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Negative Dependence, Stable Polynomials etc in ML Part 2 SUVRIT SRA & STEFANIE JEGELKA Laboratory for Information and Decision Systems Massachusetts Institute of Technology Neural information Processing Systems, 2018 ml.mit.edu

  1. Negative Dependence, 
 Stable Polynomials etc in ML Part 2 SUVRIT SRA & STEFANIE JEGELKA Laboratory for Information and Decision Systems Massachusetts Institute of Technology Neural information Processing Systems, 2018 ml.mit.edu

  2. Outline Introduction 
 Prominent example: Determinantal Point Processes 1 Stronger notions of negative dependence Intro & Implications: Sampling Theory Approximating partition functions Learning a DPP (and some variants) 2 Applications Theory & Applications Recommender systems, Nyström method, optimal design, regression, neural net pruning, negative mining, anomaly detection, etc. Perspectives and wrap-up Negative dependence, stable polynomials etc. in ML - part 1 Stefanie Jegelka (stefje@mit.edu)

  3. Theory Partition functions Learning DPPs Negative dependence, stable polynomials etc. in ML - part 2 Suvrit Sra (suvrit@mit.edu)

  4. <latexit sha1_base64="qwEaZ3oTpAJyVs2s06lKeQV+gtY=">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</latexit> <latexit sha1_base64="qwEaZ3oTpAJyVs2s06lKeQV+gtY=">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</latexit> <latexit sha1_base64="qwEaZ3oTpAJyVs2s06lKeQV+gtY=">ADTHicfVJNbxMxEHW3UEr4SuHIxSIgFQlV2QiJXipVwIELJQjSpsR5HVmN1Zt78qeLYms/QP8Gq7wI7jzP7ghJyPQ7JFjOT103tvdmdmJymUdNhu/9yKtq9d37mxe7Nx6/adu/eae/dPXV5aAT2Rq9z2E+5ASQM9lKigX1jgOlFwly8mutnl2CdzM1HnBUw1DwzMpWCY6BGzcMYq+a6v9D0/pEWp5cLHlf80Yrqswgn8qNlqH7QXQa+CeAVaZBXd0V7UZONclBoMCsWdG8TtAoeW5RCQdVgpYOCiwuewSBAwzW4oV+0U9EngRnTNLfhGKQLdj3Dc+3cTCfBqTlOXF2bk/UEr3xZe9Qczuz41o9mB4OvTRFiWDEspy0VBRzOp8gHUsLAtUsAC6sDB1RMeFhbBjm3GAGPotca27GnsmiGnSGnilIkSluMgW0FT+jrQ5lVmYTZHZBVptpl9PKs0T7aVUTjHKlDlp4MpMrqSW6muVEBH3euDKn9Rf0F9X+3X1fF09n6uvIfw+C28D964AyzG3nGbaR5KXN3/cUmzdIU7FBc35ir4LRzEAf8/nr+OVqm3bJQ/KI7JOYvCDH5A3pkh4R5Av5Sr6R79GP6Ff0O/qztEZbq5wHZCO2d/4CXo4ZSw=</latexit> <latexit sha1_base64="qwEaZ3oTpAJyVs2s06lKeQV+gtY=">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</latexit> Computing Partition functions Aim: Estimate Z µ , i.e., normalization const / partition function Pr( S ) = 1 µ ( S ) Z µ Typically intractable and often even hard to approximate (exponential number of terms to sum over, or evaluation of high-dimensional integrals / volumes) but… 4 Negative dependence, stable polynomials etc. in ML - part 2 Suvrit Sra (suvrit@mit.edu)

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