Алгоритмы в биоинформатике, осень 2016: Скрытые Марковские Модели

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    16-Jan-2017

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<ul><li><p>HMMHidden Markov Models</p></li><li><p>,</p></li><li><p> .</p><p> 0.9.</p><p> .</p><p> 95% , ?</p><p>B</p><p>0,5 0,5</p><p>+0 0,5</p><p> 0,5</p><p>0 0,9</p><p> 0,1-</p><p>E</p></li><li><p> , t , t.</p><p> ( )</p><p> +1 1, , = +1 </p><p> = = +1 = = )</p><p> = (1 = )</p></li><li><p> ( )</p><p> PAM.</p><p>PAM = ?n</p><p>1-3a, a, a, a,</p><p>a, 1-3a, a, a,</p><p>a, a, 1-3a, a,</p><p>a, a, a, 1-3a,</p><p>PAM = 1</p></li><li><p> Hidden Markov Model (HMM)</p><p> , (, ) .</p><p>+ -</p><p>HeadsTails</p><p>0.50.5</p><p>0.80.80.2</p><p>0.2</p><p>0.5</p><p>0.50.1</p><p>0.9</p></li><li><p>: .</p><p> :</p><p> = {} = {} = {()}</p><p>1, 2, , 1, 2 , </p></li><li><p> - </p><p> , , .</p><p> = max (1, , |1, , , = )</p><p>: </p><p> + 1 = max</p><p>()(+1)</p><p> 1 = (1)</p><p> :</p><p>j + 1 = argmax</p><p>()(+1)</p><p> :</p><p> = argmax</p><p>() , = +1( + 1)</p><p>1</p><p> +1</p><p>2</p><p>3</p><p>(+1)</p></li><li><p> (Forward probabilities) - </p><p> 1, , , , .</p><p> = 1, , , = | , , </p><p>: </p><p> + 1 =</p><p>()(+1)</p><p> 1 = (1)</p><p> :</p><p> 1, , ,, ) =</p><p>()</p><p>1</p><p> +1</p><p>2</p><p>3</p><p>(+1)</p></li><li><p> (Backward probabilities)</p><p>1</p><p>1 </p><p> 2()</p><p>N N</p><p>2</p><p>1</p><p>()</p><p>1()</p><p> - +1, , , , .</p><p> = +1, , , = | , , </p><p>: </p><p> 1 =</p><p>()()</p><p> = 1</p><p> :</p><p> 1, , ,, ) =</p><p> 1 1</p></li><li><p> Forward-Backward</p><p> , :</p><p> = 1, , ) = 1, , , = +1, , , = </p><p> 1, , </p><p>= ()</p><p> ()</p></li><li><p>B</p><p>0,5</p><p>0,8</p><p>0,5</p><p>0,7</p><p>+0 0,5</p><p>P 0,5</p><p>0,2</p><p>0,3</p><p>0 0,9</p><p>P 0,1-</p><p>E</p><p> Forward-Backward .</p><p> O O O O O O</p><p>+ + + + + + - - - - - - .61 .72 .83 .84 .71 .60 .42 .33 .24 .26 .33.39 .28 .17 .16 .29 .40 .58 .67 .76 .74 .67</p><p>+-</p><p>FBV</p><p> !</p></li><li><p> HMM -</p><p> , .</p><p> :</p><p> () .</p><p> = +1 + 1</p><p> =</p><p> = (1)</p><p> = ()</p><p> ()</p><p>() =,= ()</p><p> ()</p></li><li><p> HMM </p></li><li><p>HMM </p><p>G</p><p>G</p><p>M</p></li><li><p> HMM</p></li><li><p>HMM </p><p>Insertions ( ):</p><p>Deletions ( ):</p></li><li><p>HMM </p></li><li><p>HMM </p></li></ul>

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