Exact Permutation Moments for Walsh Interaction-Order Energies: A Projector Specialization of Quadratic-Form Randomization Theory

{"J601":[0],"Reproducibility":[1],"Package":[2],"This":[3,85],"package":[4,86,190],"accompanies":[5],"the":[6,36,45,50,155,189],"manuscript:":[7,195],"\\"Exact":[8],"Permutation":[9],"Moments":[10],"for":[11,32,72,164,191],"Walsh":[12,65],"Interaction-Order":[13],"Energies:A":[14],"Projector":[15],"Specialization":[16],"of":[17],"Quadratic-Form":[18],"Randomization":[19],"Theory\\"(J600,":[20],"Roshankumar":[21],"Chandaliya,":[22],"QDL":[23],"project).":[24],"The":[25],"manuscript":[26],"develops":[27],"exact":[28,70,156],"finite-sample":[29],"permutation":[30,73],"formulas":[31,71],"Walshinteraction-order":[33],"energies":[34],"on":[35],"Boolean":[37],"cube.":[38],"For":[39],"a":[40],"centered":[41],"finitepopulation":[42],"assigned":[43],"to":[44,63],"N":[46],"=":[47,55],"2^n":[48],"vertices,":[49],"degree-k":[51],"interaction-orderenergy":[52],"is":[53,158],"E_k":[54],"sum_{|A|=k}":[56],"g_hat_pi(A)^2.":[57],"By":[58],"specializing":[59],"establishedquadratic-form":[60],"randomization":[61],"theory":[62],"orthogonal":[64],"projectors,":[66],"theanalysis":[67],"yields":[68],"compact":[69],"mean,":[74],"variance,":[75],"andcross-level":[76],"covariance,":[77],"with":[78,150,169],"exhaustive":[79],"verification":[80,107,118],"at":[81,108],"N=4":[82,109],"and":[83,95,112,119,166,179],"N=8.":[84],"contains:":[87],"-":[88],"Exact":[89],"formula":[90,157],"implementation":[91],"(exact_null_moments)-":[92],"Dense":[93],"FWHT":[94],"sparse":[96],"Hamming/Krawtchouk":[97],"implementations-":[98],"Monte":[99],"Carlo":[100,163],"benchmark":[101,144,180],"(100,000":[102],"uniform":[103],"value":[104],"permutations)-":[105,115],"Exhaustive":[106],"(24":[110],"permutations)":[111],"N=8":[113],"(40,320":[114],"B=0":[116],"edge-case":[117],"B<0":[120],"impossibility":[121],"check-":[122],"Timing":[123],"distribution":[124],"CSVs":[125],"(median,":[126],"IQR,":[127],"min,":[128],"max)-":[129],"Environment":[130],"metadata":[131],"(Python":[132],"3.13.5,":[133],"NumPy":[134],"2.3.5,":[135],"Intel":[136],"Xeon":[137],"Platinum":[138],"8573C,":[139],"5-vCPU":[140],"container)-":[141],"Publication-ready":[142],"LaTeX":[143],"table-":[145],"SHA256":[146],"integrity":[147],"manifest-":[148],"README":[149],"reproduction":[151],"instructions":[152],"Key":[153],"result:":[154],"10^4–10^5×":[159],"faster":[160],"than":[161],"100,000-permutationMonte":[162],"first-":[165],"second-moment":[167],"estimation,":[168],"agreement":[170],"tomachine":[171],"precision.":[172],"License:":[173],"Source":[174],"code":[175],"—":[176,182],"MIT.":[177],"Data":[178],"outputs":[181],"CC":[183],"BY":[184],"4.0.See":[185],"LICENSE":[186],"file":[187],"in":[188],"full":[192],"text.":[193],"Companion":[194],"J600":[196],"(Zenodo":[197],"DOI:":[198],"[J600":[199],"DOI":[200],"daalo":[201],"yahan]).":[202]}