Notes on: Liu, Q., & Wang, D. (2016): Stein variational gradient descent: a general purpose bayesian inference algorithm

Table of Contents

Notation

  • liu16_stein_variat_gradien_descen_3c314f80373742988ad542a6d4ce66a111b17847.png continous rv. liu16_stein_variat_gradien_descen_1e194afee3290960492ba8552e59bbfe7a9107d8.png
  • liu16_stein_variat_gradien_descen_2cc73b37793e80d832d4e2e64136003cdcefa29e.png set if i.i.d. obersevations
  • liu16_stein_variat_gradien_descen_04016c2db0a754f30f8b3b0b87bb4fa9ea1528a8.png of the kernel liu16_stein_variat_gradien_descen_a767f47d08f3dc25c22458109e02a9cfc08e419b.png is the closure of the linear span

    liu16_stein_variat_gradien_descen_f43ea69e8a19ecab665661a0f78d474913e2c6c0.png

    equipped with inner products

    liu16_stein_variat_gradien_descen_c0cbada396f479f667230149a70159e613357c5f.png

  • liu16_stein_variat_gradien_descen_7d3f2bd4fbb26bdd8e3f7b1444bf8f460703a9d7.png with liu16_stein_variat_gradien_descen_2c1e62205e1fee3a8f2d2dedfbcbcc9cc1fe4d39.png equipped with inner product

    liu16_stein_variat_gradien_descen_b036c18799b898c1c772ec8fca4bb5d89d18dc99.png

  • Stein's operator

    liu16_stein_variat_gradien_descen_b8ccdc88e22cf828c3576c309d1f910e21521a79.png

  • Stein's discrepancy

    liu16_stein_variat_gradien_descen_08dda5a39fdb12b645e80d5e5e21f84bf7a40df5.png

    often such that

    liu16_stein_variat_gradien_descen_6de2fd39456d13648de6e1bce314df90058ba3e2.png

  • liu16_stein_variat_gradien_descen_7c973d1542fad7cdb7dfe52d544508c09780dfd8.png denotes the iteration