EigenVI: Score-Based Variational Inference Poster
A conference poster presenting EigenVI, a score-based variational inference method using orthonormal function expansions like Hermite polynomials. It details the mathematical formulation, compares it to Black-box VI, and shows results on 2D non-Gaussian targets and hierarchical models.
论文上下文
Paper title: EigenVI: score-based variational inference with orthogonal function expansions Abstract: A conference poster presenting EigenVI, a score-based variational inference method using orthonormal function expansions like Hermite polynomials. It details the mathematical formulation, compares it to Black-box VI, and shows results on 2D non-Gaussian targets and hierarchical models. Paper body (method & results): <!DOCTYPE html> <html lang="en"> <head> <meta content="text/html; charset=utf-8" http-equiv="content-type"/> <title>EigenVI: score-based variational inference with orthogonal function expansions</title> <!--Generated on Thu Oct 31 15:36:17 2024 by LaTeXML (version 0.8.8) http://dlmf.nist.gov/LaTeXML/.--> <meta content="width=device-width, initial-scale=1, shrink-to-fit=no" name="viewport"/> <link href="https://cdn.jsdelivr.net/npm/bootstrap@5.3.0/dist/css/bootstrap.min.css" rel="stylesheet" type="text/css"/> <link href="/static/browse/0.3.4/css/ar5iv.0.7.9.min.css" rel="stylesheet" type="text/css"/> <link href="/static/browse/0.3.4/css/ar5iv-fonts.0.7.9.min.css" rel="stylesheet" type="text/css"/> <link href="/static/browse/0.3.4/css/latexml_styles.css" rel="stylesheet" type="text/css"/> <script src="https://cdn.jsdelivr.net/npm/bootstrap@5.3.0/dist/js/bootstrap.bundle.min.js"></script> <script src="https://cdnjs.cloudflare.com/ajax/libs/html2canvas/1.3.3/html2canvas.min.js"></script> <script src="/static/browse/0.3.4/js/addons_new.js"></script> <script src="/static/browse/0.3.4/js/feedbackOverlay.js"></script> <base href="/html/2410.24054v1/"/></head> <body> <nav class="ltx_page_navbar"> <nav class="ltx_TOC"> <ol class="ltx_toclist"> <li class="ltx_tocentry ltx_tocentry_section"><a class="ltx_ref" href="https://arxiv.org/html/2410.24054v1#S1" title="In EigenVI: score-based variational inference with orthogonal function expansions"><span class="ltx_text ltx_ref_title"><span class="ltx_tag ltx_tag_ref">1 </span>Introduction</span></a></li> <li class="ltx_tocentry ltx_tocentry_section"> <a class="ltx_ref" href="https://arxiv.org/html/2410.24054v1#S2" title="In EigenVI: score-based variational inference with orthogonal function expansions"><span class="ltx_text ltx_ref_title"><span class="ltx_tag ltx_tag_ref">2 </span>Score-based variational inference with orthogonal function expansions</span></a> <ol class="ltx_toclist ltx_toclist_section"> <li class="ltx_tocentry ltx_tocentry_subsection"><a class="ltx_ref" href="https://arxiv.org/html/2410.24054v1#S2.SS1" title="In 2 Score-based variational inference with orthogonal function expansions ‣ EigenVI: score-based variational inference with orthogonal function expansions"><span class="ltx_text ltx_ref_title"><span class="ltx_tag ltx_tag_ref">2.1 </span>Orthogonal function expansions</span></a></li> <li class="ltx_tocentry ltx_tocentry_subsection"><a class="ltx_ref" href="https://arxiv.org/html/2410.24054v1#S2.SS2" title="In 2 Score-based variational inference with orthogonal function expansions ‣ EigenVI: score-based variational inference with orthogonal function expansions"><span class="ltx_text ltx_ref_title"><span class="ltx_tag ltx_tag_ref">2.2 </span>EigenVI</span></a></li> <li class="ltx_tocentry ltx_tocentry_subsection"><a class="ltx_ref" href="https://arxiv.org/html/2410.24054v1#S2.SS3" title="In 2 Score-based variational inference with orthogonal function expansions ‣ EigenVI: score-based variational inference with orthogonal function expansions"><span class="ltx_text ltx_ref_title"><span class="ltx_tag ltx_tag_ref">2.3 </span>EigenVI in <math alttext="\mathbb{R}^{D}" class="ltx_Math" display="inline"><semantics><msup><mi>ℝ</mi><mi>D</mi></msup><annotation-xml encoding="MathML-Content"><apply><csymbol cd="ambiguous">superscript</csymbol><ci>ℝ</ci><ci>𝐷</ci></apply></annotation-xml><annotation encoding="application/x-tex">\mathbb{R}^{D}</annotation><annotation encoding="application/x-llamapun">blackboard_R start_POSTSUPERSCRIPT italic_D end_POSTSUPERSCRIPT</annotation></semantics></math>: the Hermite family and standardization</span></a></li> </ol> </li> <li class="ltx_tocentry ltx_tocentry_section"><a class="ltx_ref" href="https://arxiv.org/html/2410.24054v1#S3" title="In EigenVI: score-based variational inference with orthogonal function expansions"><span class="ltx_text ltx_ref_title"><span class="ltx_tag ltx_tag_ref">3 </span>Related work</span></a></li> <li class="ltx_tocentry ltx_tocentry_section"> <a class="ltx_ref" href="https://arxiv.org/html/2410.24054v1#S4" title="In EigenVI: score-based variational inference with orthogonal function expansions"><span class="ltx_text ltx_ref_title"><span class="ltx_tag ltx_tag_ref">4 </span>Experiments</span></a> <ol class="ltx_toclist ltx_toclist_section"> <li class="ltx_tocentry ltx_tocentry_subsection"><a class="ltx_ref" href="https://arxiv.org/html/2410.24054v1#S4.SS1" title="In 4 Experiments ‣ EigenVI: score-based variational inference with orthogonal function expansions"><span class="ltx_text ltx_ref_title"><span class="ltx_tag ltx_tag_ref">4.1 </span>2D synthetic targets</span></a></li> <li class="ltx_tocentry ltx_tocentry_subsection"><a class="ltx_ref" href="https://arxiv.org/html/2410.24054v1#S4.SS2" title="In 4 Experiments ‣ EigenVI: score-based variational inference with orthogonal function expansions"><span class="ltx_text ltx_ref_title"><span class="ltx_tag ltx_tag_ref">4.2 </span>Non-Gaussianity: varying skew and tails in the sinh-arcsinh distribution</span></a></li> <li class="ltx_tocentry ltx_tocentry_subsection"><a class="ltx_ref" href="https://arxiv.org/html/2410.24054v1#S4.SS3" title="In 4 Experiments ‣ EigenVI: score-based variational inference with orthogonal function expansions"><span class="ltx_text ltx_ref_title"><span class="ltx_tag ltx_tag_ref">4.3 </span>Hierarchical modeling benchmarks from posteriordb</span></a></li> </ol> </li> <li class="ltx_tocentry ltx_tocentry_section"><a class="ltx_ref" href="https://arxiv.org/html/2410.24054v1#S5" title="In EigenVI: score-based variational inference with orthogonal function expansions"><span class="ltx_text ltx_ref_title"><span class="ltx_tag ltx_tag_ref">5 </span>Discussion of limitations and future work</span></a></li> <li class="ltx_tocentry ltx_tocentry_appendix"><a class="ltx_ref" href="https://arxiv.org/html/2410.24054v1#A1" title="In EigenVI: score-based variational inference with orthogonal function expansions"><span class="ltx_text ltx_ref_title"><span class="ltx_tag ltx_tag_ref">A </span>Sampling from orthogonal function expansions</span></a></li> <li class="ltx_tocentry ltx_tocentry_appendix"><a class="ltx_ref" href="https://arxiv.org/html/2410.24054v1#A2" title="In EigenVI: score-based variational inference with orthogonal function expansions"><span class="ltx_text ltx_ref_title"><span class="ltx_tag ltx_tag_ref">B </span>Calculation of moments</span></a></li> <li class="ltx_tocentry ltx_tocentry_appendix"><a class="ltx_ref" href="https://arxiv.org/html/2410.24054v1#A3" title="In EigenVI: score-based variational inference with orthogonal function expansions"><span class="ltx_text ltx_ref_title"><span class="ltx_tag ltx_tag_ref">C </span>Eigenvalue problem</span></a></li> <li class="ltx_tocentry ltx_tocentry_appendix"> <a class="ltx_ref" href="https://arxiv.org/html/2410.24054v1#A4" title="In EigenVI: score-based variational inference with orthogonal function expansions"><span class="ltx_text ltx_ref_title"><span class="ltx_tag ltx_tag_ref">D </span>Practical considerations of EigenVI</span></a> <ol class="ltx_toclist ltx_toclist_appendix"> <li class="ltx_tocentry ltx_tocentry_subsection"><a class="ltx_ref" href="https://arxiv.org/html/2410.24054v1#A4.SS1" title="In Appendix D Practical considerations of EigenVI ‣ EigenVI: score-based variational inference with orthogonal function expansions"><span class="ltx_text ltx_ref_title"><span class="ltx_tag ltx_tag_ref">D.1 </span>EigenVI vs gradient-based BBVI</span></a></li> <li class="ltx_tocentry ltx_tocentry_subsection"><a class="ltx_ref" href="https://arxiv.org/html/2410.24054v1#A4.SS2" title="In Appendix D Practical considerations of EigenVI ‣ EigenVI: score-based variational inference with orthogonal function expansions"><span class="ltx_text ltx_ref_title"><span class="ltx_tag ltx_tag_ref">D.2 </span>Choosing the number of samples <math alttext="B" class="ltx_Math" display="inline"><semantics><mi>B</mi><annotation-xml encoding="MathML-Content"><ci>𝐵</ci></annotation-xml><annotation encoding="application/x-tex">B</annotation><annotation encoding="application/x-llamapun">italic_B</annotation></semantics></math></span></a></li> </ol> </li> <li class="ltx_tocentry ltx_tocentry_appendix"> <a class="ltx_ref" href="https://arxiv.org/html/2410.24054v1#A5" title="In EigenVI: score-based variational inference with orthogonal function expansions"><span class="ltx_text ltx_ref_title"><span class="ltx_tag ltx_tag_ref">E </span>Additional experiments and details</span></a> <ol class="ltx_toclist ltx_toclist_appendix"> <li class="ltx_tocentry ltx_tocentry_subsection"><a class="ltx_ref" href="https://arxiv.org/html/2410.24054v1#A5.SS1" title="In Appendix E Additional experiments and details ‣ EigenVI: score-based variational inference with orthogonal function expansions"><span class="ltx_text ltx_ref_title"><span class="ltx_tag ltx_tag_ref">E.1 </span>Computational resources</span></a></li> <li class="ltx_tocentry ltx_tocentry_subsection"><a class="ltx_ref" href="https://arxiv.org/html/2410.24054v1#A5.SS2" title="In Appendix E Additional experiments and details ‣ EigenVI: score-based variational inference with orthogonal function expansions"><span class="ltx_text ltx_ref_title"><span class="ltx_tag ltx_tag_ref">E.2 </span>2D synthetic targets</span></a></li> <li class="ltx_tocentry ltx_tocentry_subsection"> <a class="ltx_ref" href="https://arxiv.org/html/2410.24054v1#A5.SS3" title="In Appendix E Additional experiments and details ‣ EigenVI: score-based variational inference with orthogonal function expansions"><span class="ltx_text ltx_ref_title"><span class="ltx_tag ltx_tag_ref">E.3 </span>Sinh-arcsinh targets</span></a> <ol class="ltx_toclist ltx_toclist_subsection"> <li class="ltx_tocentry ltx_tocentry_paragraph"><a class="ltx_ref" href="https://arxiv.org/html/2410.24054v1#A5.SS3.SSS0.Px1" title="In E.3 Sinh-arcsinh targets ‣ Appendix E Additional experiments and details ‣ EigenVI: score-based variational inference with orthogonal function expansions"><span class="ltx_text ltx_ref_title">2D sinh-arcsinh normal experiment</span></a></li> <li class="ltx_tocentry ltx_tocentry_paragraph"><a class="ltx_ref" href="https://arxiv.org/html/2410.24054v1#A5.SS3.SSS0.Px2" title="In E.3 Sinh-arcsinh targets ‣ Appendix E Additional experiments and details ‣ EigenVI: score-based variational inference with orthogonal function expansions"><span class="ltx_text ltx_ref_title">5D sinh-archsinh normal experiment</span></a></li> </ol> </li> <li class="ltx_tocentry ltx_tocentry_subsection"><a class="ltx_ref" href="https://arxiv.org/html/2410.24054v1#A5.SS4" title="In Appendix E Additional experiments and details ‣ EigenVI: score-based variational inference with orthogonal function expansions"><span class="ltx_text ltx_ref_title"><span class="ltx_tag ltx_tag_ref">E.4 </span>Posteriordb experiments</span></a></li> </ol> </li> <li class="ltx_tocentry ltx_tocentry_appendix"><a class="ltx_ref" href="http
