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	<title>Thinking in Learning</title>
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	<description>Bin Cao's blog</description>
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		<title>Thinking in Learning</title>
		<link>http://bcao.wordpress.com</link>
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		<item>
		<title>Order Statistic</title>
		<link>http://bcao.wordpress.com/2008/04/28/order-statistic/</link>
		<comments>http://bcao.wordpress.com/2008/04/28/order-statistic/#comments</comments>
		<pubDate>Sun, 27 Apr 2008 17:29:56 +0000</pubDate>
		<dc:creator>Bin</dc:creator>
				<category><![CDATA[Research]]></category>

		<guid isPermaLink="false">http://bcao.wordpress.com/?p=74</guid>
		<description><![CDATA[Consider the following problem: Given k bottles and 1 liter of water, we randomly split the water into these bottles. Let be the volume of water in bottle, what is the distribution of ? The problem can be model by the following process. We random generated k-1 real numbers in [0,1] with uniform distribution. Then [...]<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=bcao.wordpress.com&amp;blog=46193&amp;post=74&amp;subd=bcao&amp;ref=&amp;feed=1" width="1" height="1" />]]></description>
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		<slash:comments>1</slash:comments>
	
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		<title>Notes in Implementing RVM</title>
		<link>http://bcao.wordpress.com/2008/04/27/notes-in-implementing-rvm/</link>
		<comments>http://bcao.wordpress.com/2008/04/27/notes-in-implementing-rvm/#comments</comments>
		<pubDate>Sun, 27 Apr 2008 16:56:44 +0000</pubDate>
		<dc:creator>Bin</dc:creator>
				<category><![CDATA[Research]]></category>

		<guid isPermaLink="false">http://bcao.wordpress.com/2008/04/27/notes-in-implementing-rvm/</guid>
		<description><![CDATA[Due to the sparse property of RVM, many of the would approach infinity. This would cause the Hessian matrix to be singular and the inverse operation to be ill-posed. Therefore, we take the method in (Nabney,1999) to avoid such a problem. Let . By multiplying both side with we have . Suppose that and , [...]<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=bcao.wordpress.com&amp;blog=46193&amp;post=73&amp;subd=bcao&amp;ref=&amp;feed=1" width="1" height="1" />]]></description>
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		<slash:comments>0</slash:comments>
	
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		<title>An Interesting Discussion in Our Group</title>
		<link>http://bcao.wordpress.com/2008/03/07/an-interesting-discussion-in-our-group/</link>
		<comments>http://bcao.wordpress.com/2008/03/07/an-interesting-discussion-in-our-group/#comments</comments>
		<pubDate>Fri, 07 Mar 2008 18:26:53 +0000</pubDate>
		<dc:creator>Bin</dc:creator>
				<category><![CDATA[Research]]></category>

		<guid isPermaLink="false">http://bcao.wordpress.com/?p=71</guid>
		<description><![CDATA[Things start from my email which sent to our group mail list on an interesting passage as following Don&#8217;t delete this just because it looks weird. Believe it or not, you can read it:&#160; I cdnuolt blveiee taht I cluod aulaclty uesdnatnrd waht I was rdanieg. The phaonmneal pweor of the hmuan mnid Aoccdrnig to [...]<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=bcao.wordpress.com&amp;blog=46193&amp;post=71&amp;subd=bcao&amp;ref=&amp;feed=1" width="1" height="1" />]]></description>
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		<slash:comments>0</slash:comments>
	
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		<title>Review for Gaussian Distribution</title>
		<link>http://bcao.wordpress.com/2008/03/06/review-for-gaussian-distribution/</link>
		<comments>http://bcao.wordpress.com/2008/03/06/review-for-gaussian-distribution/#comments</comments>
		<pubDate>Thu, 06 Mar 2008 12:52:18 +0000</pubDate>
		<dc:creator>Bin</dc:creator>
				<category><![CDATA[Research]]></category>

		<guid isPermaLink="false">http://bcao.wordpress.com/?p=70</guid>
		<description><![CDATA[Gaussain distribution for univariate random variable Gaussain distribution for D-dimensional random variable Conditional distribution: where where Marginal distribution Let , and , Marginal distribution of , Conditional distribution of given where<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=bcao.wordpress.com&amp;blog=46193&amp;post=70&amp;subd=bcao&amp;ref=&amp;feed=1" width="1" height="1" />]]></description>
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		<slash:comments>0</slash:comments>
	
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		<title>Correcting Sample Selection Bias by Unlabeled Data</title>
		<link>http://bcao.wordpress.com/2007/10/17/correcting-sample-selection-bias-by-unlabeled-data/</link>
		<comments>http://bcao.wordpress.com/2007/10/17/correcting-sample-selection-bias-by-unlabeled-data/#comments</comments>
		<pubDate>Wed, 17 Oct 2007 12:06:51 +0000</pubDate>
		<dc:creator>Bin</dc:creator>
				<category><![CDATA[Uncategorized]]></category>

		<guid isPermaLink="false">http://bcao.wordpress.com/2007/10/17/correcting-sample-selection-bias-by-unlabeled-data/</guid>
		<description><![CDATA[nonparametric method which directly produces resampling weights without distribution estimation. Distribution matching; the means of the training and test points in a reproducing kernel Hilbert space are close. The author even claim that their method can in some cases outperform reweighting using the true sample bias distribution. But why it is possible? support of Pr&#8217; [...]<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=bcao.wordpress.com&amp;blog=46193&amp;post=65&amp;subd=bcao&amp;ref=&amp;feed=1" width="1" height="1" />]]></description>
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		<slash:comments>0</slash:comments>
	
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		<title>An interesting workshop in NIPS</title>
		<link>http://bcao.wordpress.com/2007/10/16/an-interesting-workshop-in-nips/</link>
		<comments>http://bcao.wordpress.com/2007/10/16/an-interesting-workshop-in-nips/#comments</comments>
		<pubDate>Tue, 16 Oct 2007 03:22:15 +0000</pubDate>
		<dc:creator>Bin</dc:creator>
				<category><![CDATA[Research]]></category>

		<guid isPermaLink="false">http://bcao.wordpress.com/2007/10/16/an-interesting-workshop-in-nips/</guid>
		<description><![CDATA[&#160; Deep Learning Workshop: Foundations and Future Directions Several helpful links to this topic: Deep Belief Networks Boltzmann machine (Wikipedia) Boltzmann Machine (Scholarpedia)<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=bcao.wordpress.com&amp;blog=46193&amp;post=62&amp;subd=bcao&amp;ref=&amp;feed=1" width="1" height="1" />]]></description>
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		<slash:comments>0</slash:comments>
	
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		<title>Analysis of Representations for Domain Adaptation</title>
		<link>http://bcao.wordpress.com/2007/10/15/analysis-of-representations-for-domain-adaptation/</link>
		<comments>http://bcao.wordpress.com/2007/10/15/analysis-of-representations-for-domain-adaptation/#comments</comments>
		<pubDate>Mon, 15 Oct 2007 17:47:08 +0000</pubDate>
		<dc:creator>Bin</dc:creator>
				<category><![CDATA[Readings]]></category>
		<category><![CDATA[Research]]></category>

		<guid isPermaLink="false">http://bcao.wordpress.com/2007/10/15/analysis-of-representations-for-domain-adaptation/</guid>
		<description><![CDATA[This is a nips paper in this year. Different from what we do about finding a good representation for domain adaptation, the authors want to propose an evaluation method for the representation and propose the question &#8220;under what conditions can we adapt a classifier trained on the source domain for use in the target domain?&#8221;. [...]<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=bcao.wordpress.com&amp;blog=46193&amp;post=60&amp;subd=bcao&amp;ref=&amp;feed=1" width="1" height="1" />]]></description>
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		<slash:comments>0</slash:comments>
	
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		<title>A trick on minimax problem</title>
		<link>http://bcao.wordpress.com/2007/10/09/a-trick-on-minimax-problem/</link>
		<comments>http://bcao.wordpress.com/2007/10/09/a-trick-on-minimax-problem/#comments</comments>
		<pubDate>Tue, 09 Oct 2007 08:20:15 +0000</pubDate>
		<dc:creator>Bin</dc:creator>
				<category><![CDATA[Uncategorized]]></category>

		<guid isPermaLink="false">http://bcao.wordpress.com/2007/10/09/a-trick-on-minimax-problem/</guid>
		<description><![CDATA[I learned a trick to convert a minimax problem into a minimum problem today. That is, if we have the problem of Then it is equivalent to the following minimum problem This is a very useful trick. Consider the problem of data selection in SVM. We&#8217;d like to select the subset of data which maximize [...]<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=bcao.wordpress.com&amp;blog=46193&amp;post=59&amp;subd=bcao&amp;ref=&amp;feed=1" width="1" height="1" />]]></description>
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		<slash:comments>0</slash:comments>
	
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			<media:title type="html">(1/2)&#124;&#124;\mathbf{w}&#124;&#124;^2</media:title>
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			<media:title type="html">c_i(\mathbf{w}\cdot\mathbf{x_i} - b) \ge 1, \quad 1 \le i \le n.</media:title>
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		<title>An easy way to train a cost sensitive model by SVM^light</title>
		<link>http://bcao.wordpress.com/2007/10/07/an-easy-way-to-train-a-cost-sensitive-model-by-svmlight/</link>
		<comments>http://bcao.wordpress.com/2007/10/07/an-easy-way-to-train-a-cost-sensitive-model-by-svmlight/#comments</comments>
		<pubDate>Sun, 07 Oct 2007 07:21:41 +0000</pubDate>
		<dc:creator>Bin</dc:creator>
				<category><![CDATA[Research]]></category>

		<guid isPermaLink="false">http://bcao.wordpress.com/2007/10/07/an-easy-way-to-train-a-cost-sensitive-model-by-svmlight/</guid>
		<description><![CDATA[Although SVMlight supports giving each example a different weight in the cost function, it does not provide the interface in its Web site and related documents. But you can find it in its code. The interface is easy to use. You just need to change the input data file format as: &#60;line&#62; .=. &#60;target&#62; cost:&#60;weight&#62; [...]<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=bcao.wordpress.com&amp;blog=46193&amp;post=56&amp;subd=bcao&amp;ref=&amp;feed=1" width="1" height="1" />]]></description>
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		<slash:comments>0</slash:comments>
	
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		<title>Tutorial Notes</title>
		<link>http://bcao.wordpress.com/2007/07/17/tutorial-nots/</link>
		<comments>http://bcao.wordpress.com/2007/07/17/tutorial-nots/#comments</comments>
		<pubDate>Tue, 17 Jul 2007 08:39:45 +0000</pubDate>
		<dc:creator>Bin</dc:creator>
				<category><![CDATA[Uncategorized]]></category>

		<guid isPermaLink="false">http://bcao.wordpress.com/2007/07/17/tutorial-nots/</guid>
		<description><![CDATA[Hal Daume III gave an excellent tutorial on Bayesian Techniques for NLP at MSRA. Although the tutorial&#8217;s name is about NLP but actually it is all about graphical models. In this tutorial, Hal showed many detail usually you cannot read directly from the papers. He also gave us some vivid illusion of abstract ideas such [...]<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=bcao.wordpress.com&amp;blog=46193&amp;post=50&amp;subd=bcao&amp;ref=&amp;feed=1" width="1" height="1" />]]></description>
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		<slash:comments>1</slash:comments>
	
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			<media:title type="html">\displaystyle \min\{1, \frac{p(x')q(x&#124;x')}{p(x)q(x'&#124;x)}\}</media:title>
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			<media:title type="html">\displaystyle q(\cdot&#124;x)</media:title>
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