Lecture: Mathematics of Big Data and Machine Learning
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- Опубликовано: 6 авг 2024
- MIT RES.LL-005 D4M: Signal Processing on Databases, Fall 2012
View the complete course: ocw.mit.edu/RESLL-005F12
Instructor: Jeremy Kepner
Jeremy Kepner talked about his newly released book, "Mathematics of Big Data," which serves as the motivational material for the D4M course.
License: Creative Commons BY-NC-SA
More information at ocw.mit.edu/terms
More courses at ocw.mit.edu
I'm an older person and I am learning this from scratch and find it fascinating and fulfilling.
great sir may i know how old are you
加油！！
Thanks MIT for free education
Thank you MIT for such high quality courses.
Thank you for bringing order to the chaos of this world and making it freely available for us to attempt to engage with.
Fixed an edit error. One of the slides was out-of-order with the video. Specifically, the slide at 1:42 to 6:18 was supposed to be a white circle on a black background.
Wow
Is this video from a newer version of the course? If yes, will all the videos be made available?
@@Avinash-vr7vq This is not a newer version of the course, just an addition to the series. See the course on MIT OpenCourseWare for the materials at: ocw.mit.edu/RESLL-005F12.
If this is supposed to be a video about mathematics, why do you make claims that cannot be proved and claim that everyone knows them?
Thank you so much. If you're involved in making this content available to us. Thank you.
Thank you so much! It was a real pleasure to watch and to think through.
Well, there are many asking where is the full course? Here is the playlist: ruclips.net/p/PLUl4u3cNGP62DPmPLrVyYfk3-Try_ftJJ
Enjoy :)
Thanks, MIT for the free lecture 😊
"Curve fitting without domain knowledge" the best tagline ever for AI ;)
Surely you mean curve over-fitting with an excessively large number of parameters ;)
Maeda Toshiie
What do you mean by “an excessively large number of parameters”?
Hahaha, exactly!
@Digital Nomad you need domain data to do curve fitting, not necessarily domain knowledge
I love it when scientists talk about Philosophy. Science takes you closer to reality, and philosophy takes you closer to the truth of this reality.
That's a beautiful way to put it. Saving this. Thanks!
Hmmm.... Sounds cool but I don't know. What is truth? Isn't reality a simulation in our brains?
@@nueythepyasuwan The truth is "we don't know, whether reality is simulation in our brain or everything including us is a simulation in one giant brain". Allegory of Cave poses a great question along with many others "the one who has been outside the cave, thinks he has found the truth, but is it not possible that he has just seen a bigger cave and cocluded that he has seen the truth?".
what are your view on kashmir ?
here it is where you perception of reality and philosoply breaks . lmao
@@user-gj7nd7rb4v Kashmir's is a complicated situation. What about a heart-break, what about when someone abuses us, what about when someone wrongs us. Our perception of reality and philosophy breaks even in these situations, because we allow it to. But remember our perception changes, reality and truth itself do not change.
Great video this was awesome! Thanks for the free learning!
Thank you for sharing this!
Thanks for uploading this🙏
thanks MIT
MIT D4M ... Searching this phrase finds other videos with the RUclips viewer. The search phrase comes from the video information directly below the video.
For interested: AISOMA AI Showreel: Real World Use Cases & Demos with Python: ruclips.net/video/dgGAJQ8sKf8/видео.html
Amazing lecture!
Thanks a lot MIT.
Interesting about how Caltech and MIT approaches ML math cores differently
;-; love the open course
wow... this is from 2012, and here we are at the end of 2018 and still learning. Just shows how far MIT is ahead in the game.
Unless he saw the future and knew about the elephant in 2015 (18:21), I don't think this is Fall 2012 xD
lol
This is not research level stuff. The theory is over three centuries old.
37:18
Jimmy Garzon
Very old stuff.
18:20 OMG I love the reference of "Le petit Prince"
I didnt get back propagation. How it works, moreever what it is.
All the instructers i have saw so far looks like they grasped the content.
Here Mr. Jeremy says most of the people just play with numbers. That gave me courage to have my own 'idea' about what is going on:
It is like having preconception about something at first. And building backup to the them as you perceive valuable data. Until preconceptions are no more needed.
Well thats my bias for deep learning. I can change it as i learn more
Say the answer to a question was 5 and you answered 2. You would then look at 5 and say, hey, I have an error of 3. However in this case you are not allowed to change your first guess. So you BACKPROPAGATE and change your guess to 2.1. And see that your error is now 2.9. You keep back-propagating till your error is 0 or close to zero.
Why the troublesome way? Why not just backpropagate and change the answer to 5 since you know the error is 3? Because in Neural Nets / Deep Neural Nets / Deep Learning. ALL those neurons are interconnected hence a small change in ur answer AFTER BACKPROPAGATING affects the other neurons hence affects the Output.
Hope that helped :)
*BACKPROPERGATE - literally means Moving (Propagate) Back
@@sheikhimraniskandar3774 Hi Imran. Glad to see a comment. I mixed different words to intensify and it sound like representing different things in the end i guess :) it is a good thing.
1Energine1
I think if you read your reply out loud, it will sound more complicated than necessary. Why not just point the poor lads to some old numerical analysis books about predictor-corrector methods for numerical “solutions” of differential equations and say “it’s a bit like that, but more complicated because of a variety of interdepencies between the component neurons”.
Hi MIT, why was this course archived. I am just a huge fan of Jeremy Keplar. He is an awesome researcher and makes stuff so exciting.
The course was updated. The redirect should have been updated too. We'll fix the link. In the meantime, here's where you can find the material now: ocw.mit.edu/resources/res-ll-005-mathematics-of-big-data-and-machine-learning-january-iap-2020/. Best wishes on your studies!
It's a great lecture ! I just wish if we could also get problems or assignments related to whatever has been taught.
We have lecture notes, maybe that might of some help. See the course on MIT OpenCourseWare for the materials at: ocw.mit.edu/RESLL-005F12.
Many thanks!
Thanks!!!
2:33 Perfect circles definitely would exist in nature. E.g. Please take a look at a hot cup of coffee after adding some butter to it. The butter drops form circles that 'look' perfect. So ideally, with pure ingredients we have a shot at having those perfect circles at the periphery of oil drops .
Sam T
It’s a fundamental tenet (i.e. an Axiom) of modern scientific thought that in such a circumstance the object you call a circle here does not exist, as it is only an approximation to a collection of discrete point that we might label as “molecules” or “atoms”, because we may believe that those spatial locations are “occupied by” individual molecules of either butter or the coffee, and most of what you think is the “material” composing an “actual ideal circle” is so-called “empty space”., and in fact, due to Brownian Motion and the Uncertainty Principle, even the better approximation, consisting of a regular n-gon where is is very large (the number of molecules “lying on” your “ideal circle”) is a figment of your imagination, in part because it could not remain as a physically realized object long enough for you to verify that claim, nor could you verify it without making it not so by merely your effort to make a measurement or observation. Besides, according to that scientific axiomatic system, even if that thing you might think is an n-gon, where n is an obscenely large integer, exists as an ideal object in our universe that reasonably approximates the “actual shape” of the “rings” you mention, those molecules are arranged not in a plane in three-space, even ever so briefly, much less in space-time, so that the claim, that such “rings” as those you mention are “perfect circles” or “ideal circles” or “perfect n-gons” or “ideal n-gons”, runs philosophically afoul of modern physics theories altogether. Whether or not those modern physics theories are “true” or “accurate descriptions of nature” is a debate in which all parties views are just as tenuous as your own expressed here.
@@hardworker5263 👍🏼🙏🏼
Or an SVG of a circle (they're not pixels lol)
So if you bring your butter bubble down to the molecular level, it would not be a perfect circle. How could it be?
Someone else mentioned the uncertainty principle: yes, that's a point even further... which gets at the sub atomic level.
Or maybe I'm not understanding your butter bubble comment.
I wish I could work with this dope man
Thanks MIT
I love this and want the book but can't afford it rn.
make 2 neural networks. one with only 2 layers but millions of neurons, one with only 2 neurons and millions of layers. whichever one makes more accurate predictions would likely signal which area is more important to neural computation
Laurence, I like your theory. But in practicality how would you do it?
If you have more depth into your theory I would be really glad to communicate with you more on this.
@@TheTechRancher no more depth other then years IT experience and some common sense problem solving, but I wish i could redo uni and do a data science degree. I don't even know where to start when it comes to learning about this stuff
@Laurence Evans, I'm a self-taught developer. Yes, a degree in Data Science will definitely help but you can find jobs that don't require degrees in Data or Computer Sciences. Just a Degree helps. There are some (and not all) good online training courses to get a good understanding of Data Science.
datacamp.com/
Data Camp to gave example. Or
treehouse.com/
Tree House.
Both I have used. To get to all the courses you have to pay a monthly fee but worth it.
But I like your Theory still. Not very practical but I still like it.
Oh, study up on math!! If you are going into this field. Calculus, Advanced Calculus, and Linear Algebra.
@@TheTechRancher seriously - thankyou. Data camp and the rest was just what I was looking for
Thanks
is it easy to understand ??? Did you get a full picture of machine learning in the end???
ty
Please inform where are other videos on this series (Mathematics of Big Data and Machine Learning
)
ocw.mit.edu/resources/res-ll-005-d4m-signal-processing-on-databases-fall-2012/index.htm
@@ThiagoRamosal thanks
Thanks @@@ThiagoRamosal
I find the title to be misleading. This course is 80%, if not more, about working with d4m, the library for Matlab developed by the professor, doing different analytics with it on some sample data.
Yes, this is course is about using D4M. As the description states, the resource is named "D4M: Signal Processing on Databases." :)
Could you tell me perhaps the part of the course with the "Mathematics of Big Data & Machine Learning"
Thanks still good material of world AI.
I didn't see how the mathematics (such as linear algebra rules or properties) of big data is actually different from mathematics of non- big data in this video, which titled "Mathematics of Big Data and Machine Learning". Can anybody offer a quick answer?
JL D
The linear Algebra is almost the same, except that the vector spaces are finite dimensional and the focus is on computational algorithms and efficiency.
The scope is essential, too. The idea is that most of the linear algebra concepts are not really used. As Hard Worker said, it's all about efficiency.
Efficiency is important, but I believe scalability is much more important in big data applications.
lol 😂
Really? Which vector spaces are infinite dimensional, in your opinion? Not in most science courses, in my experience. In fact, most science courses that should use the theory of vector spaces at all swipe at it like a drunken kitten playing with what it thinks is a ball of yarn.
In rigorous approaches to classical data analysis, one would typically consider “low dimensional” (dimension less than 1000, I guess) vector spaces and their associated infinite dimensional function spaces.
In a reasonably rigorous approach to the analysis of “big data”, one would usually use “high dimensional” (but still finite dimensional) vector spaces and their associated infinite dimensional function spaces.
Essentially, one assumes that the data lie on a finite dimensional manifold in some parameter space of fairly low dimension in both cases, but in “big data” analysis, one decides that a significant reduction of dimension (via, for example, PCA) to a related parameter space or change of coordinates is untenable or unreliable, and that more of the data points must be treated as statistically significant than in classical data analysis, and so the difficulties of the computational aspects of these kinds of problems are more tediously nuanced. However, also involved in the decision to treat a problem as a “big data” problem is the observation that (a) more data is available than in many classical data analytics situations and (b) greater computational power of more modern computational devices and paradigms are available than what are assumed in classical data analytics in low dimensional parameter spaces.
The drawing of the elephant inside a snake, is it adopted from the book The Prince? It looks awfully similar to the drawing in the book
Fire exit obstructed with a drawing board
The reference to the Little Prince
he is citing work from 2013 but the class says fall 2012. Something is obviously wrong. :P
Yeah, the textbook used for the course was published this year.
37:18
If you look at the first few seconds of the video, it has 2018 written. Also, it shows 2018 on the website.
thank god, it has a subtitles. I mean, thank MIT.
Finally enrolled in MIT😊😊🙏
Proud of the family.
Big deal. Try Caltech.
Degree data solution three three three 3 = 3 * 3
Great guy talks about great stuff and all the students just sit there without any reaction
Zlatan Onkovic
Universal university student reactions to any lecture.
kirwi kirwinson
If he cut the amount of information in half and made one joke he would quadruple the enrollment, and garnish praise from a couple more administrators, and might get to teach an extra advanced course the next time he asks for it.
@@hardworker5263 damn Hard Worker ur a menace out here in these comments. I respect it though.
To be fair, the lecturer's presentation here was sort of flat. At least to my ears.
Needlessly fuzzy, unhelpful analogies, and a lot of uhhhs and ummms.
Someone will disagree. To each their own I suppose...
i can describe the whole semester of ml in one week and this lesson in one minute.They look like they watch the apocalypse. Student years what a waste of time, the simplest thing goes for days and hours
Student years are what you make of them. I’m sure this guy would love to make this lesson, and all of his lectures, deeper, more detailed, more meaningful, more rigorous, and more useful, but if he did, all the students would drop the class and go find someone whose lectures aren’t at all challenging or deep.
“...Shove me in the shallow waters
Before I get too deep...”
~Edie Brickell and the New Bohemians
Skip to 19:10
I Love You
Why?
I am from India love you 😘
How this is from Fall 2012 and in the lecture says 2015 when talking about Deep Learning?
Time travel, sir.
There is a mistake in the video description - it is from 2018 (check the first 3 seconds of the video).
Yeay
Meat starts around 12:30.
Hi MIT how to get in MIT
See mitadmissions.org/apply/ for admissions info. Good luck!
Is that Brad Pitt from The Big Short?
I wonder if he knows who Marvin Minsky is.....would not call him a young guy in that he was born in 1929 and died in 2016....
Why first bench are empty ?
Many people would like to sit there.
Maybe because of neck strain because of constantly looking up
You only need to be in the room to hear and see the knowledge presented in this lecture.
STUDENTS HEAD GETS IN THE WAY OF BOARD AND CAMERA VIEW ....
Rakesh Dhami
lol 😂
You really think so?
www.urbandictionary.com/define.php?term=Back%20row%20baptist
sounds quite void. you have to pay for that?
I know. Maybe just fools the students into believing they are getting their money's worth.
Ron Class
I doubt it. The students first fool the admins into thinking they (the students) know more about education and about what should be taught than their professors. The admins and their legal teams fire all professors who try to give students a significant course and guys like this guy acquiesce once they see that their plans for a good and rigorous course will be trashed anyway by the C level and lower students, whose opinions drive the administrative decisions about salaries and promotions and hiring and firing.
@@hardworker5263 Man, what are you one about? Make it simpler......
A circle? Oh shit, this is advanced.
Thisisnotmyrealname8
No. It’s even more advanced than that, because he assumes that you understand enough physics and mathematics to be able to prove on your own that there is no circle.
“...there is no spoon...”
~ Spoon Boy (played by Rown Witt) in The Matrix
Oh, my God, his idea is like God's idea. And I could understand it easily also.
At 2:36, he claims something then I doubt he can prove. Specifically he claims that no perfect circle exist in nature. While I believe that he is correct that no perfect circle exist in nature, I doubt that anyone actually knows that.
00:10
Big Stikk
?
"You will experience negative inputs"
😟😧😦 is he training real working artificial intelligence?
Mistake in video description: video footage is from 2018 not 2012.
Yeah rip Socrates for doing philosophy
when was it filmed?
Fall 2012 - as per the description. The video was already published in the past; this version fixes a video editing error (see note from the publisher).
@@mdp5337 but he referred to a 2013 paper
@@adelaidekhayon2631 Sorry, I cannot find a reference to "2013" in the transcript below... A stochastic check seems to also confirm that the transcript below matches this video, and it the URL again refers to "Fall 2012". Where is that reference?
ocw.mit.edu/resources/res-ll-005-d4m-signal-processing-on-databases-fall-2012/class-videos/mathematics-for-big-data-and-machine-learning/iCAZLl6nq4c.srt
@@mdp5337 36:00 the reference if I got it right
@@adelaidekhayon2631 those slides are superimposed in post-production. There may have been posterior alterations there (updated slides).
This is s stand-up philosopher ala History of the World
Anyone from MIT?
Yes! My son is at MIT now!
12:03 lmao
Culture
Do you mean 12:06?
第一排的小姐姐是我的
37:05 The girl on the second row to the left, is falling asleep. Well, why? Because this lecture is FAR away from people's normal expectation on the Mathematics of Big data and machine learning.
You are right! As it could never be that she is working her ass off for a degree and is probably on a 3-4 hours of sleep constantly.
@@nqkoisi123 You are absolutely right since you are a genius.
beyond.twisted.meadows
You forgot about her eight hours per night playing COD and WOW, and the ten experiments in the physics lab that she’s managing for her senior honors thesis about synchronized firing of neurons as compared to their artificial neural network counterparts.
He claims that no ideal circle exists in nature. He in fact claims that we all know that.
Can he prove that claim?
I doubt it.
ahhh ahora entiendo de que garcha estan hablando...
lol
At about 10:44, he says the distributive law “makes math linear”. The effort to dumb this valuable topic down to be digested by anti-mathematical programmers is palpably putrid. Mathematics is decidedly NOT linear. Linear algebra studies the consequences of restricting oneself to linear processes in mathematics, and analysis, including Advanced Calculus, Real Analysis, etc, studies, among other things, the consequences of restricting one’s attention to locally linearizable phenomena. What these students need to study is a rigorous course in analysis and it’s applications, including numerical methods an analysis of numerical algorithms. The lack of rigor here is the problem. The discussion of philosophy is interesting, and might help the students if they pay attention, but in my experience students tend to yawn and avoid philosophical studies in favor of doing trivial problems and arguing about the grades.
@1Energine1 Your reply does not assuage my concerns about the dumbing down of the subject matter. There is absolutely NO SENSE in which the distributive law "makes math linear". However, if one does want to use linear algebra to solve some problems, one certainly should know the distributive law for arithmetic in the scalar field (or in the scalar ring, in case the linear algebra one needs to use is the theory of modules).
Of course linear algebra is a useful tool, but it is also a beautiful subject in its own right. Butchering its content is neither useful nor beautiful. Waxing philosophical out of one side of one's mouth while out the other side sweeping under the rug the need to be true to the facts and theory of the subject, is monstrously incongruous.
Why would anyone use calculus to do linear regression except in a dumbed down statistics course? Your example adds fuel to my fire. The only reason anyone ever thought about using partial differentiation to justify the formulas for the coefficients ina linear regression problem is that the students in the baby numerical methods course one is tasked to laboriously waste time on are underprepared because they aren't taught linear algebra before linear regression, and their major departments have dumbed down the curricula. I have a nice linear regression problem for you:
Estimate the year when a typical engineering degree at university in the USA will require zero credit hours, instead of the 120 to 125 credit hours that is commonly required currently. To obtain your estimate, collect data from engineering colleges in the USA between 1900 and now, and use linear regression to find a least squares linear fit.
With a few data points, my students in a sophomore course are able by the end of the term to obtain an estimate, and the standing estimate now is sometime around 2039.
This is the travesty of modern attitudes toward fundamental subjects and rigor, and the idea that you would accost me with the notion that I would be in the camp of people who would waste time using partial derivatives to justify such an important technique as linear regression is laughable, considering that you make a pretense of having understood what I wrote.
Nonlinear systems are becoming even more important now, and to understand them properly, one must understand linear systems as well. New, more effective and more efficient computational tools are being developed because of the growing interest in nonlinear algebra. Examples include the use of Gröbner bases (see en.wikipedia.org/wiki/Gr%C3%B6bner_basis), Tropical Algebra (math.berkeley.edu/~bernd/mathmag.pdf), Semidefinite Programming (en.wikipedia.org/wiki/Semidefinite_programming), Max-Plus Algebra (www.inria.fr/en/teams/maxplus), etc. In many cases, these require a seriously clean understanding of linear algebra as a fundamental bridge from freshman mathematics to advanced computational mathematical sciences, and statements like "distributivity makes the math linear" are dangerously obfuscatory in their pretense to facilitate understanding through placation of the anti-mathematical masses.
@@WriteRightMathNation thank you for commenting on this video and your reply (to someone's comment, now removed). I tried accessing the two wiki links you posted and the other two but none of them are valid anymore. Just an fyi.
I find that odd tho. Hmmm
the chinese girl dosing off lol
Nerrrrrrrds
what he shows at 9:35 is not an equation....it is an equality!!!!!
I was not able to bear this boring lecture....!
The expression he shows is an equation and it expresses a claim of equality that is verifiable in the arithmetic structure of the natural numbers, so I don’t understand why your panties are in a bunch.
These kids are paying big bucks to waist their time listening to this guy.
Should we pay to listen to you who cannot spell the verb 'waste' correctly. Also, a criticism is a broad statement that needs specific examples or explanations to be deemed credible. You should remember that the credibility of your statements reflect your own credibility.
E.S.A.D.
Mr. Jacobs - what is that you have to offer that Prof. Kepner doesn't offer to us.
Please share your research material and or your published articles demonstrating your intellectual superiority over Prof. Kepner.
absolutely boring.. for people never heard of math before.. is there a kindergarten at mit ?! :)
Data Science is marketing crap this stuff has been around for century at least.
Michael Jacobs
Three centuries...
yep cant see any value here!! LOL open your mind
have a look at siemens internet of things and machine learning based production tehcniques (reporting 18%+ increases in efficiencies of certain factories)