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	<title>De Rerum Natura &#187; Error Theory</title>
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	<link>http://www.corrada.com/blog</link>
	<description>Randomness, entropy, pattern matching, maps, geometry, knots, and scientific readings</description>
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		<title>Robust voting in uncertain environments</title>
		<link>http://www.corrada.com/blog/2008/11/17/robust-voting-in-uncertain-environments/</link>
		<comments>http://www.corrada.com/blog/2008/11/17/robust-voting-in-uncertain-environments/#comments</comments>
		<pubDate>Mon, 17 Nov 2008 05:00:15 +0000</pubDate>
		<dc:creator>Andrés</dc:creator>
				<category><![CDATA[Compressed Sensing]]></category>
		<category><![CDATA[Machine Learning]]></category>
		<category><![CDATA[Randomness]]></category>
		<category><![CDATA[precision error application]]></category>

		<guid isPermaLink="false">http://www.corrada.com/blog/?p=83</guid>
		<description><![CDATA[Combining the judgments of different recognizers is always better than using the best one alone. This observation is universal in machine learning realms. But it seldom gets used in practice. Why?
For one, it costs more to implement. Instead of one recognizer, you must deploy several. Computing cycles grow linearly with the number of recognizers if [...]]]></description>
		<wfw:commentRss>http://www.corrada.com/blog/2008/11/17/robust-voting-in-uncertain-environments/feed/</wfw:commentRss>
		<slash:comments>0</slash:comments>
		</item>
		<item>
		<title>Positive and negative precision error correlations, real or not?</title>
		<link>http://www.corrada.com/blog/2008/05/07/positive-and-negative-precision-error-correlations-real-or-not/</link>
		<comments>http://www.corrada.com/blog/2008/05/07/positive-and-negative-precision-error-correlations-real-or-not/#comments</comments>
		<pubDate>Thu, 08 May 2008 02:27:16 +0000</pubDate>
		<dc:creator>Andrés</dc:creator>
				<category><![CDATA[Compressed Sensing]]></category>
		<category><![CDATA[Error Theory]]></category>

		<guid isPermaLink="false">http://www.corrada.com/blog/?p=78</guid>
		<description><![CDATA[

All the experiments we have been carrying out with precision error have, so far, been with real data. Because of this, we do not have &#8220;ground truth&#8221; to determine if the reconstruction is correct. That changed today.
Synthetic experiments are a well-known device for studying models or algorithms. By artificially creating data where one knows exactly [...]]]></description>
		<wfw:commentRss>http://www.corrada.com/blog/2008/05/07/positive-and-negative-precision-error-correlations-real-or-not/feed/</wfw:commentRss>
		<slash:comments>0</slash:comments>
		</item>
		<item>
		<title>Not every measurement is perfect</title>
		<link>http://www.corrada.com/blog/2008/04/13/not-every-measurement-is-perfect/</link>
		<comments>http://www.corrada.com/blog/2008/04/13/not-every-measurement-is-perfect/#comments</comments>
		<pubDate>Mon, 14 Apr 2008 01:34:12 +0000</pubDate>
		<dc:creator>Andrés</dc:creator>
				<category><![CDATA[Multiple Choice Questions Exam]]></category>
		<category><![CDATA[precision error application]]></category>

		<guid isPermaLink="false">http://www.corrada.com/blog/?p=73</guid>
		<description><![CDATA[
Just to show that not all questions behave as nicely as question 9 in the previous post, here is the plot for question 6 in the same exam.The fit is not as good as for question 9. This is expected, there is no reason why the precision error should decay with a perfect exponential behavior. [...]]]></description>
		<wfw:commentRss>http://www.corrada.com/blog/2008/04/13/not-every-measurement-is-perfect/feed/</wfw:commentRss>
		<slash:comments>0</slash:comments>
		</item>
		<item>
		<title>Precision error for parse trees</title>
		<link>http://www.corrada.com/blog/2008/04/01/precision-error-for-parse-trees/</link>
		<comments>http://www.corrada.com/blog/2008/04/01/precision-error-for-parse-trees/#comments</comments>
		<pubDate>Tue, 01 Apr 2008 05:20:21 +0000</pubDate>
		<dc:creator>Andrés</dc:creator>
				<category><![CDATA[Error Theory]]></category>
		<category><![CDATA[Graph Theory]]></category>
		<category><![CDATA[Natural Language Processing]]></category>
		<category><![CDATA[parse trees]]></category>

		<guid isPermaLink="false">http://www.corrada.com/blog/?p=68</guid>
		<description><![CDATA[The precision error equations require that &#8220;ground truth&#8221; cancel out. It is easy to see what that means for elevations in a map. What does it mean for parse trees in a natural language processing task like sentence parsing?
One way to define distance between trees is to consider the total number of reverse operations that [...]]]></description>
		<wfw:commentRss>http://www.corrada.com/blog/2008/04/01/precision-error-for-parse-trees/feed/</wfw:commentRss>
		<slash:comments>0</slash:comments>
		</item>
		<item>
		<title>Asymmetry in likelihood of causing the error</title>
		<link>http://www.corrada.com/blog/2008/03/31/asymmetry-in-likelihood-of-causing-the-error/</link>
		<comments>http://www.corrada.com/blog/2008/03/31/asymmetry-in-likelihood-of-causing-the-error/#comments</comments>
		<pubDate>Mon, 31 Mar 2008 09:12:08 +0000</pubDate>
		<dc:creator>Andrés</dc:creator>
				<category><![CDATA[Error Theory]]></category>
		<category><![CDATA[Machine Learning]]></category>

		<guid isPermaLink="false">http://www.corrada.com/blog/?p=62</guid>
		<description><![CDATA[As the number of models increase, the observed pattern in prediction discrepancies allows one to decide what is causing it assuming  uniform uncertainty among all possible scenarios. The observed error pattern will be consistent with many different scenarios. In some scenarios, the noisy model predictions are due to the model being correct and the [...]]]></description>
		<wfw:commentRss>http://www.corrada.com/blog/2008/03/31/asymmetry-in-likelihood-of-causing-the-error/feed/</wfw:commentRss>
		<slash:comments>0</slash:comments>
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		<title>Minimum number of questions needed for an exam</title>
		<link>http://www.corrada.com/blog/2008/03/29/minimum-number-of-questions-needed-for-an-exam/</link>
		<comments>http://www.corrada.com/blog/2008/03/29/minimum-number-of-questions-needed-for-an-exam/#comments</comments>
		<pubDate>Sat, 29 Mar 2008 18:12:59 +0000</pubDate>
		<dc:creator>Andrés</dc:creator>
				<category><![CDATA[Randomness]]></category>
		<category><![CDATA[precision error application]]></category>
		<category><![CDATA[test assessment]]></category>

		<guid isPermaLink="false">http://www.corrada.com/blog/2008/03/29/minimum-number-of-questions-needed-for-an-exam/</guid>
		<description><![CDATA[Another application of the precision error covariance matrix is to find out the minimum number of questions needed for an exam. The linear algebra system derived from the precision erorr equations requires at least three scientific models before one can measure the precision error. More is better. But what is enough? How many questions does [...]]]></description>
		<wfw:commentRss>http://www.corrada.com/blog/2008/03/29/minimum-number-of-questions-needed-for-an-exam/feed/</wfw:commentRss>
		<slash:comments>0</slash:comments>
		</item>
		<item>
		<title>Grading mistake detection with precision error</title>
		<link>http://www.corrada.com/blog/2008/03/28/grading-mistake-detection-with-precision-error/</link>
		<comments>http://www.corrada.com/blog/2008/03/28/grading-mistake-detection-with-precision-error/#comments</comments>
		<pubDate>Fri, 28 Mar 2008 21:51:30 +0000</pubDate>
		<dc:creator>Andrés</dc:creator>
				<category><![CDATA[Randomness]]></category>
		<category><![CDATA[precision error application]]></category>
		<category><![CDATA[test assessment]]></category>

		<guid isPermaLink="false">http://www.corrada.com/blog/2008/03/28/grading-mistake-detection-with-precision-error/</guid>
		<description><![CDATA[While making a covariance matrix for eighteen questions in an introductory Physics exam I gave in the Spring of 2006, I discovered another use for the precision error measurements: grading mistake detection.
The figure shown first is my initial try. I computed the student score on each question with the function: f(correct)=1.0 ,f(incorrect)=0.0 .. Note the [...]]]></description>
		<wfw:commentRss>http://www.corrada.com/blog/2008/03/28/grading-mistake-detection-with-precision-error/feed/</wfw:commentRss>
		<slash:comments>0</slash:comments>
		</item>
		<item>
		<title>Random faster than systematic</title>
		<link>http://www.corrada.com/blog/2008/03/24/random-faster-than-systematic/</link>
		<comments>http://www.corrada.com/blog/2008/03/24/random-faster-than-systematic/#comments</comments>
		<pubDate>Mon, 24 Mar 2008 10:40:07 +0000</pubDate>
		<dc:creator>Andrés</dc:creator>
				<category><![CDATA[Compressed Sensing]]></category>
		<category><![CDATA[Error Theory]]></category>
		<category><![CDATA[Randomness]]></category>

		<guid isPermaLink="false">http://www.corrada.com/blog/2008/03/24/random-faster-than-systematic/</guid>
		<description><![CDATA[I am writing a Mathematica program to produce the precision error signal and reconstruction matrix for an arbitrary number of models. The maximum number I had tried before was ten models because it corresponded to the number of maps we have for the 29 Palms dataset.
My first try consisted of systematically creating all possible permutations [...]]]></description>
		<wfw:commentRss>http://www.corrada.com/blog/2008/03/24/random-faster-than-systematic/feed/</wfw:commentRss>
		<slash:comments>0</slash:comments>
		</item>
		<item>
		<title>Precision error tensors?</title>
		<link>http://www.corrada.com/blog/2008/03/18/precision-error-tensors-2/</link>
		<comments>http://www.corrada.com/blog/2008/03/18/precision-error-tensors-2/#comments</comments>
		<pubDate>Tue, 18 Mar 2008 10:58:05 +0000</pubDate>
		<dc:creator>Andrés</dc:creator>
				<category><![CDATA[Error Theory]]></category>
		<category><![CDATA[tensors]]></category>

		<guid isPermaLink="false">http://www.corrada.com/blog/2008/03/18/precision-error-tensors-2/</guid>
		<description><![CDATA[In previous posts I talked about precision error matrices as being tensors. Boy, was I wrong! This is another case of my intuition getting way ahead of my math and science. I know just enough math to shot myself in the foot with these speculations. I&#8217;ll explain.
Matrices are multi-dimensional arrays of numbers. A two-dimensional matrix [...]]]></description>
		<wfw:commentRss>http://www.corrada.com/blog/2008/03/18/precision-error-tensors-2/feed/</wfw:commentRss>
		<slash:comments>0</slash:comments>
		</item>
		<item>
		<title>Variations in student responses to a multiple exam for latent group discovery</title>
		<link>http://www.corrada.com/blog/2008/03/13/variations-in-student-responses-to-a-multiple-exam-for-latent-group-discovery/</link>
		<comments>http://www.corrada.com/blog/2008/03/13/variations-in-student-responses-to-a-multiple-exam-for-latent-group-discovery/#comments</comments>
		<pubDate>Fri, 14 Mar 2008 00:03:37 +0000</pubDate>
		<dc:creator>Andrés</dc:creator>
				<category><![CDATA[Error Theory]]></category>
		<category><![CDATA[Fourier Analysis]]></category>
		<category><![CDATA[Group Theory]]></category>
		<category><![CDATA[Machine Learning]]></category>
		<category><![CDATA[latent labels]]></category>

		<guid isPermaLink="false">http://www.corrada.com/blog/2008/03/13/variations-in-student-responses-to-a-multiple-exam-for-latent-group-discovery/</guid>
		<description><![CDATA[Questions in an exam are detectors of student competency. Students are detectors of the correct answers in a test. What is the variation in the student&#8217;s model of the correct exam? The precision error equations can be used to construct a covariance matrix for the students instead of the questions. What makes the difference is [...]]]></description>
		<wfw:commentRss>http://www.corrada.com/blog/2008/03/13/variations-in-student-responses-to-a-multiple-exam-for-latent-group-discovery/feed/</wfw:commentRss>
		<slash:comments>0</slash:comments>
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