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myia-ai-01 merged 5 commits into from
Sep 20, 2026
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feat(probas,#16620): Infer-5 — effets naturels NDE/NIE calculés, raccourcis CDE corrigés (P5a) #16639

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feat(probas,#16620): Infer-5 effets naturels NDE/NIE calcules + corre…
jsboige Sep 18, 2026
356b4ce
Merge branch 'main' into feature/16620-p5a-infer5-mediation
jsboige Sep 19, 2026
ea68673
chore(twin-parity,#16639): attest Probas-5 Causal-Inference pair at c…
jsboige Sep 19, 2026
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fix(infer,#16639): strip kernel-injected probeAddresses banner (9 lin…
jsboige Sep 19, 2026
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chore(twin-parity,#16639): re-attest Probas-5 Causal-Inference AFTER …
jsboige Sep 19, 2026
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307 changes: 293 additions & 14 deletions MyIA.AI.Notebooks/Probas/Infer/Infer-5-Causal-Inference.ipynb
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Expand Down Expand Up @@ -1445,6 +1560,166 @@
"Console.WriteLine($\" -> part mediee (indirect) ~= TE - CDE(M=0) = {TE - CDE0:F3} (chemin via les competences)\");"
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"Effets naturels (Pearl 2001) sur le SCM formation -> competences -> promotion :\r\n"
]
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" NDE = 0,280 (effet direct, mediateur naturel sous X=0)\r\n"
]
},
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" NIE = 0,180 (effet indirect, Y evalue sous X=1)\r\n"
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" NDE + NIE = 0,460 vs TE = 0,460 -> ecart |TE - NDE - NIE| = 0,000\r\n"
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"text": [
" Raccourci CDE : NDE =? CDE(0) -> 0,280 vs 0,300 ; part mediee =? TE-CDE(0) -> 0,180 vs 0,160\r\n"
]
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" (NDE + NIE = TE : identite algebrique ; ce qui derive, ce sont les raccourcis via CDE)\r\n"
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"source": [
"// EFFETS NATURELS (Pearl 2001) : NDE et NIE calcules sur le SCM de mediation ci-dessus.\n",
"// Pas de confondeur M <- U -> Y : la sequential ignorability tient, les quantites\n",
"// \"cross-world\" se calculent par enumeration sur le meme SCM (monde imbrique).\n",
"// P(M=m | do(X=x)) : le mediateur sous intervention (CPT direct du SCM)\n",
"double PM_doX(bool xVal, bool mVal) {\n",
" double pM1 = xVal ? 0.80 : 0.20;\n",
" return mVal ? pM1 : 1.0 - pM1;\n",
"}\n",
"\n",
"// NDE_{0,1} = Somme_m P(m|do(0)) * [P(Y|do(1),do(m)) - P(Y|do(0),do(m))]\n",
"// (mediateur a sa valeur NATURELLE sous X=0, pas figee -- c'est le contrefactuel imbrique)\n",
"double NDE = PM_doX(false, true) * (PY_doX_doM(true, true) - PY_doX_doM(false, true))\n",
" + PM_doX(false, false) * (PY_doX_doM(true, false) - PY_doX_doM(false, false));\n",
"\n",
"// NIE_{1,0} = Somme_m [P(m|do(1)) - P(m|do(0))] * P(Y=1|do(1),do(m))\n",
"// (Y sous X=1, seul le CHANGEMENT du mediateur porte l'effet)\n",
"double NIE = (PM_doX(true, true) - PM_doX(false, true)) * PY_doX_doM(true, true)\n",
" + (PM_doX(true, false) - PM_doX(false, false)) * PY_doX_doM(true, false);\n",
"\n",
"Console.WriteLine(\"Effets naturels (Pearl 2001) sur le SCM formation -> competences -> promotion :\");\n",
"Console.WriteLine($\" NDE = {NDE:F3} (effet direct, mediateur naturel sous X=0)\");\n",
"Console.WriteLine($\" NIE = {NIE:F3} (effet indirect, Y evalue sous X=1)\");\n",
"Console.WriteLine($\" NDE + NIE = {NDE + NIE:F3} vs TE = {TE:F3} -> ecart |TE - NDE - NIE| = {Math.Abs(TE - NDE - NIE):F3}\");\n",
"Console.WriteLine($\" Raccourci CDE : NDE =? CDE(0) -> {NDE:F3} vs {CDE0:F3} ; part mediee =? TE-CDE(0) -> {NIE:F3} vs {TE - CDE0:F3}\");\n",
"Console.WriteLine(\" (NDE + NIE = TE : identite algebrique ; ce qui derive, ce sont les raccourcis via CDE)\");"
]
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"id": "infer22-mediation-interp",
Expand All @@ -1462,10 +1737,14 @@
"- **NIE (Natural Indirect Effect)** = `Y_{1,M_{X=1}} - Y_{1,M_{X=0}}` : effet indirect transmis par le changement \"naturel\" de `M` quand `X` bascule de 0 a 1.\n",
"- **TE = NDE + NIE** (decomposition additive, Pearl 2001, Robins & Greenland 1992).\n",
"\n",
"Dans Infer.NET, le NDE/NIE **necessite une hypothese supplemental** : la **sequential ignorability** (ou *cross-world independence*) sur les contrefactuels `M_{X=x'}` -- c'est-a-dire que la distribution de `M` sous `do(X=x')` reste compatible avec le meme SCM. Sur notre SCM de mediation (`X -> M -> Y`, pas de confondeur `M <- U -> Y`), cette hypothese tient et **NDE = CDE a M=M\\_{X=0}**, **NIE = TE - NDE**. Avec les valeurs mesurees : **NDE = CDE(M=0) = 0,300**, **NIE = TE - NDE = 0,460 - 0,300 = 0,160** -- la part mediee est exactement l'ecart observe. **Verification immediate** :\n",
"Dans Infer.NET, le NDE/NIE **necessite une hypothese supplemental** : la **sequential ignorability** (ou *cross-world independence*) sur les contrefactuels `M_{X=x'}` -- c'est-a-dire que la distribution de `M` sous `do(X=x')` reste compatible avec le meme SCM. Sur notre SCM de mediation (`X -> M -> Y`, pas de confondeur `M <- U -> Y`), cette hypothese tient : les effets naturels sont **calculables par enumeration sur le meme SCM** (cellule suivante). Les valeurs mesurees : **NDE = 0,280**, **NIE = 0,180**, et **NDE + NIE = 0,460 = TE** -- une **identite algebrique** (le telescopage des deux sommes rend la decomposition exacte pour tout SCM discret), pas une coincidence.\n",
"\n",
"Ce que l'interaction X*M casse en revanche, ce sont les **raccourcis via le CDE** : notre monde a CDE(1) = 0,200 != CDE(0) = 0,300, donc **NDE != CDE(0)** (0,280 vs 0,300) et la \"part mediee\" TE - CDE(M=0) = 0,160 sous-estime le vrai NIE = 0,180 :\n",
"\n",
"```\n",
"NDE + NIE = CDE(M=0) + (TE - CDE(M=0)) = TE ✓ (decomposition de Pearl 2001)\n",
"NDE + NIE = TE (exacte, toujours -- identite de telescopage)\n",
"NDE = CDE(m) (faux des que CDE varie en m : interaction)\n",
"part mediee = TE - CDE(M=0) (approximation : 0,160 au lieu de 0,180 ici)\n",
"```\n",
"\n",
"**Quand CDE != NDE** : si un confondeur `U` influence **a la fois** `M` et `Y` (par exemple, le \"motivation\" qui determine a la fois les competences acquises ET la reconnaissance patronale), CDE a `do(M=0)` ne capture pas l'effet direct reel -- il faut le **NDE**, qui requiert des methodes d'inference contrefactuelle specifiques (voir section 10 et la discussion dans Pearl 2001, sec. 4). Infer.NET, comme moteur de message passing determinant sur graphes discrets, rend ce cas plus difficile (les contrefactuels \"cross-world\" sortent du formalisme d'un seul DAG).\n",
Expand Down Expand Up @@ -1514,7 +1793,7 @@
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