Learning Machine Learning (SACON May 2018)
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This document summarizes a talk on machine learning given by Subrat Panda at the SACON conference in Pune, India on May 18-19, 2018. The talk covered topics including classical definitions of machine learning, types of machine learning algorithms like supervised learning, unsupervised learning and reinforcement learning. It also discussed specific algorithms like linear regression, logistic regression, and support vector machines.
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Learning Machine Learning (SACON May 2018)
- 3. SACON
- 6. SACON Gartner Says By 2020, Artificial Intelligence Will Create More Jobs Than It Eliminates
- 7. SACON What this talk can motivate people to do § STUDENTS: § Motivates to participate in data science competitions § Further learning and add the expertise to the resume § Final year and fun projects. § PROFESSIONALS: § Find interesting data in your current project and apply machine learning § Motivates further learning and profession change. Data scientists/Machine learning engineers are highly paid professionals J § TEACHERS: § Motivates teachers to spread knowledge in the their university § Conduct hackathons SACON 2018 - Pune
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- 9. SACON Machine Learning Classical Definition § Arthur Samuel (1959): "computer’s ability to learn without being explicitly programmed.“ § Tom M Mitchel (1998): "A computer program is said to learn from experience E with respect to some class of tasks T and performance measure P if its performance at tasks in T, as measured by P, improves with experience E.“ § Optimize a performance criterion using example data or past experience.
- 10. SACON Types of Machine Learning Algorithms § Supervised Learning: Input data with labeled responses § Regression : Given a picture of a person, we have to predict their age on the basis of the given picture § Classification : Given a patient with a tumor, we have to predict whether the tumor is malignant or benign. IRIS DATASET SPECIES CLASSIFICATION TEXT CLASSIFICATION IMAGE CLASSIFICATION Linear Regression Non-Linear Regression
- 11. SACON Types of Machine Learning Algorithms § Unsupervised Learning: Input data without labeled responses. § Clustering: Take a collection of 1,000,000 different genes, and find a way to automatically group these genes into groups that are somehow similar or related by different variables, such as lifespan, location, roles, and so on. § Non Clustering: Exploratory data analysis (PCA, Auto-encoders) Customer Segmentation MNIST Digit Segmentation
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- 14. SACON Pop Quiz § Predicting housing prices based on input parameters like house size, number of rooms, location of house etc. falls under which category of machine learning problem: § A) Regression § B) Classification § C) Clustering § D) None § Automatically segmenting your customers according to the customer information falls under which category of machine learning. § A) Regression § B) Classification § C) Clustering § D) None
- 16. SACON Linear Regression • Linear regression is the simple form of Supervised learning. • In a regression problem the target variable is continuous. Living Area (Sq. feet) Year Built Price (1000$s) 2104 2012 400 1600 2013 300 2400 2014 369 1416 2013 232 3000 2015 540 . . . . . . . . . Predict Housing Price from Historical data
- 18. SACON Linear Regression • In supervised learning, our goal is, given a training set, to learn a function h : X → Y so that h(x) is a “good” predictor for the corresponding value of Y. Living Area (Sq. feet) Year Built Price (1000$s) 2104 2012 400 1600 2013 300 2400 2014 369 1416 2013 232 3000 2015 540 . . . . . . . . . • Lets consider the housing data above. X’s represents a two dimensional vector ad Y represents the price of the house.
- 20. SACON Cost Function I • Lets approximate the Y as a linear function of X. Hence the hypothesis function will be given by. • θ’s are the parameters (also called weights) parameterizing the space of linear functions mapping from X to Y. • How do we pick, or learn, the parameters θ? One reasonable method seems to be to make h(x) close to y, at least for the training examples we have. The cost function is given by: (Considering θ1 • This is the least-squares cost function that gives rise to the ordinary least squares regression model
- 21. SACON Cost Function II § We want to choose θ so as to minimize J(θ). § We can see the cost associated with different values of θ and we can see the graph has a slight bowl to its shape. § The goal is to “roll down the hill”, and find θ corresponding to the bottom of the bowl.
- 22. SACON Gradient Descent § We should use a search algorithm that starts with some “initial guess” for θ, and that repeatedly changes θ to make J(θ) smaller, until we converge to a value of θ that minimizes J(θ). § The algorithm we choose is Gradient Descent Algorithm, which starts with some initial θ and repeatedly perform the following update: § If we calculate the partial derivate , we get the following output: α = Learning Rate If α is too small: slow convergence. If α is too large: may not decrease on every iteration and thus may not converge.
- 25. SACON Other Optimization Methods: § There is an alternative to batch gradient descent that also works very well. Consider the following algorithm: § Each time we encounter a training example, we update the parameters according to the gradient of the error with respect to that single training example only. This algorithm is called Stochastic Gradient Descent(SGD). § Other examples of Optimization algorithms: BFGS, L-BFGS § Mini batch gradient descent: performs an update for every batch.
- 26. SACON Normal Equation § Normal Equation is a method to solve for θ analytically. § Our cost function looks like: § To minimize a Quadratic function, the partial derivative of the function should be equated to zero.
- 27. SACON Normal Equation § Given a training set with m examples and n features, define the design matrix X to be the m-by-n matrix give like below: § Thus, the value of θ that minimizes J(θ) is given in closed form by the equation § let y be the m-dimensional vector containing all the target values from the training set:
- 30. SACON Introduction § It is an approach to the classification problem. § The output vector is either 1 or 0 instead of a continuous range of values § y ∈ {0,1} § Binary classification problem (two values) § Linear regression wont work in the classification problem IMAGE CLASSIFICATION
- 31. SACON Logistic Regression: Hypothesis § The hypothesis should satisfy § 0 ≤ h(x) ≤ 1 § the "Sigmoid Function," also called the "Logistic Function": § We want to restrict the range to 0 and 1. This is accomplished by plugging θTx into the Logistic Function
- 35. SACON Advanced Optimization § Gradient Descent § Conjugate Gradient § BFGS § L-BFGS
- 37. SACON Overview § Intro. to Support Vector Machines (SVM) § Properties of SVM § Applications § Discussion
- 38. SACON § A Support Vector Machine (SVM) is a supervised machine learning algorithm that can be employed for both classification and regression purposes. § SVMs are more commonly used in classification problems Introduction Plot shows size and weight of several people, and there is also a way to distinguish between men and women.
- 41. SACON • We will try to select an hyperplane as far as possible from data points from each category (best hyperplane) • Because it correctly classifies the training data • And because it is the one which will generalize better with unseen data What is the Optimal Separating Hyperplane
- 46. SACON Non-linear SVMs n Datasets that are linearly separable with some noise work out great: n But what are we going to do if the dataset is just too hard? n How about… mapping data to a higher- dimensional space: 0 x 0 x 0 x x2
- 48. SACON The“Kernel Trick” n The linear classifier relies on dot product between vectors K(xi,xj)=xi Txj n If every data point is mapped into high-dimensional space via some transformation Φ: x → φ(x), the dot product becomes: K(xi,xj)= φ(xi) Tφ(xj) n A kernel function is some function that corresponds to an inner product in some expanded feature space. n Example: 2-dimensional vectors x=[x1 x2]; let K(xi,xj)=(1 + xi Txj)2 , Need to show that K(xi,xj)= φ(xi) Tφ(xj): K(xi,xj)=(1 + xi Txj)2 , = 1+ xi1 2xj1 2 + 2 xi1xj1 xi2xj2+ xi2 2xj2 2 + 2xi1xj1 + 2xi2xj2 = [1 xi1 2 √2 xi1xi2 xi2 2 √2xi1 √2xi2]T [1 xj1 2 √2 xj1xj2 xj2 2 √2xj1 √2xj2] = φ(xi) Tφ(xj), where φ(x) = [1 x1 2 √2 x1x2 x2 2 √2x1 √2x2]
- 49. SACON What Functions are Kernels? n For some functions K(xi,xj) checking that K(xi,xj)= φ(xi) Tφ(xj) can be cumbersome. n Mercer’s theorem: Every semi-positive definite symmetric function is a kernel n Semi-positive definite symmetric functions correspond to a semi-positive definite symmetric Gram matrix: K(x1,x1) K(x1,x2) K(x1,x3) … K(x1,xN) K(x2,x1) K(x2,x2) K(x2,x3) K(x2,xN) … … … … … K(xN,x1) K(xN,x2) K(xN,x3) … K(xN,xN) K=
- 50. SACON Examples of Kernel Functions n Linear: K(xi,xj)= xi Txj n Polynomial of power p: K(xi,xj)= (1+ xi Txj)p n Gaussian (radial-basis function network): n Sigmoid: K(xi,xj)= tanh(β0xi Txj + β1) ) 2 exp(),( 2 2 s ji ji xx xx - -=K
- 51. SACON Non-linear SVMs Mathematically n Dual problem formulation: n The solution is: n Optimization techniques for finding αi’s remain the same! Find α1…αN such that Q(α) =Σαi - ½ΣΣαiαjyiyjK(xi, xj) is maximized and (1) Σαiyi = 0 (2) αi ≥ 0 for all αi f(x) = ΣαiyiK(xi, xj)+ b
- 52. SACON n SVM locates a separating hyperplane in the feature space and classify points in that space n It does not need to represent the space explicitly, simply by defining a kernel function n The kernel function plays the role of the dot product in the feature space. Nonlinear SVM - Overview
- 53. SACON Properties of SVM § Flexibility in choosing a similarity function § Sparseness of solution when dealing with large data sets - only support vectors are used to specify the separating hyperplane § Ability to handle large feature spaces - complexity does not depend on the dimensionality of the feature space § Overfitting can be controlled by soft margin approach § Nice math property: a simple convex optimization problem which is guaranteed to converge to a single global solution § Feature Selection
- 54. SACON SVM Applications § SVM has been used successfully in many real-world problems § Text (and hypertext) categorization § Image classification § Bioinformatics (Protein classification, Cancer classification) § Hand-written character recognition
- 55. SACON Application 1: Cancer Classification §High Dimensional § - p>1000; n<100 §Imbalanced § - less positive samples §Many irrelevant features §Noisy Genes Patients g-1 g-2 …… g-p P-1 p-2 ……. p-n N n xxkxxK + += l),(],[ FEATURE SELECTION In the linear case, wi 2 gives the ranking of dim i SVM is sensitive to noisy (mis-labeled) data L
- 56. SACON Weakness of SVM § It is sensitive to noise - A relatively small number of mislabeled examples can dramatically decrease the performance § It only considers two classes - how to do multi-class classification with SVM? - Answer: 1) with output arity m, learn m SVM’s § SVM 1 learns “Output==1” vs “Output != 1” § SVM 2 learns “Output==2” vs “Output != 2” § : § SVM m learns “Output==m” vs “Output != m” § 2)To predict the output for a new input, just predict with each SVM and find out which one puts the prediction the furthest into the positive region.
- 57. SACON Application 2: Text Categorization § Task: The classification of natural text (or hypertext) documents into a fixed number of predefined categories based on their content. - email filtering, web searching, sorting documents by topic, etc.. § A document can be assigned to more than one category, so this can be viewed as a series of binary classification problems, one for each category
- 58. SACON Representation of Text IR’s vector space model (aka bag-of-words representation) n A doc is represented by a vector indexed by a pre- fixed set or dictionary of terms n Values of an entry can be binary or weights n Normalization, stop words, word stems n Doc x => φ(x)
- 59. SACON Text Categorization using SVM § The distance between two documents is φ(x)·φ(z) § K(x,z) = 〈φ(x)·φ(z) is a valid kernel, SVM can be used with K(x,z) for discrimination. § Why SVM? § High dimensional input space § Few irrelevant features (dense concept) § Sparse document vectors (sparse instances) § Text categorization problems are linearly separable
- 60. SACON Some Issues § Choice of kernel § Gaussian or polynomial kernel is default § If ineffective, more elaborate kernels are needed § Domain experts can give assistance in formulating appropriate similarity measures § Choice of kernel parameters § e.g. σ in Gaussian kernel § σ is the distance between closest points with different classifications § In the absence of reliable criteria, applications rely on the use of a validation set or cross-validation to set such parameters. § Optimization criterion – Hard margin v.s. Soft margin § a lengthy series of experiments in which various parameters are tested
- 62. SACON k-Nearest Neighbor Classification (kNN) § Unlike all the previous learning methods, kNN does not build model from the training data. § To classify a test instance d, define k-neighborhood P as k nearest neighbors of d § Count number n of training instances in P that belong to class cj § Estimate Pr(cj|d) as n/k § No training is needed. Classification time is linear in training set size for each test case.
- 63. SACON kNN Algorithm n k is usually chosen empirically via a validation set or cross-validation by trying a range of k values. n Distance function is crucial, but depends on applications.
- 65. SACON Discussions § kNN can deal with complex and arbitrary decision boundaries. § Despite its simplicity, researchers have shown that the classification accuracy of kNN can be quite strong and in many cases as accurate as those elaborated methods. § kNN is slow at the classification time § kNN does not produce an understandable model
- 67. SACON INTRODUCTION- What is clustering? § Clustering is the classification of objects into different groups, or more precisely, the partitioning of a data set into subsets (clusters), so that the data in each subset (ideally) share some common trait - often according to some defined distance measure.
- 68. SACON TYPES OF CLUSTERING § Hierarchical algorithms: these find successive clusters using previously established clusters. § Agglomerative ("bottom-up"): Agglomerative algorithms begin with each element as a separate cluster and merge them into successively larger clusters. § Divisive ("top-down"): Divisive algorithms begin with the whole set and proceed to divide it into successively smaller clusters. SACON 2018 - Pune CLUSTER DENDOGRAM
- 69. SACON TYPES OF CLUSTERING § Partitional clustering: Partitional algorithms determine all clusters at once. They include: § K-means and derivatives § Fuzzy c-means clustering § QT clustering algorithm
- 70. SACON TYPES OF CLUSTERING §Distance measure will determine how the similarity of two elements is calculated and it will influence the shape of the clusters. § They include: §The Euclidean distance (also called 2-norm distance) is given by: §The Manhattan distance (also called taxicab norm or 1-norm) is given by:
- 71. SACON § The maximum norm is given by: § The Mahalanobis distance corrects data for different scales and correlations in the variables. § Inner product space: The angle between two vectors can be used as a distance measure when clustering high dimensional data § Hamming distance (sometimes edit distance) measures the minimum number of substitutions required to change one member into another.
- 72. SACON K-MEANS CLUSTERING §The k-means algorithm is an algorithm to cluster n objects based on attributes into k partitions, where k < n. §It is similar to the expectation-maximization algorithm for mixtures of Gaussians in that they both attempt to find the centers of natural clusters in the data. §It assumes that the object attributes form a vector space.
- 73. SACON § An algorithm for partitioning (or clustering) N data points into K disjoint subsets Sj containing data points so as to minimize the sum-of-squares criterion where xn is a vector representing the the nth data point and uj is the geometric centroid of the data points in Sj. § Simply speaking k-means clustering is an algorithm to categorize or to group the objects based on attributes/features into K number of group. § K is positive integer number. § The grouping is done by minimizing the sum of squares of distances between data and the corresponding cluster centroid.
- 74. SACON HOW K-MEANS CLUSTERING WORKS? § Step 1: Begin with a decision on the value of k = Number of clusters § Step 2: Put any initial partition that classifies the data into k clusters. You may assign the training samples randomly, or systematically as the following: § Take the first k training sample as single- element clusters § Assign each of the remaining (N-k) training sample to the cluster with the nearest centroid. After each assignment, recompute the centroid of the gaining cluster. § Step 3: Take each sample in sequence and compute its distance from the centroid of each of the clusters. If a sample is not currently in the cluster with the closest centroid, switch this sample to that cluster and update the centroid of the cluster gaining the new sample and the cluster losing the sample. § Step 4 . Repeat step 3 until convergence is achieved, that is until a pass through the training sample causes no new assignments.
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- 77. SACON § Bias is the algorithm's tendency to consistently learn the wrong thing by not taking into account all the information in the data § Variance is the algorithm's tendency to learn random things irrespective of the real signal by fitting highly flexible models that follow the error/noise in the data too closely Bias/Variance
- 78. SACON • Generalization ability gives an algorithm’s ability to give accurate prediction new, previous unseen data • Models that are too complex for the amount of training data available are said to overfit and are not likely to generalize well to new examples • High variance can cause an algorithm to model the random noise in the training data, rather than the intended outputs (overfitting). • Models that are too simple, that do not even do well on training data, are said to underfit and also not likely to generalize well. • High bias can cause an algorithm to miss the relevant relations between features and target outputs (underfitting). Problem of high Bias/Variance
- 80. SACON Bias/Variance is a Way to Understand Overfitting and Underfitting Error/Loss on training set Dtrain Error/Loss on an unseen test set Dtest high error 80 complex classifiersimple classifier “too simple” “too complex”
- 81. SACON Definitions • Overfitting: too much reliance on the training data • Underfitting: a failure to learn the relationships in the training data • High Variance: model changes significantly based on training data • High Bias: assumptions about model lead to ignoring training data • Overfitting and underfitting cause poor generalization on the test set • A validation set for model tuning can prevent under and overfitting SACON 2018 - Pune
- 82. SACON Ways to Deal with Overfitting and Underfitting § Underfitting: § Easier to resolve § Try different machine learning models § Try stronger models with higher capacity (hyperparameter tuning) § Try more features § Overfitting § Use a resampling technique like K-fold cross validation § Improve the feature quality or remove some features § Training with more data § Early stopping § Regularization § Ensembling Early Stopping
- 83. SACON Regularization • Regularization penalizes the coefficients. In machine learning, it actually penalizes the weight matrices of the nodes. • L1 and L2 are the most common types of regularization. • These update the general cost function by adding another term known as the regularization term. Cost function = Loss (say, binary cross entropy) + Regularization term
- 84. SACON L1 and L2 Regularization § In L2, we have: § Here, lambda is the regularization parameter. It is the hyperparameter whose value is optimized for better results. L2 regularization is also known as weight decay as it forces the weights to decay towards zero (but not exactly zero). § In L1, we have: § In this, we penalize the absolute value of the weights. Unlike L2, the weights may be reduced to zero here.
- 86. SACON Artificial Neural Networks § A Single Neuron: The basic unit of computation in a neural network is the neuron, often called a node or unit. § The function f is non-linear and is called the Activation Function. § The idea of ANNs is based on the belief that working of human brain by making the right connections, can be imitated using silicon and wires as living neurons and dendrites.
- 87. SACON Activation Function § Sigmoid: takes a real-valued input and squashes it to range between 0 and 1. σ(x) = 1 / (1 + exp(−x)) § tanh: takes a real-valued input and squashes it to the range [-1, 1] tanh(x) = 2σ(2x) − 1 § ReLU: ReLU stands for Rectified Linear Unit. It takes a real-valued input and thresholds it at zero (replaces negative values with zero) f(x) = max(0, x)
- 89. SACON Neural Network Intuition (Multiple Layer layer) § Multi Layer Neural network is capable of learning complex functions. § Lets consider XNOR operation. • CASE1: X1 XNOR X2 = (A’.B’) + (A.B) NN representation • CASE2: X1 XNOR X2 = NOT [ (A+B).(A’+B’) ] NN representation = ?
- 90. SACON Back-Propagation § Back-propagation (BP) algorithms works by determining the loss (or error) at the output and then propagating it back into the network. § The weights are updated to minimize the error resulting from each neuron.
- 92. SACON Deep Learning • Deep Neural Network has a been very successful recently in the field of computer vision, Natural language Processing, Speech recognition and many more. • Some of the important/successful networks are • Convolutional Neural Network: Has been very successful in computer vision • Recurrent neural network: Has been successful in Natural Language Processing and speech recognition as well.
- 94. SACON Decision Tree § Decision Tree is the supervised learning algorithm. § We split the population or sample into two or more homogeneous sets (or sub- populations) based on most significant differentiator in input variables. 1.Root Node: It represents entire population or sample and this further gets divided into two or more homogeneous sets. 2.Splitting: It is a process of dividing a node into two or more sub-nodes. 3.Decision Node: When a sub-node splits into further sub-nodes, then it is called decision node. 4.Leaf/ Terminal Node: Nodes do not split is called Leaf or Terminal node.
- 96. SACON Methods of splitting: Information gain which node can be described easily? § Information theory is a measure to define this degree of disorganization in a system known as Entropy. Here p and q is probability of success and failure respectively in that node.
- 97. SACON Other Tree based methods § Trade-off management of bias-variance errors. § Bagging is a simple ensembling technique in which we build many independent predictors/models/learners and combine them using some model averaging techniques. § Ensemble methods involve group of predictive models to achieve a better accuracy and model stability. § Random Forest: Multiple Trees instead of single tree. It’s a bagging method § To classify a new object based on attributes, each tree gives a classification and we say the tree “votes” for that class.
- 98. SACON Other Tree based methods § Gradient Boosting is a tree ensemble technique that creates a strong classifier from a number of weak classifiers. § It works in the technique of weak learners and the additive model. § Boosting is an ensemble technique in which the predictors are not made independently, but sequentially.
- 99. SACON Iris Dataset § Three species of Iris (Iris setosa, Iris virginica and Iris versicolor). § Four features were measured from each sample: the length and the width of the sepals and petals, in centimeters.
- 100. SACON References • Andrew Ng’s Coursera Course • Scikit Learn Training example on Google • Nvidia • Sebastian Ruder’s blog • HBR • MIT Tech Review • Lots of Others • AI community in general • IDLI Community