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Class Notes. 3000 540 label. Moreover, if|x(i)−x| is small, thenw(i) is close to 1; and machine learning. about the locally weighted linear regression (LWR) algorithm which, assum- We then have, Armed with the tools of matrix derivatives, let us now proceedto find in Coding assignments enhanced with added inline support and milestone code checks 3. Lecture notes, lectures 10 - 12 - Including problem set Lecture notes, lectures 1 - 5 Cs229-notes 1 - Machine learning by andrew Cs229-notes 3 - Machine learning by andrew Cs229-notes-deep learning Week 1 Lecture Notes. to the gradient of the error with respect to that single training example only. Lastly, in our logistic regression setting,θis vector-valued, so we need to at every example in the entire training set on every step, andis calledbatch keep the training data around to make future predictions. that we saw earlier is known as aparametriclearning algorithm, because which wesetthe value of a variableato be equal to the value ofb. 2 ) For these reasons, particularly when Now, given this probabilistic model relating they(i)’s and thex(i)’s, what 1600 330 is the distribution of the y(i)’s? Instead of maximizingL(θ), we can also maximize any strictly increasing This treatment will be brief, since you’ll get a chance to explore some of the 4 Ifxis vector-valued, this is generalized to bew(i)= exp(−(x(i)−x)T(x(i)−x)/(2τ 2 )). Stanford Machine Learning. 2400 369 dient descent, and requires many fewer iterations to get very close to the Given a training set, define thedesign matrixXto be then-by-dmatrix of house). Let’s start by talking about a few examples of supervised learning problems. 2104 400 one iteration of gradient descent, since it requires findingand inverting an (GLMs). The Please sign in or register to post comments. higher “weight” to the (errors on) training examples close to the query point %�쏢 notation is simply an index into the training set, and has nothing to do with we getθ 0 = 89. theory. machine learning. Is this coincidence, or is there a deeper reason behind this?We’ll answer this Suppose we have a dataset giving the living areas and prices of 47 houses from Portland, Oregon: Living area (feet2) Price (1000$s) 2104 400 1600 330 2400 369 1416 232 3000 540..... We can plot this data: Now, given a training set, how do we pick, or learn, the parametersθ? that measures, for each value of theθ’s, how close theh(x(i))’s are to the sort. the update is proportional to theerrorterm (y(i)−hθ(x(i))); thus, for in- Keep Updating: 2019-02-18 Merge to Lecture #5 Note; 2019-01-23 Add Part 2, Gausian discriminant analysis; 2019-01-22 Add Part 1, A Review of Generative Learning Algorithms. We can also write the instead maximize thelog likelihoodℓ(θ): Hence, maximizingℓ(θ) gives the same answer as minimizing. Locally weighted linear regression is the first example we’re seeing of a So, by lettingf(θ) =ℓ′(θ), we can use We now begin our study of deep learning. Advice on applying machine learning: Slides from Andrew's lecture on getting machine learning algorithms to work in practice can be found here. rather than negative sign in the update formula, since we’remaximizing, You will have to watch around 10 videos (more or less 10min each) every week. Theme based on Materialize.css for jekyll sites. To do so, it seems natural to minimizeJ, we set its derivatives to zero, and obtain thenormal equations: Thus, the value of θ that minimizes J(θ) is given in closed form by the example. He leads the STAIR (STanford Artificial Intelligence Robot) project, whose goal is to develop a home assistant robot that can perform tasks such as tidy up a room, load/unload a dishwasher, fetch and deliver items, and prepare meals using a kitchen. 1 Neural Networks. <> case of if we have only one training example (x, y), so that we can neglect Newton’s method to minimize rather than maximize a function?) This is justlike the regression y(i)). θ= (XTX)− 1 XT~y. may be some features of a piece of email, andymay be 1 if it is a piece Let’s start by talking about a few examples of supervised learning problems. algorithm, which starts with some initialθ, and repeatedly performs the The maxima ofℓcorrespond to points The term “non-parametric” (roughly) refers the space of output values. Suppose we have a dataset giving the living areas and prices of 47 houses from Portland, Oregon: This can be checked before calculating the inverse. In this set of notes, we give a broader view of the EM algorithm, and show how it can be applied to a … We can write this assumption as “ǫ(i)∼ dient descent. for a particular value ofi, then in pickingθ, we’ll try hard to make (y(i)− CS229 Lecture notes Andrew Ng Part IV Generative Learning algorithms So far, we’ve mainly been talking about learning algorithms that model p(yjx; ), the conditional distribution of y given x. [CS229] Lecture 4 Notes - Newton's Method/GLMs. When we wish to explicitly view this as a function of Jordan,Learning in graphical models(unpublished book draft), and also McCullagh and more than one example. However, it is easy to construct examples where this method In other words, this choice? tions we consider, it will often be the case thatT(y) =y); anda(η) is thelog use it to maximize some functionℓ? A pair (x(i), y(i)) is called atraining example, and the dataset Let’s start by working with just Note that we should not condition onθ (Note the positive Similar to our derivation in the case zero. overyto 1. one training example (x, y), and take derivatives to derive the stochastic, Above, we used the fact thatg′(z) =g(z)(1−g(z)). family of algorithms. variables (living area in this example), also called inputfeatures, andy(i) CS229 Lecture Notes Andrew Ng slightly updated by TM on June 28, 2019 Supervised learning Let’s start by talking about a few examples of Since we are in the unsupervised learning setting, these … CS229 Lecture notes Andrew Ng Mixtures of Gaussians and the EM algorithm In this set of notes, we discuss the EM (Expectation-Maximization) for den-sity estimation. specifically why might the least-squares cost function J, be a reasonable One iteration of Newton’s can, however, be more expensive than then we have theperceptron learning algorithn. regression model. sort. features is important to ensuring good performance of a learning algorithm. [CS229] Lecture 6 Notes - Support Vector Machines I 05 Mar 2019 [CS229] Properties of Trace and Matrix Derivatives 04 Mar 2019 [CS229] Lecture 5 Notes - Descriminative Learning v.s. Let usfurther assume There are two ways to modify this method for a training set of that there is a choice ofT,aandbso that Equation (3) becomes exactly the hypothesishgrows linearly with the size of the training set. This therefore gives us The (unweighted) linear regression algorithm All of the lecture notes from CS229: Machine Learning 0 stars 94 forks Star Watch Code; Pull requests 0; Actions; Projects 0; Security; Insights; Dismiss Join GitHub today. Please check back of doing so, this time performing the minimization explicitly and without 2 By slowly letting the learning rateαdecrease to zero as the algorithm runs, it is also 1 Neural Networks We will start small and slowly build up a neural network, step by step. scoring. performs very poorly. We now show that this class of Bernoulli linearly independent examples is fewer than the number of features, or if the features In the third step, we used the fact thataTb =bTa, and in the fifth step We begin by re-writingJ in if it can be written in the form. For now, we will focus on the binary ��X ���f����"D�v�����f=M~[,�2���:�����(��n���ͩ��uZ��m]b�i�7�����2��yO��R�E5J��[��:��0$v�#_�@z'���I�Mi�$�n���:r�j́H�q(��I���r][EÔ56�{�^�m�)�����e����t�6GF�8�|��O(j8]��)��4F{F�1��3x g, and if we use the update rule. method to this multidimensional setting (also called the Newton-Raphson Gradient descent gives one way of minimizingJ. closed-form the value ofθthat minimizesJ(θ). time we encounter a training example, we update the parameters according to evaluatex. [�h7Z�� Step 2. CS229 Lecture notes Andrew Ng The k-means clustering algorithm In the clustering problem, we are given a training set {x(1),...,x(m)}, and want to group the data into a few cohesive “clusters.” Here, x(i) ∈ Rn as usual; but no labels y(i) are given. special cases of a broader family of models, called Generalized Linear Models Comments. 80% (5) Pages: 39 year: 2015/2016. are not linearly independent, thenXTXwill not be invertible. Here,ηis called thenatural parameter(also called thecanonical param- y(i)’s given thex(i)’s), this can also be written. CS229 Lecture notes Andrew Ng Part IX The EM algorithm In the previous set of notes, we talked about the EM algorithm as applied to ﬁtting a mixture of Gaussians. So, this The above results were obtained with batch gradient descent. In order to implement this algorithm, we have to work out whatis the cs229. are not random variables, normally distributed or otherwise.) cs229. if|x(i)−x|is large, thenw(i) is small. Copyright © 2020 StudeerSnel B.V., Keizersgracht 424, 1016 GC Amsterdam, KVK: 56829787, BTW: NL852321363B01, Cs229-notes 1 - Machine learning by andrew, IAguide 2 - Step 1. derived and applied to other classification and regression problems. continues to make progress with each example it looks at. Comments. Hence,θ is chosen giving a much Intuitively, it also doesn’t make sense forhθ(x) to take, So, given the logistic regression model, how do we fitθfor it? Incontrast, to goal is, given a training set, to learn a functionh:X 7→Yso thath(x) is a the stochastic gradient ascent rule, If we compare this to the LMS update rule, we see that it looks identical; but 1416 232 View cs229-notes3.pdf from CS 229 at Stanford University. As discussed previously, and as shown in the example above, the choice of vertical_align_top. numbers, we define the derivative offwith respect toAto be: Thus, the gradient∇Af(A) is itself ann-by-dmatrix, whose (i, j)-element is, Here,Aijdenotes the (i, j) entry of the matrixA. algorithm that starts with some “initial guess” forθ, and that repeatedly (Most of what we say here will also generalize to the multiple-class case.) In this section, we will give a set of probabilistic assumptions, under Given a set of data points {x(1),...,x(m)} associated to a set of outcomes {y(1),...,y(m)}, we want to build a classifier that learns how to predict y from x. Whether or not you have seen it previously, let’s keep Suppose that we are given a training set {x(1),...,x(m)} as usual. calculus with matrices. distributions, ones obtained by varyingφ, is in the exponential family; i.e., (price). To enable us to do this without having to write reams of algebra and If the number of bedrooms were included as one of the input features as well, our updates will therefore be given byθ:=θ+α∇θℓ(θ). we include the intercept term) called theHessian, whose entries are given In this set of notes, we give an overview of neural networks, discuss vectorization and discuss training neural networks with backpropagation. Here,∇θℓ(θ) is, as usual, the vector of partial derivatives ofℓ(θ) with respect Consider modifying the logistic regression methodto “force” it to ;�x�Y�(Ɯ(�±ٓ�[��ҥN'���͂\bc�=5�.�c�v�hU���S��ʋ��r��P�_ю��芨ņ�� ���4�h�^힜l�g�k��]\�&+�ڵSz��\��6�6�a���,�Ů�K@5�9l.�-гF�YO�Ko̰e��H��a�S+r�l[c��[�{��C�=g�\ެ�3?�ۖ-���-8���#W6Ҽ:�� byu��S��(�ߤ�//���h��6/$�|�:i����y{�y����E�i��z?i�cG.�. meanφ, written Bernoulli(φ), specifies a distribution overy∈{ 0 , 1 }, so that functionhis called ahypothesis. lowing: Here, thew(i)’s are non-negative valuedweights. mean zero and some varianceσ 2. output values that are either 0 or 1 or exactly. We could approach the classification problem ignoring the fact that y is to theθi’s; andHis and-by-dmatrix (actually,d+1−by−d+1, assuming that Defining key stakeholders’ goals • 9 one more iteration, which the updatesθ to about 1.8. malization constant, that makes sure the distributionp(y;η) sums/integrates Let’s first work it out for the partial derivative term on the right hand side. correspondingy(i)’s. In the previous set of notes, we talked about the EM algorithmas applied to fitting a mixture of Gaussians. Specifically, let’s consider thegradient descent So far, we’ve seen a regression example, and a classificationexample. if, given the living area, we wanted to predict if a dwelling is a house or an forθ, which is about 2.8. Note that, while gradient descent can be susceptible ygivenx. In this set of notes, we give an overview of neural networks, discuss vectorization and discuss training neural networks with backpropagation. y|x;θ∼Bernoulli(φ), for some appropriate definitions ofμandφas functions in Portland, as a function of the size of their living areas? Note that the superscript “(i)” in the machine learning ... » Stanford Lecture Note Part I & II; KF. θ, we can rewrite update (1) in a slightly more succinct way: The reader can easily verify that the quantity in the summation in the Seen pictorially, the process is therefore To establish notation for future use, we’ll usex(i)to denote the “input” just what it means for a hypothesis to be good or bad.) the following algorithm: By grouping the updates of the coordinates into an update of the vector To To establish notation for future use, we’ll use x(i) to denote the “input” variables (living area in this example), also called input features, and y(i) to denote the “output” or target variable that we are trying to predict The first is replace it with the following algorithm: By grouping the updates of the coordinates into an update of the vector The generalization of Newton’s date_range Feb. 18, 2019 - Monday info. pointx(i.e., to evaluateh(x)), we would: In contrast, the locally weighted linear regression algorithm does the fol- (See also the extra credit problem on Q3 of N(0, σ 2 ).” I.e., the density ofǫ(i)is given by, 3 Note that in the above step, we are implicitly assuming thatXTXis an invertible. When the target variable that we’re trying to predict is continuous, such to denote the “output” or target variable that we are trying to predict stance, if we are encountering a training example on which our prediction We now show that the Bernoulli and the Gaussian distributions are ex- according to a Gaussian distribution (also called a Normal distribution) with These quizzes are here to … a small number of discrete values. (“p(y(i)|x(i), θ)”), sinceθ is not a random variable. 0 is also called thenegative class, and 1 p(y|X;θ). lem. stream Theme based on Materialize.css for jekyll sites. The parameter. Intuitively, ifw(i)is large the entire training set before taking a single step—a costlyoperation ifnis the training set is large, stochastic gradient descent is often preferred over We will start … this family. A fairly standard choice for the weights is 4, Note that the weights depend on the particular pointxat which we’re trying large—stochastic gradient descent can start making progress right away, and x��Zˎ\���W܅��1�7|?�K��@�8�5�V�4���di'�Sd�,Nw�3�,A��է��b��ۿ,jӋ�����������N-_v�|���˟.H�Q[&,�/wUQ/F�-�%(�e�����/�j�&+c�'����i5���!L��bo��T��W$N�z��+z�)zo�������Nڇ����_� F�����h��FLz7����˳:�\����#��e{������KQ/�/��?�.�������b��F�$Ƙ��+���%�֯�����ф{�7��M�os��Z�Iڶ%ש�^� ����?C�u�*S�.GZ���I�������L��^^$�y���[.S�&E�-}A�� &�+6VF�8qzz1��F6��h���{�чes���'����xVڐ�ނ\}R��ޛd����U�a������Nٺ��y�ä Consider As before, it will be easier to maximize the log likelihood: How do we maximize the likelihood? it has a fixed, finite number of parameters (theθi’s), which are fit to the 2 Given data like this, how can we learn to predict the prices of other houses in Portland, as a function of the size of their living areas? is also something that you’ll get to experiment with in your homework. resorting to an iterative algorithm. non-parametricalgorithm. change the definition ofgto be the threshold function: If we then lethθ(x) =g(θTx) as before but using this modified definition of Newton’s method gives a way of getting tof(θ) = 0. properties of the LWR algorithm yourself in the homework. lihood estimator under a set of assumptions, let’s endow ourclassification We have: For a single training example, this gives the update rule: 1. In this method, we willminimizeJ by θ that minimizesJ(θ). function ofL(θ). After a few more classificationproblem in whichy can take on only two values, 0 and 1. Make sure you are up to date, to not lose the pace of the class. pretty much ignored in the fit. data. Let us assume that, P(y= 1|x;θ) = hθ(x) least-squares cost function that gives rise to theordinary least squares 5 The presentation of the material in this section takes inspiration from Michael I. ing there is sufficient training data, makes the choice of features less critical. %PDF-1.4 11/2 : Lecture 15 ML advice. going, and we’ll eventually show this to be a special case of amuch broader So, this is an unsupervised learning problem. of spam mail, and 0 otherwise. rather than minimizing, a function now.) generalize Newton’s method to this setting. explicitly taking its derivatives with respect to theθj’s, and setting them to distribution ofy(i)asy(i)|x(i);θ∼N(θTx(i), σ 2 ). [CS229] Lecture 5 Notes - Descriminative Learning v.s. the entire training set around. Classroom lecture videos edited and segmented to focus on essential content 2. thepositive class, and they are sometimes also denoted by the symbols “-” y(i)=θTx(i)+ǫ(i), whereǫ(i) is an error term that captures either unmodeled effects (suchas Live lecture notes ; Weak Supervision [pdf (slides)] Weak Supervision (spring quarter) [old draft, in lecture] 10/29: Midterm: The midterm details TBD. When Newton’s method is applied to maximize the logistic regres- Live lecture notes (spring quarter) [old draft, in lecture] 10/28 : Lecture 14 Weak supervised / unsupervised learning. sion log likelihood functionℓ(θ), the resulting method is also calledFisher Whereas batch gradient descent has to scan through To work our way up to GLMs, we will begin by defining exponential family p(y= 1;φ) =φ; p(y= 0;φ) = 1−φ. The notation “p(y(i)|x(i);θ)” indicates that this is the distribution ofy(i) label. I.e., we should chooseθ to is a reasonable way of choosing our best guess of the parametersθ? can then write down the likelihood of the parameters as. from Portland, Oregon: Living area (feet 2 ) Price (1000$s) To describe the supervised learning problem slightly more formally, our In the original linear regression algorithm, to make a prediction at a query 3. d-by-dHessian; but so long asdis not too large, it is usually much faster In the regression example, we hady|x;θ∼ N(μ, σ 2 ), and in the classification one, CS229 Lecture Notes Andrew Ng and Kian Katanforoosh Deep Learning We now begin our study of deep learning. nearly matches the actual value ofy(i), then we find that there is little need Newton’s method typically enjoys faster convergence than (batch) gra- interest, and that we will also return to later when we talk about learning In contrast, we will write “a=b” when we are To formalize this, we will define a function gradient descent). the same update rule for a rather different algorithm and learning problem. pages full of matrices of derivatives, let’s introduce somenotation for doing CS229 Lecture notes Andrew Ng Supervised learning Let’s start by talking about a few examples of supervised learning problems. training example. gradient descent. The probability of the data is given by CS229 Lecture notes Andrew Ng Supervised learning Lets start by talking about a few examples of supervised learning problems. θ, we will instead call it thelikelihoodfunction: Note that by the independence assumption on theǫ(i)’s (and hence also the A fixed choice ofT,aandbdefines afamily(or set) of distributions that The rule is called theLMSupdate rule (LMS stands for “least mean squares”), partition function. function ofθTx(i). We define thecost function: If you’ve seen linear regression before, you may recognize this as the familiar Class Notes Preview text. θTx(i)) 2 small. Written invectorial notation, For instance, the magnitude of batch gradient descent. [CS229] Lecture 6 Notes - Support Vector Machines I. date_range Mar. Cohort group connected via a vibrant Slack community, providing opportunities to network and collaborate with motivated learners from diverse locations and profession… Time and Location: Monday, Wednesday 4:30pm-5:50pm, links to lecture are on Canvas. and “+.” Givenx(i), the correspondingy(i)is also called thelabelfor the What if we want to not directly have anything to do with Gaussians, and in particular thew(i) The Bernoullidistribution with We now digress to talk briefly about an algorithm that’s of some historical In particular, the derivations will be a bit simpler if we principal ofmaximum likelihoodsays that we should chooseθ so as to Notes. properties that seem natural and intuitive. sort. We want to chooseθso as to minimizeJ(θ). and the parametersθwill keep oscillating around the minimum ofJ(θ); but that theǫ(i)are distributed IID (independently and identically distributed) Suppose we have a dataset giving the living areas and prices of 47 houses from Portland, Oregon: Living area (feet2) Price (1000$s) 2104 400 1600 330 2400 369 1416 232 3000 540..... We can plot this data: View cs229-notes1.pdf from CS 229 at Stanford University. Lecture videos which are organized in "weeks". via maximum likelihood. by. This professional online course, based on the on-campus Stanford graduate course CS229, features: 1. where its first derivativeℓ′(θ) is zero. more details, see Section 4.3 of “Linear Algebra Review and Reference”). cs229. 60 , θ 1 = 0.1392,θ 2 =− 8 .738. is simply gradient descent on the original cost functionJ. The topics covered are shown below, although for a more detailed summary see lecture 19. If either the number of CS229 Lecture Notes Andrew Ng updated by Tengyu Ma on April 21, 2019 Part V Kernel Methods 1.1 Feature maps Recall that in our discussion about linear regression, we considered the prob-lem of predicting the price of a house (denoted by y) from the living area of the house (denoted by x), and we t a linear function of xto the training data. Generative Learning Algorithm. Get Free Cs229 Lecture Notes now and use Cs229 Lecture Notes immediately to get % off or $ off or free shipping θ:=θ−H− 1 ∇θℓ(θ). For instance, logistic regression modeled p(yjx; ) as h (x) = g( Tx) where g is the sigmoid func-tion. class of Bernoulli distributions. orw(i)= exp(−(x(i)−x)TΣ− 1 (x(i)−x)/2), for an appropriate choice ofτor Σ. τcontrols how quickly the weight of a training example falls off with distance problem, except that the values y we now want to predict take on only Notes. Following When faced with a regression problem, why might linear regression, and the sum in the definition ofJ. ically choosing a good set of features.) . to the fact that the amount of stuff we need to keep in order to represent the merely oscillate around the minimum. model with a set of probabilistic assumptions, and then fit the parameters One reasonable method seems to be to makeh(x) close toy, at least for eter) of the distribution;T(y) is thesufficient statistic(for the distribu- Q[�|V�O�LF:֩��G���Č�Z��+�r�)�hd�6����4V(��iB�H>)Sʥ�[~1�s�x����mR�[�'���R;��^��,��M �m�����xt#�yZ�L�����Sȫ3��ř{U�K�a鸷��F��7�)`�ڻ��n!��'�����u��kE���5�W��H�|st�/��|�p�!������E��xD�D! Often, stochastic Here,αis called thelearning rate. make the data as high probability as possible. this isnotthe same algorithm, becausehθ(x(i)) is now defined as a non-linear matrix. and is also known as theWidrow-Hofflearning rule. This rule has several Nelder,Generalized Linear Models (2nd ed.). In this set of notes, we give a broader view of the EM algorithm, and show how it can be applied to a large family of estimation problems with latent variables. To do so, let’s use a search when we get to GLM models. This method looks asserting a statement of fact, that the value ofais equal to the value ofb. ��ѝ�l�d�4}�r5��R^�eㆇ�-�ڴxl�I is parameterized byη; as we varyη, we then get different distributions within In this section, letus talk briefly talk CS229 Lecture notes Andrew Ng Part V Support Vector Machines This set of notes presents the … cosmetically similar to the density of a Gaussian distribution, thew(i)’s do Even in such cases, it is iterations, we rapidly approachθ= 1.3. approximations to the true minimum. Whenycan take on only a small number of discrete values (such as Lecture notes, lectures 10 - 12 - Including problem set. CS229 Lecture Notes Andrew Ng (updates by Tengyu Ma) Supervised learning. as in our housing example, we call the learning problem aregressionprob- This quantity is typically viewed a function ofy(and perhapsX), maximizeL(θ). minimum. Office hours and support from Stanford-affiliated Course Assistants 4. “good” predictor for the corresponding value ofy. Let us assume that the target variables and the inputs are related via the to change the parameters; in contrast, a larger change to theparameters will For historical reasons, this There is 39 pages This algorithm is calledstochastic gradient descent(alsoincremental 1 ,... , n}—is called atraining set. amples of exponential family distributions. gradient descent getsθ“close” to the minimum much faster than batch gra- method) is given by update rule above is just∂J(θ)/∂θj(for the original definition ofJ). make predictions using locally weighted linear regression, we need to keep like this: x h predicted y(predicted price) (actually n-by-d+ 1, if we include the intercept term) that contains the. Quizzes (≈10-30min to complete) at the end of every week. (When we talk about model selection, we’ll also see algorithms for automat- distributions with different means. We will also useX denote the space of input values, andY CS229: Additional Notes on … the training examples we have. possible to “fix” the situation with additional techniques,which we skip here for the sake We will also show how other models in the GLM family can be For a functionf : Rn×d 7→ Rmapping from n-by-d matrices to the real for a fixed value ofθ. in practice most of the values near the minimum will be reasonably good operation overwritesawith the value ofb. As we varyφ, we obtain Bernoulli Notes. Previous projects: A … problem set 1.). θ, we can rewrite update (2) in a slightly more succinct way: In this algorithm, we repeatedly run through the training set, and each .. 5 0 obj Let’s discuss a second way A Chinese Translation of Stanford CS229 notes 斯坦福机器学习CS229课程讲义的中文翻译 - Kivy-CN/Stanford-CS-229-CN svm ... » Stanford Lecture Note Part V; KF. Identifying your users’. the same algorithm to maximizeℓ, and we obtain update rule: (Something to think about: How would this change if we wanted to use Take an adapted version of this course as part of the Stanford Artificial Intelligence Professional Program. Nonetheless, it’s a little surprising that we end up with possible to ensure that the parameters will converge to the global minimum rather than of linear regression, we can use gradient ascent. distributions. The quantitye−a(η)essentially plays the role of a nor- be made if our predictionhθ(x(i)) has a large error (i.e., if it is very far from givenx(i)and parameterized byθ. Let’s now talk about the classification problem. that we’ll be using to learn—a list ofn training examples{(x(i), y(i));i= 500 1000 1500 2000 2500 3000 3500 4000 4500 5000. matrix-vectorial notation. Generative Learning Algorithm 18 Feb 2019 [CS229] Lecture 4 Notes - Newton's Method/GLMs 14 Feb 2019 ?��"Bo�&g���x����;���b� ��}M����Ng��R�[�B߉�\���ܑj��\���hci8e�4�╘��5�2�r#įi ���i���?^�����,���:�27Q Once we’ve fit theθi’s and stored them away, we no longer need to which least-squares regression is derived as a very naturalalgorithm. update: (This update is simultaneously performed for all values ofj = 0,... , d.) if there are some features very pertinent to predicting housing price, but Ifw(i) is small, then the (y(i)−θTx(i)) 2 error term will be an alternative to batch gradient descent that also works very well. how we saw least squares regression could be derived as the maximum like- Given data like this, how can we learn to predict the prices ofother houses of simplicty. Note: This is being updated for Spring 2020.The dates are subject to change as we figure out deadlines. equation This is a very natural algorithm that overall. discrete-valued, and use our old linear regression algorithm to try to predict Type of prediction― The different types of predictive models are summed up in the table below: Type of model― The different models are summed up in the table below: x. to local minima in general, the optimization problem we haveposed here, 1 We use the notation “a:=b” to denote an operation (in a computer program) in. P(y= 0|x;θ) = 1−hθ(x), Note that this can be written more compactly as, Assuming that thentraining examples were generated independently, we �_�. date_range Feb. 14, 2019 - Thursday info. In this section, we will show that both of these methods are (Note also that while the formula for the weights takes a formthat is vertical_align_top. We say that a class of distributions is in theexponential family The rightmost figure shows the result of running ofxandθ. changesθ to makeJ(θ) smaller, until hopefully we converge to a value of (Note however that it may never “converge” to the minimum, repeatedly takes a step in the direction of steepest decrease ofJ. Suppose we have a dataset giving the living areas and prices of 47 houses used the facts∇xbTx=band∇xxTAx= 2Axfor symmetric matrixA(for GitHub is home to over 50 million developers working together to host and review code, manage projects, and build software together. CS229 Lecture Notes Andrew Ng Deep Learning. The following notes represent a complete, stand alone interpretation of Stanford's machine learning course presented by Professor Andrew Ng and originally posted on the ml-class.org website during the fall 2011 semester. that we’d left out of the regression), or random noise. Syllabus and Course Schedule. For instance, if we are trying to build a spam classifier for email, thenx(i) In this example,X=Y=R. CS229 Lecture notes Andrew Ng Part IX The EM algorithm. 05, 2019 - Tuesday info. equation exponentiation. label. We’d derived the LMS rule for when there was only a single training

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