{
  "aliases": null,
  "backlinks": [
    {
      "field": "defines",
      "target": "FF2KNFNTB7"
    }
  ],
  "body": "\n## Summary\n\nInformation geometry studies families of [[probability distributions|0DVDCMA2DK]] as manifolds, using the tools of differential geometry.\nThe central structure is the Fisher information metric, a [[Riemannian metric|Q61VFHCH2J]] on the parameter space, together with a family of [[affine connections|JX65KSVHSJ]] called the $\\alpha$-connections.\nOn finite sample spaces, Chentsov's theorem shows that the Fisher metric is, up to a constant factor, the only metric invariant under sufficient statistics.\nThe field was developed largely by Shun-ichi Amari and has applications in statistics, machine learning and information theory.\n\n## Explanations\n\n### L1 human\n\nA statistical model is a family of distributions described by a few parameters, like the mean and standard deviation of a normal distribution.\nEach choice of parameters is a point, so the model is a space of points.\nInformation geometry measures the distance between two nearby points by how easily data can tell the two distributions apart.\nFor normal distributions, two distributions with means $0$ and $1$ are far apart when the standard deviation is small and close when it is large.\nWith this distance the family of normal distributions becomes a copy of the hyperbolic plane.\n",
  "commit": "547b6eddb8f2feb8d579f2d633d22a27b7e132fc",
  "front": {
    "kind": "concept",
    "msc": [
      "53B12",
      "62B11"
    ],
    "name": "Information geometry",
    "same_as": {
      "wikidata": "Q3798604",
      "wikipedia": "Information geometry"
    },
    "sources": [
      {
        "url": "https://en.wikipedia.org/wiki/Information_geometry"
      }
    ],
    "tag": "F64Z9541DV"
  },
  "kind": "concept",
  "link": "https://math2.tamnd.com/node/F64Z9541DV/",
  "links": null,
  "markdown": "https://math2.tamnd.com/node/F64Z9541DV.md",
  "msc": [
    "53B12",
    "62B11"
  ],
  "name": "Information geometry",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/F64/F64Z9541DV.md",
  "status": null,
  "tag": "F64Z9541DV",
  "uri": "m2://F64Z9541DV",
  "url": "https://math2.tamnd.com/wiki/information-geometry/",
  "writing": {
    "tag": "F64Z9541DV",
    "kind": "concept",
    "level": "W0",
    "next": [
      {
        "what": "an inventory row",
        "note": "the row of the inventory that the node accounts for",
        "have": 0,
        "want": 1
      },
      {
        "what": "a source with a locator",
        "have": 0,
        "want": 1
      }
    ]
  }
}