– Cédric Beny (Perimeter Institute/University of Hanover) : Dimensionality reduction from coarse-grained Fisher metric

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22 mai 2015    

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$Title\; :\; Dimensionality\; reduction\; from\; coarse-grained\; Fisher\; metric\backslash n\backslash nAbstract\; :\; In\; physics,\; one\; is\; often\; interested\; in\; describing\; only\; the\; large-scale\backslash nproperties\; of\; complex\; statistical\; states.\; Renormalisation\; is\; the\backslash nproblem\; of\; finding\; the\; most\; relevant\; variables\; for\; that\; purpose.\; I\backslash nwill\; show\; how\; a\; method\; developed\; in\; that\; context\; can\; be\; used\; for\; the\backslash ndimensional\; reduction\; of\; abstract\; data.\; The\; approach\; yields\; a\; “PCA\backslash nkernel”\; whose\; diagonalisation\; amounts\; to\; finding\; the\; perturbations\; of\backslash nthe\; empirical\; distribution\; whose\; distinguishability\; is\; least\; affected\backslash nby\; a\; certain\; noise\; model\; (coarse-graining).\; This\; approach\; is\; invariant\backslash nunder\; arbitrary\; changes\; of\; coordinates.\; The\; kernel,\; however,\; requires\backslash nthe\; calculation\; of\; a\; partition\; function\; which\; must\; be\; approximated.\; I\backslash npresent\; two\; numerical\; examples.[$

– Cédric Beny (Perimeter Institute/University of Hanover) : Dimensionality reduction from coarse-grained Fisher metric

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22 mai 2015    

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$Title\; :\; Dimensionality\; reduction\; from\; coarse-grained\; Fisher\; metric\backslash n\backslash nAbstract\; :\; In\; physics,\; one\; is\; often\; interested\; in\; describing\; only\; the\; large-scale\backslash nproperties\; of\; complex\; statistical\; states.\; Renormalisation\; is\; the\backslash nproblem\; of\; finding\; the\; most\; relevant\; variables\; for\; that\; purpose.\; I\backslash nwill\; show\; how\; a\; method\; developed\; in\; that\; context\; can\; be\; used\; for\; the\backslash ndimensional\; reduction\; of\; abstract\; data.\; The\; approach\; yields\; a\; “PCA\backslash nkernel”\; whose\; diagonalisation\; amounts\; to\; finding\; the\; perturbations\; of\backslash nthe\; empirical\; distribution\; whose\; distinguishability\; is\; least\; affected\backslash nby\; a\; certain\; noise\; model\; (coarse-graining).\; This\; approach\; is\; invariant\backslash nunder\; arbitrary\; changes\; of\; coordinates.\; The\; kernel,\; however,\; requires\backslash nthe\; calculation\; of\; a\; partition\; function\; which\; must\; be\; approximated.\; I\backslash npresent\; two\; numerical\; examples.[$