Mathematics of Machine Learning

Mathematics of Machine Learning


Hello world it’s Suraj and the mathematics of machine learning is it necessary to know math for machine learning Absolutely machine learning is math. It’s all math in this video I’m gonna help you understand. Why we use math in machine learning by example machine learning is all about Creating an algorithm that can learn from data to make a prediction that prediction could be what an object in a picture looks like or What the next price for gasoline might be in a certain country or what the best? Combination of drugs to cure a certain disease might be machine learning is built on mathematical prerequisites and Sometimes it feels like learning them might be a bit overwhelming, but it isn’t or is it no It’s not as long as you understand why they’re used it’ll make machine learning a lot more fun You can have a full time job Doing machine learning and not know a single thing about the math behind the functions you’re using But that’s no fun is it you want to know why something works? And why one model is better than another machine learning is powered by the diamond of? Statistics calculus linear algebra and probability statistics is at the core of everything Calculus tells us how to learn and optimize our model linear algebra makes running these algorithms feasible on massive data sets and Probability helps predict the likelihood of an event occurring So let’s start from scratch with an interesting problem The problem is to predict the price of an apartment in an up-and-coming neighborhood in New York City Let’s say Harlem shout-out to Harlem. Yo Westside represent, okay? let’s say that all we’ll know when we Eventually make a prediction is the price per square foot of a given apartment, that’s the only marker? We’ll use to predict the price of the apartment as a whole and love for us We’ve got a data set of apartments with two columns in the first column We’ve got the price per square foot of an apartment in the second column We’ve got the price of the apartment as a whole there’s got to be some kind of correlation here and if we build a predictive model We can learn what that correlation is so that in the future if all we’re given is the price per square foot of a house We can predict the price of it if we were to graph out this data Let’s graph this out with the x-axis measuring the price per square foot and the y-axis Measuring the price of a house it would be a scatter plot Ideally we could find a line that intersects as many data points as possible and then we could just plug in some input data into our line and out comes the prediction poof in mathematics the field of statistics acts as a collection of techniques that extract useful information From data. It’s a tool for creating an understanding from a set of numbers Statistical inference is the process of making a prediction about a larger population of data based on a smaller sample as in what can we infer about a Populations parameters based on a sample statistic sounds pretty similar to what we’re trying to do right now, right? Since we’re trying to create a line. We’ll use a statistical inference technique called linear regression this allows us to summarize and study the relationship between two variables a lemma one variable X is regarded as the Independent variable the other variable Y is regarded as the dependent variable the way we can represent linear Regression is by using the equation y equals MX plus B Y is the prediction X is the input? B is the point where the line intersects the y-axis and M is the slope of the line We already know what the x value would be and why is our prediction if we had M. And B We would have a full equation plug and play easy prediction, but the question is how do we get these variables? Naive way would be for us to just try out a bunch of different values Over and over and over again and plot the line over time using our eyes We could try and estimate just how well fit the line. We draw is But that doesn’t seem efficient does it we do know there exists some ideal values for M And B such that the line when drawn using those values Would be the best fit for our data set let’s say we did have a bunch of time on our hands And we decided to try out a bunch of predicted values for M. And B we need some way of measuring how good our predicted values are we’ll need to use what’s called an error function an Error function will tell us how far off the actual Y value is from our predicted value There are lots of different types of statistical error functions out there But let’s just try a simple one called least squares This is what it looks like we’ll make an apartment price prediction for each of our data points based on our own intuition We can use this function to double check against the actual apartment price value it will subtract each predicted value from the actual value and Then it will square each of those differences the Sigma that little a looking thing denotes that we are doing this not just for one data point but for Every single data point we have M data points to be specific This is our total error value. We can create a three dimensional graph now We know the x axis and the y axis they will be all the potential m and B values respectively But let’s add another axis the z axis and on the z axis would be all the potential error values for every single combination of M and B if we were to actually graph this out It would look just like this this kind of bowl like shape Cup it firmly in your hand like a nice Bowl if we find that data point at the bottom of the bowl the smallest error value. That would be our ideal m And B values that would give us the line of best fit But how do we actually do that now we need to borrow from the math discipline? as calculus the study of change It’s got an optimization technique called gradient descent that will help us discover the minimum value iteratively It will use the error for a given data point to compute What’s called the gradient of our unknown variable and we can use the gradient to update our two variables? Then we’ll move on to the next data point and repeat the process over and over and over again Slowly like a ball rolling down a bowl. We’ll find what our minimum value is see calculus Helps us find the direction of change in what direction? Should we change the unknown variables MMB in our function such that its? Prediction is more optimal aka the error is smallest, but apartment prices Don’t just depend on the price per square foot right Also included are different features like the number of bedrooms and the number of Bathrooms as well as the average price of homes within a mile if we factored in those features as well our regression line would look More like this there are now multiple variables to consider so we can call it a multivariate regression problem the branch of math concerned with the study of Multivariate spaces and the linear transformations between them is called linear algebra it gives us a set of operations that we can perform on groups of numbers known as matrices our training set now becomes an M by I Matrix of M samples that have I feature x’ instead of a single variable with a weight each of the features has a weight So that’s an example of how three of the four main branches of math dealing with machine learning are used But what about the fourth probability all right? So let’s just scratch this example what if instead of predicting the price of an apartment? We want to predict whether or not it’s in prime condition or not we want to be able to Classify a house with the probability of it being prime or not prime Probability is the measure of likelihood of something we can use a probabilistic technique called logistic? Regression to help us do this since this time our data is categorical as in it has different categories or classes instead of predicting a value or predicting the Probability of an occurrence since the probability goes between 0 and 100 we can’t use an infinitely stretching line We’re left with some threshold passed some point X We are more likely than not looking at a prime house We’ll use an s-shaped curve given by the sigmoid function to do this Once we optimize our function will plug in input data and get a probabilistic class value just like that so to summarize machine learning consists mainly of statistics calculus linear algebra and probability theory Calculus tells us how to optimize linear algebra makes executing algorithms feasible on massive data sets Probability helps predict the likelihood of a certain outcome and statistics tells us what our goal is This week’s coding challenge is to create a logistic regression model from scratch in Python on an interesting data set github links go in the comment section and winners will be announced in a week, please subscribe For more programming videos and for now I’ve got to build Thanks for watching

100 thoughts on “Mathematics of Machine Learning”

  1. My question is, if I m not good or my level is moderate in mathematics, then should I go into A.I or not? Let me to know this? Or which I.T technology should I use?

  2. Man, this is the video which made me really understand where i am standing (in terms of learning) and what needs to be learnt more. Came as a motivation for me. 🙂 🙂

  3. Your voice audio is horribly irritating to ears. Please use a microphone that's smooth enough. And will make your video's audio quite interesting to listen. Or please lower down the gain of your mic.

  4. This was better than many, but still its not good for beginners. I means lot of things are not told detail. I might sound totally stupid with below questions, but I am a beginner
    Q1. How do you get this pink line at 2:55 ?
    Q2. in Y=mx+b, how can X be independent ?
    Q3. In this video where specifically you told about the prediction that was made by algorithm we develop , and how we compare it with the correct data ?

  5. Its the best video for intro.
    But I want to learn these for four mathematics concept because I will start learn machine learning within next 4 or 5 days.
    Have anyone good and complete MOOC or tutorial about this ??

  6. Thanks for this video
    do i have to remember all this concepts while facing Data Analyst interview…?
    any suggestion on how to prepare for data analyst will be helpful..

  7. Thank you Siraj for the clear, accurate, concise and enlightening overview of machine learning. It answers my most fundamental question that is always on my mind, viz., Why am I doing what I am doing? Thanks again!

  8. Michael E. Campbell

    Well done!! The demonstration on linear algebra was exactly the visual I was needing to understand the role of LA in machine learning.

  9. Hi ! Please, does anybody have any idea how to use artificial neural network to "teach" a self-driving car when to steer, to the left or to the right, by which angle… ?
    I’m a beginner in this field, so I chose to work on a very simple model consisting of a car riding on a single-lane road and meeting no obstacles.
    What do you suggest as parameters ?
    Any suggestion of other simple models is welcome. Thank you in advance.

  10. Thanks really awesome thank you appreciate the time you're taken to educate and teach and share your knowledge man, thanks bro so awesome!

  11. At 7:40, it should be “multivariable” regression rather than “multivariate” regression because the latter refers to multiple response variables.

  12. 6:10 .. I feel you bro .. When you took a pause before saying "bowl"..😂🤣.. but yes your videos are great .. entertaining and informative 🔥

  13. Братская Мастерская

    Пиздец я хуй теперь пойму что мне делать, никогда не понимал математику, а тут ML и блять опять "математика важна и математика – это весело" . Ааааааа

  14. Hi friends. On this specific subject (multivariable regression) I recommend everyone to check on Professor Wooldridge's CEO salary case where you can perform a regression on many variables in order to determine how each one explains the dependent variable (CEO's salaries). Go econometrics!

  15. Hey Siraj, recently I have developed interest in learning Data sceince, but my problem is that I have not studied math in my high School and graduation. But I have interest in learning math. Can you please guide me how to start learning math and from where with regards to the Data sceince.

  16. statistics and probability these two topics i have been ignoring since school till college and now when i try to learn ML a topic i am interested in it is comming back to haunt me arghhhhhh
    Any suggestions on how to like em topics and understand em coz the name itself makes my learning mood go off and i don't get anything 🙁

  17. Osmanjan Talipjan

    dude .i am studying at applied math for master degree, graduation thesis is relative with quantum information. but I am also interesting for machine learning. can I learn it?what can I do for start?

  18. But bro in one of your love streams you've said that it isn't necessary to know math what about that? Anyway nice video

  19. Couldn't choose a sub so this'll work
    https://chrome.google.com/webstore/detail/threelly-ai-for-youtube/dfohlnjmjiipcppekkbhbabjbnikkibo

  20. Justine Kyle Rivera

    Hello, what if the current price of the apartment is way higher than the average home within miles away because of it's more lavish than the traditional?

  21. vignesh padmanabhan

    I haven’t seen anyone explaining the use of math in such a wonderful way for machine learning until now. If you could make the Andrew ng ML and DL series with python .. I will be the first to join and I am pretty sure everyone here will join . I really need a course which covers everything overall man .. right from math to programming to algorithms … you never get the right structure anywhere and investing time that way is tough man given the time I have daily .. working and studying after 9pm is tough.. I wanna invest 2 hours of my day for this, if there is a well structured course available. I really wish you do this whole thing.

  22. Hi Siraj! Thank you for your videos! I have a question regarding node.js and python. For machine learning, I really would like to know your view on coding with node.js vs python. I kind of know python but recently heard about the flexibility of node.js. I was about to start learning node.js but in most of your videos (and in many other Machine learning related videos) you mention python. So, now I am really not sure where to start. Should I learn python? or Node.js? (I am planning to hopefully use machine learning for my senior project. So I really want to dedicate my time to the right stuff so as not to take a lot of time. (This is my fear talking after realizing the years I have wasted doing nothing))

  23. The ads for Raid: just buy an ant 🐜 eater and release it your house, instead of spraying chemicals, safer for kids and now you have a new pet

  24. Nice video, i currently studying engineering n i would say that ive done most of the math in my first year….so i just wondering is it enough if i just have the mathematical insight or do i need to master the four mathematical subject to become proficient in this field?… because im quiet familiar with the math but i am no master

  25. sir need ur help.. i am economics graduate(graduated this year ) with masters .. i learned maths economics stats .. but all i have to know how to use it in machine,, so if i only learn pyjthon will it be sufficient for me get a good job,,yeah ill be applying to those companies which demands python knowledge ,,

  26. You should give English subtitles in your video so that person like me can understand the whole thing because I am weak in understanding English accents spoken by people.
    Cause I have no English environment of conversation.
    I am a Hindi and Sindhi native speaker.
    If you give English subtitles also, you can help us learning math and English as well.
    Your video is so qualitiful but it is useless for me. Cause lack of subtitles make us unable to understand the matter.

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