Machine Learning: Basics PDF

Machine Learning: the basics Learning from examples Machine Learning: Basics 1 Outline of this lecture Objects, features, measurements,... datasets and feature space Traditional pattern recognition: classification Class posterior probabilities and Bayes’ rule Bayes’ cl...

Machine Learning: the basics Learning from examples Machine Learning: Basics 1 Outline of this lecture Objects, features, measurements,... datasets and feature space Traditional pattern recognition: classification Class posterior probabilities and Bayes’ rule Bayes’ classifier and Bayes’ error Misclassification costs Machine Learning: Basics 2 Learning from Examples Given some examples, we may perform: clustering outlier detection classification regression … on new objects. We assume that no complete physical model is known! Machine Learning: Basics 3  Generalization We don't want to just describe the data... We want to predict for new, unseen data! Machine Learning: Basics 4  Generalization Training set: All examples are labeled This set is used to train/develop our system Test set: These examples cannot be used to train our system The examples do not have to be labeled When labels are available, we can objectively evaluate our system Machine Learning: Basics 5 Features To do these tasks automatically, we have to encode the objects. Objects are typically encoded by defining features: shape weight color 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 T x = [x1 , x2 ,..., xM ] Machine Learning: Basics 6 Datasets When we measure the features of many objects: we obtain a dataset. dataset For classification: feature feature vector labeled object measurement Machine Learning: Basics 7 How to define features? Note that features reduce, and give a specific view of the objects: YOU (the user) is responsible for it Good features allow for pattern recognition, bad features allow for nothing Other (than feature vector) approaches of defining objects are: Dissimilarity approach Structural pattern recognition (graphs) Feature approach is very well developed, other approaches are still more research. Machine Learning: Basics 8 Noise in the measurements The measurements will never be perfect Objects within a class will vary We need to apply some statistics to cover all the variations Machine Learning: Basics 9 Measurements Task: distinguish between 3 types of Iris flowers: (Images from Wikipedia) Iris Setosa Iris Versicolor Iris Virginica Measurements: sepal width, sepal length, petal width, petal length. Machine Learning: Basics 10 Objects in feature space We can interpret the x2 measurements as a vector in a vector space: T AAADGnicpVJNa9VAFJ0Xv+rz61WXgoS+CoIlJEWsG+GhGzdChb62kIlhMrnpGzofYWbSJoTs/Aku/QVu9Re4E7duuveHOMmroK2C6IEwh3Pumdy53KzkzNgwPBl5Fy5eunxl5er42vUbN29NVm/vGlVpCnOquNL7GTHAmYS5ZZbDfqmBiIzDXnb4vPf3jkAbpuSObUpIBDmQrGCUWCelk3tYELvIirbunsZ1Gm3U6eZGEATufJm83kkn0zAIB/jnSXRKprM1/PDtyazZTldH33CuaCVAWsqJMXEUljZpibaMcujGuDJQEnpIDiB2VBIBJmmHh3T+fafkfqG0+6T1B/XnREuEMY3IXGXftjnr9eLvvLiyxZOkZbKsLEi6/FFRcd8qv5+KnzMN1PLGEUI1c736dEE0odbNbow1SDimSggic3wENI6SdhgcXShGYew7OCFTdYszxfPeWsc5MyUnjbENh6Fai3Yadeu4kj+Kuu4PWQu1/aegce2X/xX9iws6txfR2S04T3Y3g+hx8OiVW5BnaIkVdBetoQcoQltohl6gbTRHFL1B79EH9NF7533yPntflqXe6DRzB/0C7+t3jasEaA== x = [x1 , x2 ,..., xM ] This originates in principle from a probability density over the whole feature space p(x, y) x1 Machine Learning: Basics 11 Classification y1 AAAB6nicbVDLSgNBEOyNrxhfUY9eBoPgKeyKr2PQi8eI5gHJEmYns8mQ2dllplcISz7BiwdFvPpF3vwbJ8keNLGgoajqprsrSKQw6LrfTmFldW19o7hZ2tre2d0r7x80TZxqxhsslrFuB9RwKRRvoEDJ24nmNAokbwWj26nfeuLaiFg94jjhfkQHSoSCUbTSw7jn9coVt+rOQJaJl5MK5Kj3yl/dfszSiCtkkhrT8dwE/YxqFEzySambGp5QNqID3rFU0YgbP5udOiEnVumTMNa2FJKZ+nsio5Ex4yiwnRHFoVn0puJ/XifF8NrPhEpS5IrNF4WpJBiT6d+kLzRnKMeWUKaFvZWwIdWUoU2nZEPwFl9eJs2zqndZvbg/r9Ru8jiKcATHcAoeXEEN7qAODWAwgGd4hTdHOi/Ou/Mxby04+cwh/IHz+QMQdo2r Given labeled data: x Assign to each object a class label y AAAB6HicbVDLSgNBEOz1GeMr6tHLYBA8hV3xdQx68ZiAeUCyhNlJbzJmdnaZmRXCki/w4kERr36SN//GSbIHTSxoKKq66e4KEsG1cd1vZ2V1bX1js7BV3N7Z3dsvHRw2dZwqhg0Wi1i1A6pRcIkNw43AdqKQRoHAVjC6m/qtJ1Sax/LBjBP0IzqQPOSMGivVx71S2a24M5Bl4uWkDDlqvdJXtx+zNEJpmKBadzw3MX5GleFM4KTYTTUmlI3oADuWShqh9rPZoRNyapU+CWNlSxoyU39PZDTSehwFtjOiZqgXvan4n9dJTXjjZ1wmqUHJ5ovCVBATk+nXpM8VMiPGllCmuL2VsCFVlBmbTdGG4C2+vEya5xXvqnJZvyhXb/M4CnAMJ3AGHlxDFe6hBg1ggPAMr/DmPDovzrvzMW9dcfKZI/gD5/MH6v2NBw== In effect splits the y3 AAAB6nicbVDLSgNBEOyNrxhfUY9eBoPgKez6Pga9eIxoHpAsYXbSmwyZnV1mZoWw5BO8eFDEq1/kzb9xkuxBowUNRVU33V1BIrg2rvvlFJaWV1bXiuuljc2t7Z3y7l5Tx6li2GCxiFU7oBoFl9gw3AhsJwppFAhsBaObqd96RKV5LB/MOEE/ogPJQ86osdL9uHfaK1fcqjsD+Uu8nFQgR71X/uz2Y5ZGKA0TVOuO5ybGz6gynAmclLqpxoSyER1gx1JJI9R+Njt1Qo6s0idhrGxJQ2bqz4mMRlqPo8B2RtQM9aI3Ff/zOqkJr/yMyyQ1KNl8UZgKYmIy/Zv0uUJmxNgSyhS3txI2pIoyY9Mp2RC8xZf/kuZJ1buont+dVWrXeRxFOIBDOAYPLqEGt1CHBjAYwBO8wKsjnGfnzXmftxacfGYffsH5+AYTfo2t feature space in separate regions y2 AAAB6nicbVDLSgNBEOz1GeMr6tHLYBA8hd3g6xj04jGieUCyhNnJbDJkdnaZ6RXCkk/w4kERr36RN//GSbIHTSxoKKq66e4KEikMuu63s7K6tr6xWdgqbu/s7u2XDg6bJk414w0Wy1i3A2q4FIo3UKDk7URzGgWSt4LR7dRvPXFtRKwecZxwP6IDJULBKFrpYdyr9kplt+LOQJaJl5My5Kj3Sl/dfszSiCtkkhrT8dwE/YxqFEzySbGbGp5QNqID3rFU0YgbP5udOiGnVumTMNa2FJKZ+nsio5Ex4yiwnRHFoVn0puJ/XifF8NrPhEpS5IrNF4WpJBiT6d+kLzRnKMeWUKaFvZWwIdWUoU2naEPwFl9eJs1qxbusXNyfl2s3eRwFOIYTOAMPrqAGd1CHBjAYwDO8wpsjnRfn3fmYt644+cwR/IHz+QMR+o2s Machine Learning: Basics 12 The general model Function f should give the predicted output. f (x) y AAAB6HicbVDLSgNBEOz1GeMr6tHLYBA8hV3xdQx68ZiAeUCyhNlJbzJmdnaZmRXCki/w4kERr36SN//GSbIHTSxoKKq66e4KEsG1cd1vZ2V1bX1js7BV3N7Z3dsvHRw2dZwqhg0Wi1i1A6pRcIkNw43AdqKQRoHAVjC6m/qtJ1Sax/LBjBP0IzqQPOSMGivVx71S2a24M5Bl4uWkDDlqvdJXtx+zNEJpmKBadzw3MX5GleFM4KTYTTUmlI3oADuWShqh9rPZoRNyapU+CWNlSxoyU39PZDTSehwFtjOiZqgXvan4n9dJTXjjZ1wmqUHJ5ovCVBATk+nXpM8VMiPGllCmuL2VsCFVlBmbTdGG4C2+vEya5xXvqnJZvyhXb/M4CnAMJ3AGHlxDFe6hBg1ggPAMr/DmPDovzrvzMW9dcfKZI/gD5/MH6v2NBw== x and... 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Machine Learning: Basics 13 Output of the model For each object in the feature space, we should estimate: AAAB+HicbVC7TsMwFL3hWcqjAUYWiwqpLFWCeI0VLIxFog+prSrHdVqrjhPZDiKEfgkLAwix8ils/A1OmwFajmTp6Jx7dY+PF3GmtON8W0vLK6tr64WN4ubW9k7J3t1rqjCWhDZIyEPZ9rCinAna0Exz2o4kxYHHacsbX2d+655KxUJxp5OI9gI8FMxnBGsj9e1SVEmeugHWI89PHybHfbvsVJ0p0CJxc1KGHPW+/dUdhCQOqNCEY6U6rhPpXoqlZoTTSbEbKxphMsZD2jFU4ICqXjoNPkFHRhkgP5TmCY2m6u+NFAdKJYFnJrOIat7LxP+8Tqz9y17KRBRrKsjskB9zpEOUtYAGTFKieWIIJpKZrIiMsMREm66KpgR3/suLpHlSdc+rZ7en5dpVXkcBDuAQKuDCBdTgBurQAAIxPMMrvFmP1ov1bn3MRpesfGcf/sD6/AHgipM/ p(y|x) In practice we fit a function: f (x) Machine Learning: Basics 14 Pattern Recognition pipeline y learning, fitting, x training known find find model objects features features f(x) new extract z y classify evaluation object features applying, generalization testing Machine Learning: Basics 15 Classification, how to do it? Given a feature, and a training set, where is the blue class? Gaussian Data 1 0.8 0.6 0.4 0.2 0 !2 !1 0 1 2 3 4 5 Feature 1 Machine Learning: Basics 16  Class posterior probability For each object we want to estimate p(blue|feature 1) Gaussian Data 1 0.8 p(blue|feature 1) 0.6 0.4 0.2 0 !2 !1 0 1 2 3 4 5 Feature 1 Machine Learning: Basics 17 Class posterior probability For each object we want to estimate p(y|x) AAAB+HicbVC7TsMwFL3hWcqjAUYWiwqpLFWCeI0VLIxFog+prSrHdVqrjhPZDiKEfgkLAwix8ils/A1OmwFajmTp6Jx7dY+PF3GmtON8W0vLK6tr64WN4ubW9k7J3t1rqjCWhDZIyEPZ9rCinAna0Exz2o4kxYHHacsbX2d+655KxUJxp5OI9gI8FMxnBGsj9e1SVEmeugHWI89PHybHfbvsVJ0p0CJxc1KGHPW+/dUdhCQOqNCEY6U6rhPpXoqlZoTTSbEbKxphMsZD2jFU4ICqXjoNPkFHRhkgP5TmCY2m6u+NFAdKJYFnJrOIat7LxP+8Tqz9y17KRBRrKsjskB9zpEOUtYAGTFKieWIIJpKZrIiMsMREm66KpgR3/suLpHlSdc+rZ7en5dpVXkcBDuAQKuDCBdTgBurQAAIxPMMrvFmP1ov1bn3MRpesfGcf/sD6/AHgipM/ Gaussian Data 1 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00 X AAACA3icbVDLSsNAFJ34rPUVdaebwSLUTUnE10YounFZwT6gCWEynbRDZ5IwMxFDLLjxV9y4UMStP+HOv3HSZqGtBy4czrmXe+/xY0alsqxvY25+YXFpubRSXl1b39g0t7ZbMkoEJk0csUh0fCQJoyFpKqoY6cSCIO4z0vaHV7nfviNC0ii8VWlMXI76IQ0oRkpLnrnryIR7FMbV1KMPDkdq4AfZ/ejwwvbMilWzxoCzxC5IBRRoeOaX04twwkmoMENSdm0rVm6GhKKYkVHZSSSJER6iPulqGiJOpJuNfxjBA630YBAJXaGCY/X3RIa4lCn3dWd+pJz2cvE/r5uo4NzNaBgnioR4sihIGFQRzAOBPSoIVizVBGFB9a0QD5BAWOnYyjoEe/rlWdI6qtmntZOb40r9soijBPbAPqgCG5yBOrgGDdAEGDyCZ/AK3own48V4Nz4mrXNGMbMD/sD4/AGTG5d8 !2!2 !1!1 00 11 Feature 22 Feature1 1 33 44 55 p(yi |x) = 1 i Machine Learning: Basics 19  Classify new objects Assign the label of the class with the largest posterior probability Gaussian Data 1 p(y1 |x) > p(y0.82 |x) p(y2 |x) > p(y1 |x) 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|x) = p(y2 |x) AAACDnicbZC7TsMwFIYdriXcAowsFlWlslRJxW1BqmBhLBK9SG1UOa7TWnWcyHYQUegTsPAqLAwgxMrMxtvgtBlKyy9Z+vWdc+Rzfi9iVCrb/jGWlldW19YLG+bm1vbOrrW335RhLDBp4JCFou0hSRjlpKGoYqQdCYICj5GWN7rO6q17IiQN+Z1KIuIGaMCpTzFSGvWsUlROes5jN0Bq6Pnpw/gYXpoZq86ynlW0K/ZEcNE4uSmCXPWe9d3thzgOCFeYISk7jh0pN0VCUczI2OzGkkQIj9CAdLTlKCDSTSfnjGFJkz70Q6EfV3BCZydSFEiZBJ7uzFaU87UM/lfrxMq/cFPKo1gRjqcf+TGDKoRZNrBPBcGKJdogLKjeFeIhEggrnaCpQ3DmT140zWrFOauc3p4Ua1d5HAVwCI5AGTjgHNTADaiDBsDgCbyAN/BuPBuvxofxOW1dMvKZA/BHxtcvMa2blw== 0.2 0 !2 !1 0 1 2 3 4 5 Feature 1 Machine Learning: Basics 20  Classify new objects Assign the label of the class with the largest posterior probability Gaussian Data 1 p(y1 |x) > p(y0.82 |x) p(y2 |x) > p(y1 |x) 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