Moni nonse! Dzina langa ndine Sasha, ndine CTO & Co-Founder ku LoyaltyLab. Zaka ziwiri zapitazo, ine ndi anzanga, mofanana ndi ophunzira onse osauka, tinapita madzulo kukagula moŵa m’sitolo yapafupi pafupi ndi nyumba yathu. Tinakhumudwa kwambiri kuti wogulitsa, podziwa kuti tidzabwera ku mowa, sanapereke kuchotsera pa chips kapena crackers, ngakhale izi zinali zomveka! Sitinamvetsetse chifukwa chake izi zikuchitika ndipo tinaganiza zoyambitsa kampani yathu. Chabwino, monga bonasi, dzipatseni kuchotsera Lachisanu lililonse pa tchipisi zomwezo.

Ndipo zonse zidafika poti ndikuwonetsa zinthu paukadaulo wazogulitsa NVIDIA GTC. Ndife okondwa kugawana ntchito yathu ndi anthu ammudzi, kotero ndikusindikiza lipoti langa m'nkhani.

Mau oyamba

Monga wina aliyense koyambirira kwa ulendowu, tidayamba ndikuwunika momwe ma recommender systems amapangidwira. Ndipo zomanga zodziwika kwambiri zidakhala zamtundu uwu:

Lili ndi magawo awiri:

1. Sampula ofuna kuyamikira pogwiritsa ntchito chitsanzo chosavuta komanso chachangu, nthawi zambiri chogwirizana.
2. Kuyika kwa osankhidwa omwe ali ndi mtundu wovuta kwambiri komanso wodekha, poganizira zonse zomwe zingatheke mu data.

Pambuyo pake ndigwiritsa ntchito mawu awa:

• wosankhidwa / wosankhidwa kuti avomereze - gulu lazogulitsa zomwe zitha kuphatikizidwa muzolimbikitsa popanga.
• ofuna m'zigawo / Sola / ofuna m'zigawo njira - ndondomeko kapena njira yopezera "omwe akulangizidwa" kuchokera ku deta yomwe ilipo.

Gawo loyamba limaphatikizapo kugwiritsa ntchito mitundu yosiyanasiyana ya kusefa kwachigwirizano. Wotchuka kwambiri - ALS. Ndizodabwitsa kuti zolemba zambiri zokhudzana ndi machitidwe a recommender zimangowonetsa kusintha kosiyanasiyana kwa zitsanzo zogwirira ntchito pagawo loyamba, koma palibe amene amalankhula zambiri za njira zina zachitsanzo. Kwa ife, njira yogwiritsira ntchito zitsanzo zogwirizanitsa zokha ndi kukhathamiritsa kosiyanasiyana nazo sizinagwire ntchito ndi khalidwe lomwe tinkayembekezera, choncho tinafufuza kafukufuku makamaka pa gawo ili. Ndipo kumapeto kwa nkhaniyi ndikuwonetsa momwe tinatha kuwongolera ALS, yomwe inali maziko athu.

Ndisanapitirire kufotokoza njira yathu, ndikofunika kuzindikira kuti muzovomerezeka zenizeni, pamene kuli kofunika kuti tiganizire zomwe zinachitika mphindi 30 zapitazo, palibe njira zambiri zomwe zingagwire ntchito panthawi yofunikira. Koma, kwa ife, tiyenera kusonkhanitsa malingaliro osaposa kamodzi patsiku, ndipo nthawi zambiri - kamodzi pa sabata, zomwe zimatipatsa mwayi wogwiritsa ntchito zitsanzo zovuta ndikuwongolera khalidwe kangapo.

Tiyeni titenge ngati zoyambira zomwe ma metric okha ALS amawonetsa pantchito yochotsa ofuna. Ma metrics ofunikira omwe timawunika ndi awa:

• Kulondola - kuchuluka kwa anthu osankhidwa bwino kuchokera kwa omwe asankhidwa.
• Kumbukirani ndi kuchuluka kwa osankhidwa omwe anachitika mwa omwe anali mu nthawi yomwe mukufuna.
• F1-score - F-muyeso wowerengedwa pa mfundo ziwiri zam'mbuyo.

Tiwonanso ma metric amtundu womaliza pambuyo polimbikitsa kukwera kwapamwamba ndi zina zowonjezera. Palinso ma metric akulu atatu apa:

• precision@5 - kuchuluka kwazinthu zochokera pamwamba pa 5 malinga ndi kuthekera kwa wogula aliyense.
• response-rate@5 - kutembenuka kwamakasitomala kuchokera paulendo wopita kusitolo kukagula zinthu zosachepera zamunthu imodzi (zogulitsa 5 pakuperekedwa kumodzi).
• avg roc-auc pa wogwiritsa ntchito - avareji roc-auc kwa wogula aliyense.

Ndikofunika kuzindikira kuti ma metric onsewa amayezedwa kutsimikizika kwanthawi yayitali, ndiko kuti, maphunziro amapezeka m'masabata oyambirira a k, ndipo k + 1 sabata imatengedwa ngati deta yoyesera. Choncho, kukwera ndi kutsika kwa nyengo kunali ndi zotsatira zochepa pa kutanthauzira kwa khalidwe la zitsanzo. Kupitilira pa ma graph onse, abscissa axis iwonetsa nambala ya sabata pakutsimikizika, ndipo axis yolumikizana idzawonetsa mtengo wa metric yomwe yatchulidwa. Ma grafu onse amachokera ku deta yochokera kwa kasitomala mmodzi kotero kuti kufananitsa pakati pa wina ndi mzake ndikolondola.

Tisanayambe kufotokoza njira yathu, choyamba timayang'ana zoyambira, zomwe ndi chitsanzo chophunzitsidwa ndi ALS.
Ma metric otengera ofuna kubweza:

Ma metric omaliza:

Ndikuwona kukhazikitsidwa kwa ma algorithms onse ngati mtundu wina wamalingaliro abizinesi. Chifukwa chake, mwachisawawa, chitsanzo chilichonse chogwirizana chingaganizidwe ngati lingaliro lakuti "anthu amakonda kugula zomwe anthu ofanana nawo amagula." Monga ndanenera kale, sitinangokhalira kuwerengera motere, ndipo apa pali malingaliro ena omwe amagwira ntchito bwino pazamalonda pa intaneti:

1. Zomwe ndagula kale.
2. Zofanana ndi zomwe ndidagula kale.
3. Nthawi yogula kale.
4. Zotchuka ndi gulu/mtundu.
5. Kugula kwina kwazinthu zosiyanasiyana sabata ndi sabata (unyolo wa Markov).
6. Zogulitsa zofanana ndi ogula, malinga ndi mawonekedwe opangidwa ndi mitundu yosiyanasiyana (Word2Vec, DSSM, etc.).

Mudagulapo chiyani?

Chodziwika bwino kwambiri chomwe chimagwira ntchito bwino m'magolosale. Apa timatenga zinthu zonse zomwe mwini khadi la kukhulupirika adagula m'masiku otsiriza a K (nthawi zambiri masabata 1-3), kapena K masiku chaka chapitacho. Pogwiritsa ntchito njirayi yokha, timapeza ma metric awa:

Apa ndi zodziwikiratu kuti tikatenga nthawi yayitali, timakumbukira kwambiri komanso timakhala ndi zolondola mochepera komanso mosiyana. Pafupifupi, "masabata a 2 otsiriza" amapereka zotsatira zabwino kwa makasitomala.

Zofanana ndi zomwe ndidagula kale

N'zosadabwitsa kuti pa malonda ogulitsa "zomwe ndinagula kale" zimagwira ntchito bwino, koma kuchotsa ofuna okha kuchokera ku zomwe wogwiritsa ntchito wagula kale sizozizira kwambiri, chifukwa sizingatheke kudabwitsa wogula ndi chinthu china chatsopano. Chifukwa chake, tikupangira kuti tiwongolere pang'ono izi pogwiritsa ntchito mitundu yogwirizana. Kuchokera pamavekita omwe tidalandira pamaphunziro a ALS, titha kupeza zinthu zofanana ndi zomwe wogwiritsa ntchito adagula kale. Lingaliro ili ndilofanana kwambiri ndi "mavidiyo ofanana" muzochita zowonera kanema, koma popeza sitikudziwa zomwe wogwiritsa ntchito akudya / kugula panthawi inayake, tikhoza kungoyang'ana zofanana ndi zomwe adagula kale, makamaka. popeza Ife Tikudziwa kale momwe zimagwirira ntchito. Pogwiritsa ntchito njirayi pazamalonda m'masabata 2 apitawa, timapeza ma metric awa:

ndi k - kuchuluka kwa zinthu zofananira zomwe zabwezedwa pa chinthu chilichonse chomwe wogula wagula m'masiku 14 apitawa.
Njirayi idagwira ntchito bwino kwambiri kwa kasitomala wathu, yemwe kunali kofunikira kuti asavomereze chilichonse chomwe chinali kale m'mbiri yogula.

Nthawi yogula mochedwa

Monga tadziwira kale, chifukwa cha kuchuluka kwafupipafupi kwa katundu wogula, njira yoyamba imagwira ntchito bwino pa zosowa zathu zenizeni. Koma bwanji za katundu monga wochapira ufa/shampoo/ etc. Ndiko kuti, ndi zinthu zomwe sizingatheke kufunikira sabata iliyonse kapena ziwiri komanso zomwe njira zam'mbuyomu sizingachotse. Izi zimatsogolera ku lingaliro lotsatirali - likuyenera kuwerengera nthawi yogula chinthu chilichonse pafupifupi kwa makasitomala omwe adagula chinthucho kwambiri. k kamodzi. Kenako chotsani zomwe wogulayo akuyenera kuti zatha. Nthawi zowerengedwera za katundu zitha kuyang'aniridwa ndi maso anu kuti zikukwanira:

Kenako tiwona ngati kutha kwa nthawi yazinthuzo kugwera mkati mwa nthawi yomwe malingaliro apanga ndikupanga ndikuwonetsa zomwe zimachitika. Njirayi ikhoza kufotokozedwa motere:

Pano tili ndi milandu yayikulu iwiri yomwe ingaganizidwe:

1. Kodi ndikofunikira kuyesa zinthu kuchokera kwa makasitomala omwe agula zinthu zosakwana K nthawi.
2. Kodi ndikofunikira kuyesa chinthu ngati kutha kwa nthawi yake kusanayambike nthawi yomwe mukufuna.

Chithunzi chotsatirachi chikuwonetsa zotsatira zomwe njirayi imapeza ndi ma hyperparameter osiyanasiyana:

ft - Tengani makasitomala okhawo omwe agula malonda osachepera K (pano K=5) nthawi
tm - Tengani osankhidwa okha omwe akugwera mkati mwa nthawi yomwe mukufuna

N’zosadabwitsa kuti akutha (0, 0) chachikulu timakumbukira ndi chaching'ono molondola, popeza pansi pa chikhalidwe ichi osankhidwa ambiri amatengedwa. Komabe, zotsatira zabwino zimatheka pamene ife si chitsanzo mankhwala kwa makasitomala amene anagula mankhwala ena osachepera k nthawi ndi kuchotsa, kuphatikizapo katundu, kutha kwa nthawi yomwe imagwera nthawi yomwe chandamale isanafike.

Zotchuka ndi gulu

Lingaliro lina lodziwikiratu ndikuyesa zinthu zotchuka m'magulu osiyanasiyana kapena mitundu. Apa tikuwerengera wogula aliyense pamwamba-k "zokondedwa" magulu/mitundu ndikuchotsa "zotchuka" mugululi. Kwa ife, tidzasankha "zokondedwa" ndi "zotchuka" ndi chiwerengero cha kugula kwa mankhwala. Ubwino wowonjezera wa njirayi ndikugwiritsa ntchito kwake poyambira kuzizira. Izi ndizo, kwa makasitomala omwe agula zochepa kwambiri, kapena sanapite ku sitolo kwa nthawi yaitali, kapena angopereka khadi lokhulupirika. Kwa iwo, ndizosavuta komanso kwabwino kugulitsa zinthu zomwe zimakonda makasitomala komanso zomwe zili ndi mbiri. Zotsatira zake ndi:

Apa nambala pambuyo pa mawu akuti "gulu" amatanthauza mlingo wa zisa za gulu.

Ponseponse, sizosadabwitsanso kuti magulu ocheperako amapeza zotsatira zabwino, chifukwa amatulutsa zolondola "zokonda" za ogula.

Kugula kwazinthu zosiyanasiyana sabata ndi sabata

Njira yosangalatsa yomwe sindinayiwone m'nkhani zokhuza machitidwe a recommender ndi njira yosavuta komanso nthawi yomweyo yowerengera ma unyolo a Markov. Apa timatenga masabata a 2, ndiye kwa kasitomala aliyense timapanga zinthu ziwiri [ogulidwa m’sabata i]-[ogulidwa m’sabata j], pamene j > i, ndipo kuchokera apa timawerengera chinthu chilichonse mwayi wosinthira ku chinthu china sabata yamawa. Ndiko kuti, pa katundu aliyense producti-productj Timawerengera chiwerengero chawo mu awiriawiri opezeka ndikugawa ndi chiwerengero cha awiriawiri, kumene mankhwala anali mu sabata yoyamba. Kuti tichotse ofuna, timatenga risiti yomaliza ya wogula ndikuchotsa pamwamba-k zomwe mwina zikubwera kuchokera ku matrix osinthika omwe tidalandira. Njira yopangira kusintha kwa matrix ikuwoneka motere:

Kuchokera pazitsanzo zenizeni za kusintha kwa kuthekera kwa matrix tikuwona zochitika zosangalatsa zotsatirazi:

Apa mutha kuwona kudalira kosangalatsa komwe kumawululidwa pamachitidwe ogula: mwachitsanzo, okonda zipatso za citrus kapena mtundu wa mkaka womwe amatha kusintha kupita ku wina. Ndizosadabwitsanso kuti zinthu zomwe zimagulidwa pafupipafupi, monga batala, zimathera pano.

Ma metrics munjira ndi unyolo wa Markov ndi awa:

k - kuchuluka kwazinthu zomwe zimatengedwa pa chinthu chilichonse chomwe chagulidwa kuchokera pakuchita komaliza kwa wogula.
Monga tikuonera, zotsatira zabwino zikuwonetsedwa ndi kasinthidwe ndi k=4. Kukwera mu sabata 4 kumatha kufotokozedwa ndi machitidwe anyengo patchuthi. 

Zogulitsa zofanana ndi ogula, molingana ndi mikhalidwe yomangidwa ndi mitundu yosiyanasiyana

Tsopano tafika ku gawo lovuta kwambiri komanso losangalatsa - kufunafuna oyandikana nawo apafupi kutengera ma vector a makasitomala ndi zinthu zopangidwa molingana ndi mitundu yosiyanasiyana. Mu ntchito yathu timagwiritsa ntchito mitundu itatu yotere:

• ALS
• Word2Vec (Item2Vec yantchito zotere)
• DSSM

Tachita kale ndi ALS, mutha kuwerenga momwe imaphunzirira apa. Pankhani ya Word2Vec, timagwiritsa ntchito kukhazikitsidwa kodziwika bwino kwachitsanzo kuchokera genim. Poyerekeza ndi zolembazo, timatanthauzira zoperekedwa ngati risiti yogulira. Chifukwa chake, popanga vekitala yazinthu, chitsanzocho chimaphunzira kulosera za chinthucho mu risiti "chinthu" chake (zotsalira zomwe zili mu risiti). Mu data ya ecommerce, ndibwino kugwiritsa ntchito gawo la wogula m'malo mwa risiti; anyamata ochokera Ozon. Ndipo DSSM ndiyosangalatsa kwambiri kulongosola. Poyamba, idalembedwa ndi anyamata ochokera ku Microsoft ngati chitsanzo chakusaka, Mutha kuwerenga pepala lofufuzira loyambirira pano. Kapangidwe kachitsanzo kakuwoneka motere:

ndi Q - funso, kusaka kwa ogwiritsa ntchito, D[i] - chikalata, tsamba la intaneti. Kulowetsa kwachitsanzo ndi zomwe zapempha ndi masamba, motsatira. Pambuyo pa gawo lililonse lolowera pali zigawo zingapo zolumikizidwa (multilayer perceptron). Kenaka, chitsanzocho chimaphunzira kuchepetsa cosine pakati pa ma vector omwe amapezeka m'magawo otsiriza a chitsanzo.
Ntchito zolangizira zimagwiritsa ntchito zomangamanga zomwezo, m'malo mwa pempho pali wogwiritsa ntchito, ndipo m'malo mwa masamba pali zinthu. Ndipo kwa ife, zomanga izi zimasinthidwa kukhala zotsatirazi:

Tsopano, kuti muwone zotsatira zake, ikuyenera kuphimba mfundo yomaliza - ngati pa ALS ndi DSSM tafotokozera momveka bwino ma vectors ogwiritsira ntchito, ndiye kuti pa Word2Vec timangokhala ndi ma vectors a mankhwala. Apa, kuti tipange vekitala ya ogwiritsa ntchito, tafotokoza njira zazikulu zitatu:

1. Ingowonjezerani ma vector, ndiye pa mtunda wa cosine zimakhala kuti tidangowerengera zomwe zidachitika mumbiri yogula.
2. Vector mwachidule ndi kulemera kwa nthawi.
3. Kuyeza katundu ndi TF-IDF coefficient.

Pankhani ya kulemera kwa mzere wa vekitala wogula, timachokera ku lingaliro lakuti chinthu chomwe wosuta adagula dzulo chimakhala ndi chikoka chachikulu pa khalidwe lake kusiyana ndi zomwe adagula miyezi isanu ndi umodzi yapitayo. Chifukwa chake timaganizira sabata yapita ya wogulayo ndi 1, ndi zomwe zidachitika motsatira ½, ⅓, ndi zina zotero.

Kwa ma coefficients a TF-IDF, timachita chimodzimodzi monga mu TF-IDF pamalemba, timangowona wogula ngati chikalata, ndi cheke ngati chopereka, motsatana, mawuwo ndi chinthu. Mwanjira iyi, vekitala ya wogwiritsa ntchitoyo imasunthira kwambiri kuzinthu zachilendo, pomwe zinthu zomwe zimachitika pafupipafupi komanso zodziwika bwino kwa wogula sizingasinthe kwambiri. Njirayi ikhoza kufotokozedwa motere:

Tsopano tiyeni tiwone ma metric. Izi ndi zomwe zotsatira za ALS zimawonekera:

Ma metric a Item2Vec okhala ndi mitundu yosiyanasiyana yomanga vekitala yogula:

Pachifukwa ichi, njira yofanana ndendende imagwiritsidwa ntchito monga momwe timayambira. Kusiyana kokha ndi k titi tigwiritse ntchito. Kuti mugwiritse ntchito mitundu yogwirizana yokha, muyenera kutenga pafupifupi 50-70 zinthu zapafupi kwambiri kwa kasitomala aliyense.

Ndipo ma metrics molingana ndi DSSM:

Kodi kuphatikiza njira zonse?

Chabwino, mukuti, koma chotani ndi zida zazikulu zotere zochotsera anthu? Momwe mungasankhire kasinthidwe koyenera kwa data yanu? Nazi mavuto angapo:

1. Ndikofunikira kuti mwanjira ina muchepetse malo osakira ma hyperparameter munjira iliyonse. Ndizowona, zodziwikiratu kulikonse, koma kuchuluka kwa mfundo zomwe zingatheke ndizazikulu kwambiri.
2. Pogwiritsa ntchito njira yaying'ono yocheperako yokhala ndi ma hyperparameter apadera, mungasankhire bwanji masinthidwe abwino kwambiri a metric yanu?

Sitinapezebe yankho lolondola ku funso loyamba, kotero timapitirira kuchokera ku zotsatirazi: pa njira iliyonse, malo ofufuzira a hyperparameter amalembedwa, malingana ndi ziwerengero zina zomwe tili nazo. Chifukwa chake, podziwa nthawi yayitali pakati pa kugula kuchokera kwa anthu, titha kuganiza kuti ndi nthawi yanji yoti tigwiritse ntchito "zomwe zidagulidwa kale" ndi "nthawi yogula kale".

Ndipo titatha kudutsa chiwerengero chokwanira cha mitundu yosiyanasiyana ya njira zosiyanasiyana, timawona zotsatirazi: kukhazikitsidwa kulikonse kumatulutsa chiwerengero cha anthu omwe akufuna kukhala nawo ndipo kumakhala ndi mtengo wina wamtengo wapatali kwa ife (kumbukirani). Tikufuna kupeza chiwerengero cha osankhidwa, kutengera mphamvu zathu zovomerezeka zamakompyuta, ndi metric yothekera kwambiri. Apa vuto mokongola kugwera mu vuto chikwama.

Apa chiwerengero cha osankhidwa ndi kulemera kwa ingot, ndipo njira yokumbukira ndiyo mtengo wake. Komabe, pali mfundo zina ziwiri zomwe ziyenera kuganiziridwa mukamagwiritsa ntchito algorithm:

• Njira zitha kukhala zogwirizana ndi omwe amawapeza.
• Nthawi zina, kudzakhala kolondola kutenga njira imodzi kawiri ndi magawo osiyanasiyana, ndipo kutulutsa kwa phungu kuchokera koyamba sikukhala gawo lachiwiri.

Mwachitsanzo, ngati titenga kukhazikitsidwa kwa njira ya "zomwe ndagula kale" ndi nthawi zosiyanasiyana zobweza, ndiye kuti magulu awo a anthu omwe akufuna kukhala nawo adzakhazikika pakati pawo. Nthawi yomweyo, magawo osiyanasiyana "ogula nthawi ndi nthawi" potuluka samapereka mphambano yathunthu. Chifukwa chake, timagawaniza njira zotsatsira ndi magawo osiyanasiyana kukhala midadada kuti kuchokera mu block iliyonse tikufuna kutenga njira imodzi yochotsa ndi ma hyperparameter ena. Kuti muchite izi, muyenera kukhala ochenjera pang'ono pakukwaniritsa vuto la knapsack, koma ma asymptotics ndi zotsatira zake sizisintha.

Kuphatikiza kwanzeru kumeneku kumatithandiza kupeza ma metrics otsatirawa poyerekeza ndi mitundu yogwirizana chabe:

M'ma metrics omaliza tikuwona chithunzi chotsatirachi:

Komabe, apa mutha kuwona kuti pali mfundo imodzi yomwe idavumbulutsidwa pamalangizo omwe ndi othandiza pabizinesi. Tsopano tangophunzira momwe tingachitire ntchito yabwino yolosera zomwe wogwiritsa ntchito adzagula, mwachitsanzo, sabata yamawa. Koma kungopereka kuchotsera pa chinthu chomwe adzagula kale sikozizira kwambiri. Koma ndizabwino kukulitsa chiyembekezo, mwachitsanzo, pazotsatira zotsatirazi:

1. Malire/chiwongola dzanja kutengera zomwe mukufuna.
2. Chiyerekezo chamakasitomala.
3. Kuchuluka kwa maulendo.

Chifukwa chake timachulukitsa zomwe tapeza ndi ma coefficients osiyanasiyana ndikuziyikanso kuti zinthu zomwe zimakhudza ma metric omwe ali pamwambapa afike pamwamba. Palibe yankho lokonzekera lomwe liyenera kugwiritsidwa ntchito. Timayesanso ma coefficients oterowo popanga. Koma apa pali njira zosangalatsa zomwe nthawi zambiri zimatipatsa zotsatira zabwino:

1. Chulukitsani ndi mtengo/malire a chinthucho.
2. Chulukitsani ndi chiphaso chapakati chomwe chimawonekera. Kotero katundu adzabwera, zomwe nthawi zambiri amatenga chinthu china.
3. Chulukitsani ndi kuchuluka kwa maulendo omwe ogula malondawa amayendera, kutengera malingaliro akuti mankhwalawa amapangitsa anthu kuti azibwerera pafupipafupi.

Titayesa ndi ma coefficients, tidapeza ma metric awa pakupanga:

ndi kutembenuka kwazinthu zonse - gawo lazinthu zogulidwa pazogulitsa zonse zomwe tidapanga.

Wowerenga mwachidwi adzawona kusiyana kwakukulu pakati pa ma metric a pa intaneti ndi pa intaneti. Khalidweli likufotokozedwa ndikuti sizinthu zonse zosefera zosinthika zomwe zingalimbikitsidwe zitha kuganiziridwa pophunzitsa chitsanzocho. Kwa ife, ndi nkhani yabwinobwino pamene theka la omwe adabwezeredwa atha kusefedwa; izi ndizomwe zimachitika m'makampani athu.

Pankhani ya ndalama, nkhani yotsatirayi imapezeka, zikuwonekeratu kuti pambuyo pa kukhazikitsidwa kwa malingaliro, ndalama za gulu loyesa zikukula kwambiri, tsopano kuwonjezeka kwapakati pa ndalama ndi malingaliro athu ndi 3-4%:

Pomaliza, ndikufuna kunena kuti ngati mukufuna malingaliro omwe sianthawi yeniyeni, ndiye kuti kuwonjezeka kwakukulu kwaubwino kungapezeke pakuyesa ndikuchotsa ofuna kuvomereza. Kuchuluka kwa nthawi kwa mbadwo wawo kumapangitsa kuti azitha kuphatikiza njira zambiri zabwino, zomwe zonse zidzapereka zotsatira zabwino pa bizinesi.

Ndidzakhala wokondwa kucheza mu ndemanga ndi aliyense amene apeza mfundo zosangalatsa. Mutha kundifunsa mafunso panokha pa uthengawo. Ndimagawananso malingaliro anga okhudza AI / zoyambira mu wanga telegram channel -olandiridwa :)

Source: www.habr.com