqamvwca8abp8ozcoy/oi/m6lv1yzj0h8efo2w8sr5ax</latexit> <latexit sha1_base64="bk4aozpvsnjfgdmb/oozznvig0w=">aaab6hicbvbnt8jaej3if+ix6thlrmliibre9ej04hescytqko0yhzxtttndmpcgx+dfg8z49sd589+4qa8kvmssl/dmmjmvtaxxxnw/ndlg5tb2tnm3srd/chhupt5p6yrtdh2wier1q6prcim+4uzgn1vi41bgj5zczf3oeyrne/lgpikgmr1jhnfgjzva7ug15tbdbcg68qpsgwlnqfwrp0xyfqm0tfcte56bmicnynamcfbpzxptyiz0hd1ljy1rb/ni0bm5smqqrimyjq1zql8nchprpy1d2xltm9ar3lz8z+tljrojci7tzkbky0vrjohjypxrmuqkmrftsyht3n5k2jgqyoznpmjd8fzfxiftq7rn1r2ww2vcfngu4qzo4ri8uiyg3emtfgca8ayv8oy8oi/ou/oxbc05xcwp/ihz+qoxcyzw</latexit> NBMF on D-Wave We can put in QUBO form by constraining it to binary values only and constructing a QUBO for each column. O Malley D, Vesselinov VV, Alexandrov BS, Alexandrov LB (2018) Nonnegative/Binary matrix factorization with a D-Wave quantum annealer. PLoS ONE 13(12): e

10 Optimisation task on D-Wave We want to optimise each column of such that turn into QUBO O Malley D, Vesselinov VV, Alexandrov BS, Alexandrov LB (2018) Nonnegative/Binary matrix factorization with a D-Wave quantum annealer. PLoS ONE 13(12): e

11 Customer 994 Model: SEAT LEON CUPRA Exterior colour: Urban Silver Interior colour: Magic Black Discount package Rear view camera system Dark tinted side windows Power-adjustable heated and electric SEAT FULL LINK Convenience package rain light Integrated maps SD card w/ Mapcare Adaptive Cruise Control ACC Navigation system Driver assistance pack front camera Interior LED light package Family package curtains DAB Digital Audio Broadcasting Keyless locking and starting system Safety package warning signal on front Recommendation of an alternative color scheme: Exterior colour: Desire Red Interior colour: Rodium Gray 11

12 Customer 44 Model: SEAT LEON ST Exterior colour: Desire Red Interior colour: Deep Black Discount package Rear view camera system Driver assistance pack front camera SEAT FULL LINK SEAT complete LED headlamps w/ sep LED Adaptive Cruise Control ACC Connectivity Box for navigation system Digital instrument cluster 16-inch reduced spare wheel Mapcare integrated maps update Recommendation of additional accessory: Air conditioning system 12

13 Conclusion POC hybrid recommendation system works run on larger dataset iterative algorithms take a long time to execute! 13

14 Thanks for your attention!

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