<div dir="ltr"><div class="gmail_quote"><div dir="ltr" class="gmail_attr"><br></div><br><div lang="EN-US" link="#0563C1" vlink="#954F72"><div class="m_-119509418010010637WordSection1"><p class="MsoNormal" style="background:white"><a href="https://statistics.yale.edu/" title="Home" target="_blank"><b><span style="font-size:22.0pt;font-family:"Lucida Sans",sans-serif;color:#286dc0;text-decoration:none">Department of Statistics and Data Science </span></b></a><span style="font-size:22.0pt;font-family:"Lucida Sans",sans-serif;color:#222222"><u></u><u></u></span></p><h1 style="margin-right:0in;margin-bottom:0in;margin-left:0in;margin-bottom:.0001pt;background:white"><span style="font-family:"Times New Roman",serif;color:#003c76;text-transform:uppercase;font-weight:normal">YIAN MA</span><span style="font-size:13.5pt;font-family:"Times New Roman",serif;color:#222222">, <span class="m_-119509418010010637odd">University of California, Berkeley</span></span><span style="font-size:13.5pt;font-family:"Times New Roman",serif;color:#222222;font-weight:normal"><u></u><u></u></span></h1><p class="MsoNormal" style="background:white"><u></u><img width="196" height="235" style="width:2.0416in;height:2.4479in" src="cid:168b9c609a06917eb2" align="left" hspace="12" alt="https://statistics.yale.edu/sites/default/files/styles/user_picture_node/public/unnamed.jpg?itok=ak2oyU1C"><u></u><span style="font-size:13.0pt;font-family:"Times New Roman",serif;color:#222222"><u></u><u></u></span></p><p class="MsoNormal" style="background:white"><b><span style="font-size:13.0pt;font-family:"Times New Roman",serif;color:#222222">Date</span></b><span style="font-size:13.0pt;font-family:"Times New Roman",serif;color:#222222">: Monday, February 04, 2019<u></u><u></u></span></p><p class="MsoNormal" style="background:white"><b><span style="font-size:13.0pt;font-family:"Times New Roman",serif;color:#222222">Time</span></b><span style="font-size:13.0pt;font-family:"Times New Roman",serif;color:#222222">: 4:00PM to 5:15PM<u></u><u></u></span></p><p class="MsoNormal" style="background:white"><b><span style="font-size:13.0pt;font-family:"Times New Roman",serif;color:#222222">Location</span></b><span class="m_-119509418010010637fn"><span style="font-size:13.0pt;font-family:"Times New Roman",serif;color:#222222">: Dunham Lab </span></span><span class="m_-119509418010010637map-icon"><span style="font-size:13.0pt;font-family:"Times New Roman",serif;color:#222222;letter-spacing:.6pt"><a href="http://maps.google.com/?q=10+Hillhouse+Avenue%2C+Room+220%2C+New+Haven%2C+CT%2C+%2C+us" target="_blank"><span style="color:#286dc0">see map</span></a> </span></span><span style="font-size:13.0pt;font-family:"Times New Roman",serif;color:#222222"><u></u><u></u></span></p><p class="MsoNormal" style="background:white"><span style="font-size:13.0pt;font-family:"Times New Roman",serif;color:#222222">10 Hillhouse Avenue, Room 220<u></u><u></u></span></p><p class="MsoNormal" style="background:white"><span class="m_-119509418010010637locality"><span style="font-size:13.0pt;font-family:"Times New Roman",serif;color:#222222">New Haven</span></span><span style="font-size:13.0pt;font-family:"Times New Roman",serif;color:#222222">, <span class="m_-119509418010010637region">CT</span><u></u><u></u></span></p><p class="MsoNormal" style="background:white"><span style="font-size:13.0pt;font-family:"Times New Roman",serif;color:#222222"><a href="https://sites.google.com/view/yianma" target="_blank"><span style="color:#003c76">Website</span></a><u></u><u></u></span></p><p class="MsoNormal" style="background:white"><b><span style="font-size:13.0pt;font-family:"Times New Roman",serif;color:#222222"><u></u> <u></u></span></b></p><p class="MsoNormal" style="background:white"><b><span style="font-size:13.0pt;font-family:"Times New Roman",serif;color:#222222"><u></u> <u></u></span></b></p><p class="MsoNormal" style="background:white"><b><span style="font-size:13.0pt;font-family:"Times New Roman",serif;color:#222222"><u></u> <u></u></span></b></p><p class="MsoNormal" style="background:white"><b><span style="font-size:13.0pt;font-family:"Times New Roman",serif;color:#222222"><u></u> <u></u></span></b></p><p class="MsoNormal" style="background:white"><b><span style="font-size:13.0pt;font-family:"Times New Roman",serif;color:#222222"><u></u> <u></u></span></b></p><p class="MsoNormal" style="background:white"><b><span style="font-size:13.0pt;font-family:"Times New Roman",serif;color:#222222">Title: <i>Bridging MCMC and Optimization<u></u><u></u></i></span></b></p><p class="MsoNormal" style="background:white"><b><span style="font-size:13.0pt;font-family:"Times New Roman",serif;color:#222222"><u></u> <u></u></span></b></p><p class="MsoNormal" style="background:white"><b><span style="font-size:13.0pt;font-family:"Times New Roman",serif;color:#222222">Information and Abstract: <u></u><u></u></span></b></p><p style="margin-right:0in;margin-bottom:12.0pt;margin-left:0in;background:white;box-sizing:inherit"><span style="font-size:13.0pt;font-family:"Times New Roman",serif;color:#222222">In this talk, I will discuss three ingredients of optimization theory in the context of MCMC: Non-convexity, Acceleration, and stochasticity. I will focus on a class of non-convex objective functions arising from mixture models. For that class of objective functions, I will demonstrate that the computational complexity of a simple MCMC algorithm scales linearly with the model dimension, while optimization problems are NP-hard.<u></u><u></u></span></p><p style="margin-right:0in;margin-bottom:12.0pt;margin-left:0in;background:white;box-sizing:inherit"><span style="font-size:13.0pt;font-family:"Times New Roman",serif;color:#222222">I will then study MCMC algorithms as optimization over the KL-divergence in the space of measures. By incorporating a momentum variable, I will discuss an algorithm which performs accelerated gradient descent over the KL-divergence. Using optimization-like ideas, a suitable Lyapunov function is constructed to prove that an accelerated convergence rate is obtained.<u></u><u></u></span></p><p style="margin-right:0in;margin-bottom:12.0pt;margin-left:0in;background:white;box-sizing:inherit"><span style="font-size:13.0pt;font-family:"Times New Roman",serif;color:#222222">Finally, I will present a complete recipe for constructing stochastic gradient MCMC algorithms that translates the task of finding a valid sampler into one of  choosing two matrices. I will then describe how stochastic gradient MCMC algorithms can be applied to applications involving temporally correlated data, where the challenge arises from the need to break the dependencies when considering minibatches of observations.  </span><span style="font-size:13.5pt;font-family:"Times New Roman",serif;color:#222222"><u></u><u></u></span></p><p class="MsoNormal" style="line-height:18.0pt;background:white"><a><b><span style="font-size:16.0pt;font-family:Mallory;color:red;text-decoration:none">3:45 p.m.</span></b></a><b><span style="font-size:16.0pt;font-family:Mallory;color:red">   Pre-talk tea Dunham Lab, Suite 222, Breakroom 228<u></u><u></u></span></b></p><p class="MsoNormal" style="background:white;vertical-align:baseline"><span style="font-size:12.0pt;font-family:Mallory">For more details and upcoming events visit our website at </span><a href="http://statistics.yale.edu/" target="_blank"><span style="font-size:12.0pt;font-family:Mallory;color:#0563c1">http://statistics.yale.edu/</span></a><span style="font-size:12.0pt;font-family:Mallory"> .<u></u><u></u></span></p><p class="MsoNormal"><u></u> <u></u></p><p class="MsoNormal"><u></u> <u></u></p><p class="MsoNormal"><u></u> <u></u></p></div></div>_______________________________________________<br>
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