Update SGPR_notes.ipynb
"The integral results in:\n",
"\n",
"$$\n",
- "p(\\mathbf f^\\star) = \\mathcal N(\\mathbf f^\\star\\,|\\, \\mathbf K_{\\star u}\\mathbf K_{uu}^{-1}\\mathbf m, \\,\\mathbf K_{\\star\\star} - \\mathbf K_{\\star u}\\mathbf K_{uu}^{-1}\\mathbf K_{u\\star} + \\mathbf K_{\\star u}\\mathbf K_{uu}^{-1}\\mathbf \\Lambda^{-1}\\mathbf K_{uu}^{-1}\\mathbf K_{u\\star})\n",
+ "p(\\mathbf f^\\star) = \\mathcal N(\\mathbf f^\\star\\,|\\, \\mathbf K_{\\star u}\\mathbf K_{uu}^{-1}\\mathbf m, \\,\\mathbf K_{\\star\\star} - \\mathbf K_{\\star u}\\mathbf K_{uu}^{-1}\\mathbf K_{u\\star} + \\mathbf K_{\\star u}\\mathbf K_{uu}^{-1}\\mathbf \\Lambda \\mathbf K_{uu}^{-1}\\mathbf K_{u\\star})\n",
"$$\n",
"\n",
"Note from our above definitions we have:\n",
"\n",
"$$\n",
- "\\mathbf K_{uu}^{-1}\\mathbf \\Lambda^{-1}\\mathbf K_{uu}^{-1} = \n",
+ "\\mathbf K_{uu}^{-1}\\mathbf \\Lambda \\mathbf K_{uu}^{-1} = \n",
"\\mathbf L^{-\\top}\\mathbf B^{-1}\\mathbf L^{-1}\n",
"$$\n",
"\n",
