A Note on the Adaptive LASSO for Zero-Inflated Poisson Regression

<table class="fixed-width table-group" id="tab4"><tr><td><table class="table"><colgroup><col style="width:10.54em"/><col style="width:5.18em"/><col style="width:8.53em"/></colgroup><tr><td class="thead-hr" colspan="3"><hr/></td></tr><tr class="thead"><td class="align_left">Methods </td><td class="align_center">BIC </td><td class="align_center">Time (in seconds)</td></tr><tr><td class="thead-hr" colspan="3"><hr/></td></tr><tr><td class="align_left">EM LASSO</td><td class="align_center">9062.744</td><td class="align_center"> 50.252</td></tr><tr><td class="align_left">AMAZonn - EM AL</td><td class="align_center">9002.487</td><td class="align_center">  <svg height="8.55521pt" id="M200" style="vertical-align:-0.2063904pt" version="1.1" viewbox="-0.0498162 -8.34882 34.3917 8.55521" width="34.3917pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M412 140C382 77 369 73 315 73H129L270 222C362 320 402 379 402 466C402 571 322 635 234 635C177 635 130 609 99 576L42 495L64 475C90 514 133 568 201 568C274 568 318 519 318 435C318 349 255 267 193 193C144 135 87 78 32 23V0H405C417 45 427 89 440 131L412 140Z"></path></g><g transform="matrix(.013,0,0,-0.013,6.24,0)"><path d="M137 343C167 482 260 545 321 574C357 591 397 603 429 609L423 641C382 634 335 622 295 608C189 570 37 457 37 238C37 84 125 -12 242 -12C362 -12 447 89 447 209C447 311 374 393 267 393C247 393 226 386 204 376L137 343ZM227 337C318 337 361 256 361 173C361 105 336 22 258 22C176 22 126 120 126 240C126 266 127 291 132 310C155 323 189 337 227 337Z"></path></g><g transform="matrix(.013,0,0,-0.013,12.48,0)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z"></path></g><g transform="matrix(.013,0,0,-0.013,15.444,0)"><path d="M412 140C382 77 369 73 315 73H129L270 222C362 320 402 379 402 466C402 571 322 635 234 635C177 635 130 609 99 576L42 495L64 475C90 514 133 568 201 568C274 568 318 519 318 435C318 349 255 267 193 193C144 135 87 78 32 23V0H405C417 45 427 89 440 131L412 140Z"></path></g><g transform="matrix(.013,0,0,-0.013,21.684,0)"><path d="M384 0V27C293 34 287 42 287 114V635C232 613 172 594 109 583V559L157 557C201 555 205 550 205 499V114C205 42 199 34 109 27V0H384Z"></path></g><g transform="matrix(.013,0,0,-0.013,27.924,0)"><path d="M153 550H386L412 615L406 623H120L82 318C104 327 142 338 184 338C294 338 347 275 347 187C347 112 305 39 221 39C160 39 119 71 97 89C88 97 80 96 71 90C59 80 50 67 49 57C48 45 52 36 66 23C80 9 123 -12 169 -12C221 -11 288 15 342 59C403 109 431 165 431 225C431 308 366 395 238 395C212 395 165 379 127 364L153 550Z"></path></g></svg></td></tr><tr><td class="align_left">AMAZonn - EM SEAL</td><td class="align_center"> <svg height="8.48998pt" id="M201" style="vertical-align:-0.2324896pt" version="1.1" viewbox="-0.0498162 -8.25749 48.7454 8.48998" width="48.7454pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M262 635C141 635 57 556 57 461C57 387 108 338 166 306C137 289 92 261 74 245C56 228 32 204 32 157C32 55 118 -12 249 -12C346 -12 472 51 472 178C472 266 409 313 339 351C378 376 396 392 412 406C435 428 445 453 445 480C445 569 371 635 262 635ZM246 595C286 595 338 561 338 475C338 417 318 386 301 370C224 406 172 439 172 507C172 549 199 595 246 595ZM260 28C210 28 152 72 152 169C152 221 175 265 204 287C301 235 350 209 351 137C352 71 315 28 260 28Z"></path></g><g transform="matrix(.013,0,0,-0.013,6.5,0)"><path d="M253 635C100 635 24 509 24 420C24 314 97 231 217 231C234 231 251 236 275 248L324 274C298 154 195 47 47 21L53 -15C98 -14 184 2 223 18C365 74 471 201 471 382C471 519 398 635 253 635ZM232 595C310 595 335 485 335 387C335 365 334 340 330 313C316 307 300 300 275 300C202 300 156 374 156 460C156 525 178 595 232 595Z"></path></g><g transform="matrix(.013,0,0,-0.013,13,0)"><path d="M262 635C141 635 57 556 57 461C57 387 108 338 166 306C137 289 92 261 74 245C56 228 32 204 32 157C32 55 118 -12 249 -12C346 -12 472 51 472 178C472 266 409 313 339 351C378 376 396 392 412 406C435 428 445 453 445 480C445 569 371 635 262 635ZM246 595C286 595 338 561 338 475C338 417 318 386 301 370C224 406 172 439 172 507C172 549 199 595 246 595ZM260 28C210 28 152 72 152 169C152 221 175 265 204 287C301 235 350 209 351 137C352 71 315 28 260 28Z"></path></g><g transform="matrix(.013,0,0,-0.013,19.5,0)"><path d="M440 175C403 110 395 108 335 108H173L293 222C391 316 432 379 432 457C432 568 349 635 250 635C187 635 137 610 100 573L36 479L65 456C97 502 138 544 199 544C268 544 303 495 303 425C303 349 264 274 194 191C145 133 86 78 33 26V0H434C445 42 457 105 473 164L440 175Z"></path></g><g transform="matrix(.013,0,0,-0.013,26.098,0)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z"></path></g><g transform="matrix(.013,0,0,-0.013,29.062,0)"><path d="M253 635C100 635 24 509 24 420C24 314 97 231 217 231C234 231 251 236 275 248L324 274C298 154 195 47 47 21L53 -15C98 -14 184 2 223 18C365 74 471 201 471 382C471 519 398 635 253 635ZM232 595C310 595 335 485 335 387C335 365 334 340 330 313C316 307 300 300 275 300C202 300 156 374 156 460C156 525 178 595 232 595Z"></path></g><g transform="matrix(.013,0,0,-0.013,35.562,0)"><path d="M440 175C403 110 395 108 335 108H173L293 222C391 316 432 379 432 457C432 568 349 635 250 635C187 635 137 610 100 573L36 479L65 456C97 502 138 544 199 544C268 544 303 495 303 425C303 349 264 274 194 191C145 133 86 78 33 26V0H434C445 42 457 105 473 164L440 175Z"></path></g><g transform="matrix(.013,0,0,-0.013,42.062,0)"><path d="M486 174V231H396V629H324C229 512 123 368 15 215V174H269V116C269 55 264 41 179 34V0H477V34C403 41 396 51 396 112V174H486ZM269 231H90C155 335 219 427 267 493H269V231Z"></path></g></svg></td><td class="align_center"> 26.528</td></tr><tr class="table-tr"><td colspan="3"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>Model selection performance of EM LASSO and AMAZonn on German health care data.</div>

Journal of Probability and Statistics

A Note on the Adaptive LASSO for Zero-Inflated Poisson Regression

Table 4