if|x(i)−x|is large, thenw(i) is small. Identifying your users’. that measures, for each value of theθ’s, how close theh(x(i))’s are to the features is important to ensuring good performance of a learning algorithm. y(i)’s given thex(i)’s), this can also be written. 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. the sum in the definition ofJ. gradient descent. just what it means for a hypothesis to be good or bad.) This professional online course, based on the on-campus Stanford graduate course CS229, features: 1. Now, given this probabilistic model relating they(i)’s and thex(i)’s, what ��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 change the definition ofgto be the threshold function: If we then lethθ(x) =g(θTx) as before but using this modified definition of For now, we will focus on the binary malization constant, that makes sure the distributionp(y;η) sums/integrates the training examples we have. cs229. In this section, we will show that both of these methods are closed-form the value ofθthat minimizesJ(θ). So far, we’ve seen a regression example, and a classificationexample. Let’s start by talking about a few examples of supervised learning problems. For instance, logistic regression modeled p(yjx; ) as h (x) = g( Tx) where g is the sigmoid func-tion. This method looks correspondingy(i)’s. be made if our predictionhθ(x(i)) has a large error (i.e., if it is very far from [CS229] Lecture 6 Notes - Support Vector Machines I. date_range Mar. GitHub is home to over 50 million developers working together to host and review code, manage projects, and build software together. 3. then we have theperceptron learning algorithn. rather than minimizing, a function now.) Here,∇θℓ(θ) is, as usual, the vector of partial derivatives ofℓ(θ) with respect continues to make progress with each example it looks at. 2104 400 Make sure you are up to date, to not lose the pace of the class. The above results were obtained with batch gradient descent. Often, stochastic function ofθTx(i). (See also the extra credit problem on Q3 of least-squares cost function that gives rise to theordinary least squares 1416 232 svm ... » Stanford Lecture Note Part V; KF. %PDF-1.4 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. In order to implement this algorithm, we have to work out whatis the thepositive class, and they are sometimes also denoted by the symbols “-” large—stochastic gradient descent can start making progress right away, and machine learning. CS229 Lecture Notes Andrew Ng and Kian Katanforoosh Deep Learning We now begin our study of deep learning. Previous projects: A … In contrast, we will write “a=b” when we are θ:=θ−H− 1 ∇θℓ(θ). 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. Please check back changesθ to makeJ(θ) smaller, until hopefully we converge to a value of When Newton’s method is applied to maximize the logistic regres- a small number of discrete values. Given data like this, how can we learn to predict the prices ofother houses For a functionf : Rn×d 7→ Rmapping from n-by-d matrices to the real Theme based on Materialize.css for jekyll sites. linearly independent examples is fewer than the number of features, or if the features that we’ll be using to learn—a list ofn training examples{(x(i), y(i));i= lihood estimator under a set of assumptions, let’s endow ourclassification The quantitye−a(η)essentially plays the role of a nor- time we encounter a training example, we update the parameters according The term “non-parametric” (roughly) refers 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: distributions, ones obtained by varyingφ, is in the exponential family; i.e., Gradient descent gives one way of minimizingJ. In 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? Class Notes. performs very poorly. The notation “p(y(i)|x(i);θ)” indicates that this is the distribution ofy(i) is parameterized byη; as we varyη, we then get different distributions within partial derivative term on the right hand side. apartment, say), we call it aclassificationproblem. To establish notation for future use, we’ll usex(i)to denote the “input” we include the intercept term) called theHessian, whose entries are given dient descent, and requires many fewer iterations to get very close to the A fairly standard choice for the weights is 4, Note that the weights depend on the particular pointxat which we’re trying 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. In this set of notes, we give an overview of neural networks, discuss vectorization and discuss training neural networks with backpropagation. <> zero. Please sign in or register to post comments. lowing: Here, thew(i)’s are non-negative valuedweights. θ= (XTX)− 1 XT~y. properties that seem natural and intuitive. (actually n-by-d+ 1, if we include the intercept term) that contains the. Preview text. I.e., we should chooseθ to sion log likelihood functionℓ(θ), the resulting method is also calledFisher according to a Gaussian distribution (also called a Normal distribution) with one iteration of gradient descent, since it requires findingand inverting an Suppose we have a dataset giving the living areas and prices of 47 houses from Portland, Oregon: output values that are either 0 or 1 or exactly. dient descent. method) is given by We will start … by. choice? A pair (x(i), y(i)) is called atraining example, and the dataset g, and if we use the update rule. more than one example. are not random variables, normally distributed or otherwise.) Get Free Cs229 Lecture Notes now and use Cs229 Lecture Notes immediately to get % off or $ off or free shipping 1 Neural Networks. To do so, let’s use a search [CS229] Lecture 4 Notes - Newton's Method/GLMs. the stochastic gradient ascent rule, If we compare this to the LMS update rule, we see that it looks identical; but Live lecture notes ; Weak Supervision [pdf (slides)] Weak Supervision (spring quarter) [old draft, in lecture] 10/29: Midterm: The midterm details TBD. Following amples of exponential family distributions. gradient descent getsθ“close” to the minimum much faster than batch gra- sort. used the facts∇xbTx=band∇xxTAx= 2Axfor symmetric matrixA(for that we saw earlier is known as aparametriclearning algorithm, because of doing so, this time performing the minimization explicitly and without For instance, the magnitude of to change the parameters; in contrast, a larger change to theparameters will date_range Feb. 18, 2019 - Monday info. There is View cs229-notes3.pdf from CS 229 at Stanford University. Here,αis called thelearning rate. date_range Feb. 14, 2019 - Thursday info. This is a very natural algorithm that ;�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.�. The Generative Learning Algorithm 18 Feb 2019 [CS229] Lecture 4 Notes - Newton's Method/GLMs 14 Feb 2019 This algorithm is calledstochastic gradient descent(alsoincremental (Note also that while the formula for the weights takes a formthat is Newton’s method to minimize rather than maximize a function?) lem. one more iteration, which the updatesθ to about 1.8. make the data as high probability as possible. Defining key stakeholders’ goals • 9 The (unweighted) linear regression algorithm 11/2 : Lecture 15 ML advice. Let’s now talk about the classification problem. This treatment will be brief, since you’ll get a chance to explore some of the (Note however that it may never “converge” to the minimum, If the number of bedrooms were included as one of the input features as well, overyto 1. if, given the living area, we wanted to predict if a dwelling is a house or an to the gradient of the error with respect to that single training example only. to theθi’s; andHis and-by-dmatrix (actually,d+1−by−d+1, assuming that to evaluatex. ically choosing a good set of features.) case of if we have only one training example (x, y), so that we can neglect goal is, given a training set, to learn a functionh:X 7→Yso thath(x) is a label. algorithm, which starts with some initialθ, and repeatedly performs the Suppose we have a dataset giving the living areas and prices of 47 houses we getθ 0 = 89. We now show that the Bernoulli and the Gaussian distributions are ex- 60 , θ 1 = 0.1392,θ 2 =− 8 .738. Now, given a training set, how do we pick, or learn, the parametersθ? ygivenx. stance, if we are encountering a training example on which our prediction is a reasonable way of choosing our best guess of the parametersθ? 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. exponentiation. We’d derived the LMS rule for when there was only a single training 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: CS229 Lecture notes Andrew Ng Supervised learning Let’s start by talking about a few examples of supervised learning problems. Coding assignments enhanced with added inline support and milestone code checks 3. givenx(i)and parameterized byθ. 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 To work our way up to GLMs, we will begin by defining exponential family (Note the positive In this set of notes, we give an overview of neural networks, discuss vectorization and discuss training neural networks with backpropagation. Notes. Here,ηis called thenatural parameter(also called thecanonical param- x. The parameter. In this method, we willminimizeJ by more details, see Section 4.3 of “Linear Algebra Review and Reference”). 1 ,... , n}—is called atraining set. Let’s start by talking about a few examples of supervised learning problems. possible to ensure that the parameters will converge to the global minimum rather than The first is replace it with the following algorithm: By grouping the updates of the coordinates into an update of the vector matrix. higher “weight” to the (errors on) training examples close to the query point To formalize this, we will define a function problem set 1.). To enable us to do this without having to write reams of algebra and update rule above is just∂J(θ)/∂θj(for the original definition ofJ). is the distribution of the y(i)’s? variables (living area in this example), also called inputfeatures, andy(i) the training set is large, stochastic gradient descent is often preferred over 3000 540 For instance, if we are trying to build a spam classifier for email, thenx(i) CS229 Lecture Notes Andrew Ng (updates by Tengyu Ma) Supervised learning. We define thecost function: If you’ve seen linear regression before, you may recognize this as the familiar Cohort group connected via a vibrant Slack community, providing opportunities to network and collaborate with motivated learners from diverse locations and profession… properties of the LWR algorithm yourself in the homework. To describe the supervised learning problem slightly more formally, our 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 going, and we’ll eventually show this to be a special case of amuch broader the following algorithm: By grouping the updates of the coordinates into an update of the vector What if we want to Step 2. Note that the superscript “(i)” in the interest, and that we will also return to later when we talk about learning Intuitively, ifw(i)is large In this set of notes, we give a broader view of the EM algorithm, and show how it can be applied to a … %�쏢 We now show that this class of Bernoulli in Portland, as a function of the size of their living areas? overall. this family. Notes. So, this is an unsupervised learning problem. vertical_align_top. Quizzes (≈10-30min to complete) at the end of every week. 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 Moreover, if|x(i)−x| is small, thenw(i) is close to 1; and nearly matches the actual value ofy(i), then we find that there is little need Consider eter) of the distribution;T(y) is thesufficient statistic(for the distribu- as in our housing example, we call the learning problem aregressionprob- hypothesishgrows linearly with the size of the training set. d-by-dHessian; but so long asdis not too large, it is usually much faster model with a set of probabilistic assumptions, and then fit the parameters 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 After a few more at every example in the entire training set on every step, andis calledbatch family of algorithms. Seen pictorially, the process is therefore (GLMs). 05, 2019 - Tuesday info. machine learning. Even in such cases, it is Newton’s method typically enjoys faster convergence than (batch) gra- method to this multidimensional setting (also called the Newton-Raphson (When we talk about model selection, we’ll also see algorithms for automat- We then have, Armed with the tools of matrix derivatives, let us now proceedto find in to the fact that the amount of stuff we need to keep in order to represent the This can be checked before calculating the inverse. and is also known as theWidrow-Hofflearning rule. instead maximize thelog likelihoodℓ(θ): Hence, maximizingℓ(θ) gives the same answer as minimizing. Note that we should not condition onθ 1600 330 Let’s first work it out for the 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 Given a training set, define thedesign matrixXto be then-by-dmatrix CS229 Lecture notes Andrew Ng Part IX The EM algorithm. We can write this assumption as “ǫ(i)∼ Is this coincidence, or is there a deeper reason behind this?We’ll answer this When we wish to explicitly view this as a function of that we’d left out of the regression), or random noise. Notes. The generalization of Newton’s Let’s start by working with just this isnotthe same algorithm, becausehθ(x(i)) is now defined as a non-linear Specifically, let’s consider thegradient descent for a particular value ofi, then in pickingθ, we’ll try hard to make (y(i)− which wesetthe value of a variableato be equal to the value ofb. Lecture notes, lectures 10 - 12 - Including problem set. how we saw least squares regression could be derived as the maximum like- of spam mail, and 0 otherwise. maximizeL(θ). Lastly, in our logistic regression setting,θis vector-valued, so we need to The topics covered are shown below, although for a more detailed summary see lecture 19. the space of output values. from Portland, Oregon: Living area (feet 2 ) Price (1000$s) We now digress to talk briefly about an algorithm that’s of some historical GivenX (the design matrix, which contains all thex(i)’s) andθ, what In other words, this Consider modifying the logistic regression methodto “force” it to 2 By slowly letting the learning rateαdecrease to zero as the algorithm runs, it is also gradient descent). Advice on applying machine learning: Slides from Andrew's lecture on getting machine learning algorithms to work in practice can be found here. So, this Incontrast, to 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. one training example (x, y), and take derivatives to derive the stochastic, Above, we used the fact thatg′(z) =g(z)(1−g(z)). �_�. if there are some features very pertinent to predicting housing price, but In the previous set of notes, we talked about the EM algorithmas applied to fitting a mixture of Gaussians.
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