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115 hunch net-2005-09-26-Prediction Bounds as the Mathematics of Science


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Introduction: “Science” has many meanings, but one common meaning is “the scientific method ” which is a principled method for investigating the world using the following steps: Form a hypothesis about the world. Use the hypothesis to make predictions. Run experiments to confirm or disprove the predictions. The ordering of these steps is very important to the scientific method. In particular, predictions must be made before experiments are run. Given that we all believe in the scientific method of investigation, it may be surprising to learn that cheating is very common. This happens for many reasons, some innocent and some not. Drug studies. Pharmaceutical companies make predictions about the effects of their drugs and then conduct blind clinical studies to determine their effect. Unfortunately, they have also been caught using some of the more advanced techniques for cheating here : including “reprobleming”, “data set selection”, and probably “overfitting by review”


Summary: the most important sentenses genereted by tfidf model

sentIndex sentText sentNum sentScore

1 “Science” has many meanings, but one common meaning is “the scientific method ” which is a principled method for investigating the world using the following steps: Form a hypothesis about the world. [sent-1, score-1.008]

2 The ordering of these steps is very important to the scientific method. [sent-4, score-0.544]

3 In particular, predictions must be made before experiments are run. [sent-5, score-0.327]

4 Given that we all believe in the scientific method of investigation, it may be surprising to learn that cheating is very common. [sent-6, score-0.897]

5 Pharmaceutical companies make predictions about the effects of their drugs and then conduct blind clinical studies to determine their effect. [sent-9, score-0.548]

6 It isn’t too surprising to observe this: when the testers of a drug have $10 9 or more riding on the outcome the temptation to make the outcome “right” is extreme. [sent-11, score-0.679]

7 When conducting experiments of some new phenomena, it is common for the experimental apparatus to simply not work right. [sent-13, score-0.583]

8 (Of course, the more common outcome is that the drugs effectiveness is just overstated. [sent-18, score-0.422]

9 Each prediction bound has a number of things in common: They assume that the data is independently and identically drawn. [sent-21, score-0.411]

10 This is well suited to experimental situations where experimenters work very hard to make different experiments be independent. [sent-22, score-0.692]

11 This is important for experimental testing of predictions because the distribution that observations are expected to come from is a part of the theory under test. [sent-25, score-0.31]

12 These two properties above form an ‘equivalence class’ over different mathematical bounds where each bound can be trusted to an equivalent degree. [sent-26, score-0.548]

13 Inside of this equivalent class there are several that may be helpful in determining whether deviations from the scientific method are reasonable or not. [sent-27, score-0.845]

14 The most basic test set bound corresponds to the scientific method above. [sent-28, score-0.822]

15 The Occam’s Razor bound allows a careful reordering of steps (1), (2) and step (3). [sent-29, score-0.664]

16 More “interesting” bounds like the VC-bound and the PAC-Bayes bound allow more radical alterations of these steps. [sent-30, score-0.62]

17 The Sample Compression bound allows careful disposal of some datapoints. [sent-32, score-0.509]

18 Progressive Validation bounds (such as here , here or here ) allow hypotheses to be safely reformulated in arbitrary ways as experiments progress. [sent-33, score-0.439]

19 Scientific experimenters looking for a little extra flexibility in the scientific method may find these approaches useful. [sent-34, score-0.821]

20 (And if they don’t, maybe there is another bound in this equivalence class that needs to be worked out. [sent-35, score-0.485]


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tfidf for this blog:

wordName wordTfidf (topN-words)

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