Harvard CS50’s Artificial Intelligence with Python – Full University Course - Ep57

is like some audiowaveforms and learn python for aithose audio waveforms areof course dependent upon this hiddenState and you can infer based on thoseaudio waveforms what the words spokenlikely were but you might not know with100% certainty what that hidden Stateactually is and it might be a task totry and predict given this observationgiven given these audio waveforms canyou figure out what the actual wordsspoken are likewise you might imagine ona website true user engagement might beinformation you don't directly haveaccess to but you can observe data likewebsite or app analytics about how oftenwas this button clicked or how often arepeople interacting with a page in aparticular way and you can use that toinfer things about your users as well sothis type of problem comes up all thetime when we're dealing with AI andtrying to infer things about the worldthat often AI doesn't really know thathidden true state of the world all theAI has access to is some observationthat is related to the hidden true statebut it's not direct there might be somenoise there the audio waveform mighthave some additional noise that might bedifficult to parse the sensor data mightnot be exactly correct there's somenoise that might not allow you toconclude with certainty what the hiddenstate is but can allow you to infer whatit might be and so the simple examplewe'll take a look at here is Imaginingthe hidden State as the weather whetherit's sunny or rainy or not and imagineyou are uh programming an AI inside of abuilding that maybe has access to just acamera to inside the building and allyou have access to is an observation asto whether or not employees are bringingan umbrella into the building or not youcan detect whether it's an umbrella ornot and so you might have an observationas to whether or not an umbrella isbrought into the building or not andusing that information you want topredict whether it's sunny or rainy evenif you don't know what the underlyingweather is so the underlying weathermight be sunny or rainy and if it'sraining obviously people are more likelyto bring an umbrella and so whether ornot people bring an umbrella yourobservation tells you something aboutthe hidden State and of course this is abit of a contrived example but the ideahere is to think about this more broadlyin terms of more generally Anytime Youobserve something it having to do withsome underlying hidden State and so totry and model this type of idea where wehave these hidden States andobservations rather than just use amarov model which has state state statestate Each of which is connected by thattransition Matrix that we descriedbefore we're going to use what we call ahidden marov model very similar to amarov model but this is going to allowus to Model A system that has hiddenstates that we don't directly observealong with some observed event that wedo actually see and so in addition tothat transition model that we still needof saying you know given the underlyingstate of the world if it's sunny orrainy what's the probability oftomorrow's weather we also need anothermodel that given some state is going togive us an observation of like green yessomeone brings an umbrella into theoffice or red no nobody brings umbrellasinto the office and so the observationmight be that if it's sunny then oddsare nobody's going to bring an umbrellato the office but maybe some people arejust being cautious and they do bring anumbrella to the office anyways and ifit's raining then with much higherprobability then people are going tobring umbrellas into the office butmaybe if the rain was unexpected peopledidn't bring an umbrella and so theymight have some other probability aswell so using the observations you canbegin to predict with reasonablelikelihood what the underlying state iseven if you don't actually get toobserve the underlying state if youdon't get to see what the hidden stateis actually equal to this here we'lloften call the sensor model uh it's Alalso often called the emissionprobabilities because the state theunderlying State emits some sort ofemission that you then observe and sothat can be another way of describingthat same idea and the sensor Markovassumption that we're going to use isthis an assumption that the evidencevariable the thing we observe theemission that gets produced depends onlyon the corresponding State meaning I canpredict whether or not people will bringumbrellas or not entirely dependent juston whether it is sunny or rainy today ofcourse again this assumption might nothold in practice that in practice itmight depend whether or not people bringumbrellas might depend not just ontoday's weather but also on yesterday'sweather and the day before but forsimplification purposes it can behelpful to apply this sort of assumptionjust to allow us to be able to reasonabout these probabilities a little moreeasily and if we're able to approximateit we can still often get a very goodanswer and so what these hidden marovmodels end up looking like is a littlesomething like this where now ratherthan just have one chain of States likesun sun rain rain rain we instead havethis upper level which is the underlyingstate of the world is it sunny or is itrainy and those are connected by thattransition Matrix we described beforebut each of these States produces anemission produces an observationthat I see that on this day it was sunnyand people didn't bring umbrellas and onthis day it was sunny but people didbring umbrellas and on this day it wasraining and people did bring umbrellasand so on and so forth and so each ofthese underlying States represented by Xsubt for X sub1 012 so on and so forthproduces some sort of observation oremission which is what the E stands fore subz e sub 1 E sub 2 so on and soforth and so this too is a way of tryingto represent this idea and what you wantto think about is that these underlyingstates are the true nature of the worldthe robot's position as it moves overtime and that produces some sort ofsensor data that might be observed orwhat people are actually saying andusing the emission data of what audiowaveforms you detect in order

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