Building Machine Learning Systems with Python - Richert, Coelho

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Chapter 6 Similarly, we do this for the prior probabilities: Accounting for arithmetic underflows There is yet another roadblock. In reality, we work with probabilities much smaller than the ones we have dealt with in the toy example. In reality, we also have more than two features, which we multiply with each other. This will quickly lead to the point where the accuracy provided by NumPy does not suffice anymore: >>> import numpy as np >>> np.set_printoptions(precision=20) # tell numpy to print out more digits (default is 8) >>> np.array([2.48E-324]) array([ 4.94065645841246544177e-324]) >>> np.array([2.47E-324]) array([ 0.]) So, how probable is it that we will ever hit a number like 2.47E-324? To answer this, we just have to imagine a likelihood for the conditional probabilities of 0.0001 and then multiply 65 of them together (meaning that we have 65 low probable feature values) and you've been hit by the arithmetic underflow: >>> x=0.00001 >>> x**64 # still fine 1e-320 >>> x**65 # ouch 0.0 A float in Python is typically implemented using double in C. To find out whether it is the case for your platform, you can check it as follows: >>> import sys >>> sys.float_info sys.float_info(max=1.7976931348623157e+308, max_exp=1024, max_10_ exp=308, min=2.2250738585072014e-308, min_exp=-1021, min_10_exp=-307, dig=15, mant_dig=53, epsilon=2.220446049250313e-16, radix=2, rounds=1) To mitigate this, you could switch to math libraries such as mpmath (http://code. google.com/p/mpmath/) that allow arbitrary accuracy. However, they are not fast enough to work as a NumPy replacement. [ 125 ]
Classification II – Sentiment Analysis Fortunately, there is a better way to take care of this, and it has to do with a nice relationship that we maybe still know from school: If we apply it to our case, we get the following: As the probabilities are in the interval between 0 and 1, the log of the probabilities lies in the interval -∞ and 0. Don't get irritated with that. Higher numbers are still a stronger indicator for the correct class—it is only that they are negative now. There is one caveat though: we actually don't have log in the formula's nominator (the part preceding the fraction). We only have the product of the probabilities. In our case, luckily we are not interested in the actual value of the probabilities. We simply want to know which class has the highest posterior probability. We are lucky because if we find this: Then we also have the following: [ 126 ]
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Building Machine Learning Systems w
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Credits Authors Willi Richert Luis
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Luis Pedro Coelho is a Computationa
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Maurice HT Ling completed his PhD.
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Table of Contents Preface 1 Chapter
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Table of Contents Tuning the instan
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Table of Contents Improving classif
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Preface You could argue that it is
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Preface What you need for this book
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Downloading the example code You ca
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Getting Started with Python Machine
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Learning How to Classify with Real-
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Chapter 2 We are using Matplotlib;
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Chapter 2 The last few lines select
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Chapter 2 error = 0.0 for ei in ran
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Chapter 2 We can play around with t
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Chapter 2 Features and feature engi
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Chapter 2 In the preceding screensh
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Chapter 2 Binary and multiclass cla
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Clustering - Finding Related Posts
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Chapter 3 How to do it More robust
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Chapter 3 This means that the first
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Chapter 3 ... post = posts[i] ... i
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Chapter 3 If you have a clear pictu
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Chapter 3 Extending the vectorizer
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Chapter 3 0.0 >>> print(tfidf("b",
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Chapter 3 Flat clustering divides t
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Because the cluster centers are mov
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Chapter 3 'D:\\data\\379\\raw\\comp
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As we have learned previously, we w
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Chapter 3 Position Similarity Excer
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Chapter 3 But before you go there,
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Page 93 and 94: Topic Modeling Sparsity means that
Page 95 and 96: Topic Modeling Although daunting at
Page 97 and 98: Topic Modeling … for tj,v in t:
Page 99 and 100: Topic Modeling Finally, we build th
Page 101 and 102: Topic Modeling Alternatively, we ca
Page 103 and 104: Topic Modeling Topic modeling was f
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Page 134 and 135: Chapter 6 Getting to know the Bayes
Page 136 and 137: Using Naive Bayes to classify Given
Page 138 and 139: Chapter 6 This denotation "" leads
Page 142 and 143: Chapter 6 A quick look at the previ
Page 144 and 145: Chapter 6 To keep our experimentati
Page 146 and 147: Chapter 6 Y = np.zeros(Y.shape[0])
Page 148 and 149: Chapter 6 ° ° Experiment with whe
Page 150 and 151: Chapter 6 We have to be patient whe
Page 152 and 153: Chapter 6 First, we define a range
Page 154 and 155: Chapter 6 Determining the word type
Page 156 and 157: Chapter 6 Successfully cheating usi
Page 158 and 159: Chapter 6 Our first estimator Now w
Page 160 and 161: Chapter 6 for d in documents: allca
Page 162 and 163: Regression - Recommendations You ha
Page 164 and 165: Chapter 7 The preceding graph shows
Page 166 and 167: Chapter 7 Root mean squared error a
Page 168 and 169: Penalized regression The important
Page 170 and 171: Chapter 7 P greater than N scenario
Page 172 and 173: Chapter 7 So, we can see that the d
Page 174 and 175: Chapter 7 Fortunately, scikit-learn
Page 176 and 177: [ 161 ] Chapter 7 The loading of th
Page 178: Chapter 7 Summary In this chapter,
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Page 185 and 186: Weights Regression - Recommendation
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Regression - Recommendations Improv
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Regression - Recommendations Improv
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Classification III - Music Genre Cl
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Chapter 9 Matplotlib provides the c
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[ 185 ] Chapter 9
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Chapter 9 def create_fft(fn): sampl
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Chapter 9 ax.set_yticks(range(len(g
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Chapter 9 On the left-hand side gra
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[ 193 ] Chapter 9 Improving classif
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We get the following promising resu
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Chapter 9 Summary In this chapter,
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Computer Vision - Pattern Recogniti
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Dimensionality Reduction Sketching
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Dimensionality Reduction However, t
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Dimensionality Reduction To underst
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Dimensionality Reduction In order t
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Dimensionality Reduction Asking the
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Dimensionality Reduction n_ feature
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Dimensionality Reduction Sketching
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Dimensionality Reduction Limitation
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Dimensionality Reduction Now, MDS t
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Dimensionality Reduction Of course,
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Big(ger) Data • Your algorithms c
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Big(ger) Data sleep(4) return 2*x @
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Big(ger) Data Looking under the hoo
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Big(ger) Data def write_result(ofna
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Big(ger) Data Amazon Web Services i
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Big(ger) Data In EC2 parlance, a ru
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Big(ger) Data In this system, pip i
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Big(ger) Data Keys, keys, and more
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Big(ger) Data We can use the same j
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Where to Learn More about Machine L
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• Machined Learnings at http://ww
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Index A AcceptedAnswerId attribute
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F false negative 41 false positive
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inary matrix of recommendations, us
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sklearn.naive_bayes package 127 skl
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NumPy Beginner's Guide - Second Edi
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