Pith Number

pith:C5KGNOKK

pith:2000:C5KGNOKKSCK4AD565NCV7CDUVA

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The information bottleneck method

Fernando C. Pereira (ATT Shannon Laboratory), Naftali Tishby (Hebrew University, NEC Research Institute), William Bialek (NEC Research Institute)

Compressing a signal X through limited codewords can preserve all the information it provides about another signal Y.

arxiv:physics/0004057 v1 · 2000-04-24 · physics.data-an · cond-mat.dis-nn · cs.LG · nlin.AO

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Claims

C1strongest claim

This constrained optimization problem can be seen as a generalization of rate distortion theory in which the distortion measure d(x, x̃) emerges from the joint statistics of X and Y. This approach yields an exact set of self consistent equations for the coding rules X → X̃ and X̃ → Y.

C2weakest assumption

The joint distribution p(x,y) is known or can be reliably estimated from data, allowing the mutual information terms and the iterative re-estimation procedure to be computed exactly.

C3one line summary

The information bottleneck method finds a compressed representation T of X that preserves maximal mutual information with Y by solving a variational optimization problem that generalizes rate-distortion theory.

References

6 extracted · 6 resolved · 0 Pith anchors

[1] Extracting relevant informati on

[2] T. M. Cover and J. A. Thomas, Elements of Information Theory (Wiley, New York, 1991) 1991

[3] Information geometry and alternating mini- mization procedures 1984

[4] Computation of channel capacity and rate d istortion func- tion 1972

[5] Agglomerative information bot tleneck 1999

Formal links

3 machine-checked theorem links

Cited by

153 papers in Pith

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Receipt and verification

First computed	2026-07-04T14:43:14.754516Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

175466b94a9095c00fbeeb455f8874a822daaf87c76038dd73ef348c7d00abbf

Aliases

arxiv: physics/0004057 · arxiv_version: physics/0004057v1 · doi: 10.48550/arxiv.physics/0004057 · pith_short_12: C5KGNOKKSCK4 · pith_short_16: C5KGNOKKSCK4AD56 · pith_short_8: C5KGNOKK

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/C5KGNOKKSCK4AD565NCV7CDUVA \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 175466b94a9095c00fbeeb455f8874a822daaf87c76038dd73ef348c7d00abbf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "21faebfb4a2797cd3e9e920b1c58a9a676764a44e288113469512f98541a83af",
    "cross_cats_sorted": [
      "cond-mat.dis-nn",
      "cs.LG",
      "nlin.AO"
    ],
    "license": "",
    "primary_cat": "physics.data-an",
    "submitted_at": "2000-04-24T15:22:30Z",
    "title_canon_sha256": "b6b86581531d14c4a709055a43bdb23e259450d072b82c00da696a9f456ea64a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "physics/0004057",
    "kind": "arxiv",
    "version": 1
  }
}