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<!DOCTYPE html><html lang="en-US"><head><title>PreFer data challenge</title><meta property="og:title" content="PreFer data challenge"><meta name="author" content="Simone Meneghello, Alessio Piraccini, Gianluca Tori"><meta property="article:author" content="Simone Meneghello, Alessio Piraccini, Gianluca Tori"><meta charset="UTF-8"><meta name="viewport" content="width=device-width,height=device-height,initial-scale=1.0"><meta name="apple-mobile-web-app-capable" content="yes"><meta http-equiv="X-UA-Compatible" content="ie=edge"><meta property="og:type" content="website"><meta name="twitter:card" content="summary"><style>@media screen{body[data-bespoke-view=""] .bespoke-marp-parent>.bespoke-marp-osc>button,body[data-bespoke-view=next] .bespoke-marp-parent>.bespoke-marp-osc>button,body[data-bespoke-view=presenter] .bespoke-marp-presenter-container .bespoke-marp-presenter-info-container button,body[data-bespoke-view=presenter] .bespoke-marp-presenter-container 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.bespoke-marp-parent>.bespoke-marp-osc{background:#000000a6;border-radius:7px;bottom:50px;color:#fff;contain:paint;display:block;font-family:Helvetica,Arial,sans-serif;font-size:16px;left:50%;line-height:0;opacity:1;padding:12px;position:absolute;touch-action:manipulation;transform:translateX(-50%);transition:opacity .2s linear;-webkit-user-select:none;user-select:none;white-space:nowrap;will-change:transform;z-index:1;view-transition-name:__bespoke_marp_transition_osc__}body[data-bespoke-view=""] .bespoke-marp-parent>.bespoke-marp-osc>*,body[data-bespoke-view=next] .bespoke-marp-parent>.bespoke-marp-osc>*{margin-left:6px}body[data-bespoke-view=""] .bespoke-marp-parent>.bespoke-marp-osc>:first-child,body[data-bespoke-view=next] .bespoke-marp-parent>.bespoke-marp-osc>:first-child{margin-left:0}body[data-bespoke-view=""] .bespoke-marp-parent>.bespoke-marp-osc>span,body[data-bespoke-view=next] .bespoke-marp-parent>.bespoke-marp-osc>span{opacity:.8}body[data-bespoke-view=""] .bespoke-marp-parent>.bespoke-marp-osc>span[data-bespoke-marp-osc=page],body[data-bespoke-view=next] .bespoke-marp-parent>.bespoke-marp-osc>span[data-bespoke-marp-osc=page]{display:inline-block;min-width:140px;text-align:center}body[data-bespoke-view=""] .bespoke-marp-parent>.bespoke-marp-osc>button[data-bespoke-marp-osc=fullscreen],body[data-bespoke-view=""] .bespoke-marp-parent>.bespoke-marp-osc>button[data-bespoke-marp-osc=next],body[data-bespoke-view=""] .bespoke-marp-parent>.bespoke-marp-osc>button[data-bespoke-marp-osc=presenter],body[data-bespoke-view=""] .bespoke-marp-parent>.bespoke-marp-osc>button[data-bespoke-marp-osc=prev],body[data-bespoke-view=next] .bespoke-marp-parent>.bespoke-marp-osc>button[data-bespoke-marp-osc=fullscreen],body[data-bespoke-view=next] .bespoke-marp-parent>.bespoke-marp-osc>button[data-bespoke-marp-osc=next],body[data-bespoke-view=next] .bespoke-marp-parent>.bespoke-marp-osc>button[data-bespoke-marp-osc=presenter],body[data-bespoke-view=next] .bespoke-marp-parent>.bespoke-marp-osc>button[data-bespoke-marp-osc=prev]{height:32px;line-height:32px;width:32px}body[data-bespoke-view=""] .bespoke-marp-parent.bespoke-marp-inactive,body[data-bespoke-view=next] .bespoke-marp-parent.bespoke-marp-inactive{cursor:none}body[data-bespoke-view=""] .bespoke-marp-parent.bespoke-marp-inactive>.bespoke-marp-osc,body[data-bespoke-view=next] .bespoke-marp-parent.bespoke-marp-inactive>.bespoke-marp-osc{opacity:0;pointer-events:none}body[data-bespoke-view=""] svg.bespoke-marp-slide,body[data-bespoke-view=next] svg.bespoke-marp-slide{height:100%;left:0;position:absolute;top:0;width:100%}body[data-bespoke-view=""] .bespoke-progress-parent{background:#222;display:flex;height:5px;width:100%}body[data-bespoke-view=""] .bespoke-progress-parent+.bespoke-marp-parent{top:5px}body[data-bespoke-view=""] .bespoke-progress-parent .bespoke-progress-bar{background:#0288d1;flex:0 0 0;transition:flex-basis .2s cubic-bezier(0,1,1,1)}body[data-bespoke-view=next]{background:#0000}body[data-bespoke-view=presenter]{background:#161616}body[data-bespoke-view=presenter] .bespoke-marp-presenter-container{display:grid;font-family:Helvetica,Arial,sans-serif;grid-template:"current dragbar next" minmax(140px,1fr) "current dragbar note" 2fr "info dragbar note" 3em;grid-template-columns:minmax(3px,var(--bespoke-marp-presenter-split-ratio,66%)) 0 minmax(3px,1fr);height:100%;left:0;position:absolute;top:0;width:100%}body[data-bespoke-view=presenter] .bespoke-marp-presenter-container .bespoke-marp-parent{grid-area:current;overflow:hidden;position:relative}body[data-bespoke-view=presenter] .bespoke-marp-presenter-container .bespoke-marp-parent svg.bespoke-marp-slide{height:calc(100% - 40px);left:20px;pointer-events:none;position:absolute;top:20px;-webkit-user-select:none;user-select:none;width:calc(100% - 40px)}body[data-bespoke-view=presenter] .bespoke-marp-presenter-container .bespoke-marp-parent svg.bespoke-marp-slide.bespoke-marp-active{filter:drop-shadow(0 3px 10px rgba(0,0,0,.5))}body[data-bespoke-view=presenter] .bespoke-marp-presenter-container .bespoke-marp-presenter-dragbar-container{background:#0288d1;cursor:col-resize;grid-area:dragbar;margin-left:-3px;opacity:0;position:relative;transition:opacity .4s linear .1s;width:6px;z-index:10}body[data-bespoke-view=presenter] .bespoke-marp-presenter-container .bespoke-marp-presenter-dragbar-container:hover{opacity:1}body[data-bespoke-view=presenter] .bespoke-marp-presenter-container .bespoke-marp-presenter-dragbar-container.active{opacity:1;transition-delay:0s}body[data-bespoke-view=presenter] .bespoke-marp-presenter-container .bespoke-marp-presenter-next-container{background:#222;cursor:pointer;display:none;grid-area:next;overflow:hidden;position:relative}body[data-bespoke-view=presenter] .bespoke-marp-presenter-container .bespoke-marp-presenter-next-container.active{display:block}body[data-bespoke-view=presenter] .bespoke-marp-presenter-container .bespoke-marp-presenter-next-container iframe.bespoke-marp-presenter-next{background:#0000;border:0;display:block;filter:drop-shadow(0 3px 10px rgba(0,0,0,.5));height:calc(100% - 40px);left:20px;pointer-events:none;position:absolute;top:20px;-webkit-user-select:none;user-select:none;width:calc(100% - 40px)}body[data-bespoke-view=presenter] .bespoke-marp-presenter-container .bespoke-marp-presenter-note-container{background:#222;color:#eee;grid-area:note;position:relative;z-index:1}body[data-bespoke-view=presenter] .bespoke-marp-presenter-container .bespoke-marp-presenter-note-container button{height:1.5em;line-height:1.5em;width:1.5em}body[data-bespoke-view=presenter] .bespoke-marp-presenter-container .bespoke-marp-presenter-note-container .bespoke-marp-presenter-note-wrapper{display:block;inset:0;position:absolute}body[data-bespoke-view=presenter] .bespoke-marp-presenter-container .bespoke-marp-presenter-note-container .bespoke-marp-presenter-note-buttons{background:#000000a6;border-radius:4px;bottom:0;display:flex;gap:4px;margin:12px;opacity:0;padding:6px;pointer-events:none;position:absolute;right:0;transition:opacity .2s linear}body[data-bespoke-view=presenter] .bespoke-marp-presenter-container .bespoke-marp-presenter-note-container .bespoke-marp-presenter-note-buttons:focus-within,body[data-bespoke-view=presenter] .bespoke-marp-presenter-container .bespoke-marp-presenter-note-container .bespoke-marp-presenter-note-wrapper:focus-within+.bespoke-marp-presenter-note-buttons,body[data-bespoke-view=presenter] .bespoke-marp-presenter-container .bespoke-marp-presenter-note-container:hover .bespoke-marp-presenter-note-buttons{opacity:1;pointer-events:auto}body[data-bespoke-view=presenter] .bespoke-marp-presenter-container .bespoke-marp-presenter-note-container .bespoke-marp-note{box-sizing:border-box;font-size:calc(1.1em*var(--bespoke-marp-note-font-scale, 1));height:calc(100% - 40px);margin:20px;overflow:auto;padding-right:3px;white-space:pre-wrap;width:calc(100% - 40px);word-wrap:break-word;scrollbar-color:#eeeeee80 #0000;scrollbar-width:thin}body[data-bespoke-view=presenter] .bespoke-marp-presenter-container .bespoke-marp-presenter-note-container .bespoke-marp-note::-webkit-scrollbar{width:6px}body[data-bespoke-view=presenter] .bespoke-marp-presenter-container .bespoke-marp-presenter-note-container .bespoke-marp-note::-webkit-scrollbar-track{background:#0000}body[data-bespoke-view=presenter] .bespoke-marp-presenter-container .bespoke-marp-presenter-note-container .bespoke-marp-note::-webkit-scrollbar-thumb{background:#eeeeee80;border-radius:6px}body[data-bespoke-view=presenter] .bespoke-marp-presenter-container .bespoke-marp-presenter-note-container .bespoke-marp-note:empty{pointer-events:none}body[data-bespoke-view=presenter] .bespoke-marp-presenter-container .bespoke-marp-presenter-note-container .bespoke-marp-note.active{display:block}body[data-bespoke-view=presenter] .bespoke-marp-presenter-container .bespoke-marp-presenter-note-container .bespoke-marp-note p:first-child{margin-top:0}body[data-bespoke-view=presenter] .bespoke-marp-presenter-container .bespoke-marp-presenter-note-container .bespoke-marp-note p:last-child{margin-bottom:0}body[data-bespoke-view=presenter] .bespoke-marp-presenter-container .bespoke-marp-presenter-info-container{align-items:center;box-sizing:border-box;color:#eee;display:flex;flex-wrap:nowrap;grid-area:info;justify-content:center;overflow:hidden;padding:0 10px}body[data-bespoke-view=presenter] .bespoke-marp-presenter-container .bespoke-marp-presenter-info-container .bespoke-marp-presenter-info-page,body[data-bespoke-view=presenter] .bespoke-marp-presenter-container .bespoke-marp-presenter-info-container .bespoke-marp-presenter-info-time,body[data-bespoke-view=presenter] .bespoke-marp-presenter-container .bespoke-marp-presenter-info-container .bespoke-marp-presenter-info-timer{box-sizing:border-box;display:block;padding:0 10px;white-space:nowrap;width:100%}body[data-bespoke-view=presenter] .bespoke-marp-presenter-container .bespoke-marp-presenter-info-container button{height:1.5em;line-height:1.5em;width:1.5em}body[data-bespoke-view=presenter] .bespoke-marp-presenter-container .bespoke-marp-presenter-info-container .bespoke-marp-presenter-info-page{order:2;text-align:center}body[data-bespoke-view=presenter] .bespoke-marp-presenter-container .bespoke-marp-presenter-info-container .bespoke-marp-presenter-info-page .bespoke-marp-presenter-info-page-text{display:inline-block;min-width:120px;text-align:center}body[data-bespoke-view=presenter] .bespoke-marp-presenter-container .bespoke-marp-presenter-info-container .bespoke-marp-presenter-info-time{color:#999;order:1;text-align:left}body[data-bespoke-view=presenter] .bespoke-marp-presenter-container .bespoke-marp-presenter-info-container .bespoke-marp-presenter-info-timer{color:#999;order:3;text-align:right}body[data-bespoke-view=presenter] .bespoke-marp-presenter-container .bespoke-marp-presenter-info-container .bespoke-marp-presenter-info-timer:hover{cursor:pointer}}@media print{.bespoke-marp-presenter-info-container,.bespoke-marp-presenter-next-container,.bespoke-marp-presenter-note-container{display:none}}</style><style>div#\:\$p > svg > foreignObject > section{width:1280px;height:720px;box-sizing:border-box;overflow:hidden;position:relative;scroll-snap-align:center center;-webkit-text-size-adjust:100%;text-size-adjust:100%}div#\:\$p > svg > foreignObject > section::after{bottom:0;content:attr(data-marpit-pagination);padding:inherit;pointer-events:none;position:absolute;right:0}div#\:\$p > svg > foreignObject > section:not([data-marpit-pagination])::after{display:none}div#\:\$p > svg > foreignObject > section :is(h1, marp-h1){font-size:2em;margin:0.67em 0}div#\:\$p > svg > foreignObject > section video::-webkit-media-controls{will-change:transform}@page {size:1280px 720px;margin:0}@media print{html, body{background-color:#fff;margin:0;page-break-inside:avoid;break-inside:avoid-page}div#\:\$p > svg > foreignObject > section{page-break-before:always;break-before:page}div#\:\$p > svg > foreignObject > section, div#\:\$p > svg > foreignObject > section *{-webkit-print-color-adjust:exact!important;animation-delay:0s!important;animation-duration:0s!important;color-adjust:exact!important;transition:none!important}div#\:\$p > svg[data-marpit-svg]{display:block;height:100vh;width:100vw}}div#\:\$p > svg > foreignObject > :where(section){container-type:size}div#\:\$p > svg > foreignObject > section img[data-marp-twemoji]{background:transparent;height:1em;margin:0 .05em 0 .1em;vertical-align:-.1em;width:1em}/*!
* Marp default theme.
*
* @theme default
* @author Yuki Hattori
*
* @auto-scaling true
* @size 16:9 1280px 720px
* @size 4:3 960px 720px
*/div#\:\$p > svg > foreignObject > section{--base-size-4:calc(var(--marpit-root-font-size, 1rem) * 0.25);--base-size-8:calc(var(--marpit-root-font-size, 1rem) * 0.5);--base-size-16:calc(var(--marpit-root-font-size, 1rem) * 1);--base-text-weight-normal:400;--base-text-weight-medium:500;--base-text-weight-semibold:600;--fontStack-monospace:ui-monospace, SFMono-Regular, SF Mono, Menlo, Consolas, Liberation Mono, monospace;}div#\:\$p > svg > foreignObject > section [data-theme=light],div#\:\$p > svg > foreignObject > section{color-scheme:light;--focus-outlineColor:#0969da;--fgColor-default:#1f2328;--fgColor-muted:#636c76;--fgColor-accent:#0969da;--fgColor-success:#1a7f37;--fgColor-attention:#9a6700;--fgColor-danger:#d1242f;--fgColor-done:#8250df;--bgColor-default:#fff;--bgColor-muted:#f6f8fa;--bgColor-neutral-muted:#afb8c133;--bgColor-attention-muted:#fff8c5;--borderColor-default:#d0d7de;--borderColor-muted:#d0d7deb3;--borderColor-neutral-muted:#afb8c133;--borderColor-accent-emphasis:#0969da;--borderColor-success-emphasis:#1a7f37;--borderColor-attention-emphasis:#bf8700;--borderColor-danger-emphasis:#cf222e;--borderColor-done-emphasis:#8250df;--color-prettylights-syntax-comment:#57606a;--color-prettylights-syntax-constant:#0550ae;--color-prettylights-syntax-constant-other-reference-link:#0a3069;--color-prettylights-syntax-entity:#6639ba;--color-prettylights-syntax-storage-modifier-import:#24292f;--color-prettylights-syntax-entity-tag:#0550ae;--color-prettylights-syntax-keyword:#cf222e;--color-prettylights-syntax-string:#0a3069;--color-prettylights-syntax-variable:#953800;--color-prettylights-syntax-brackethighlighter-unmatched:#82071e;--color-prettylights-syntax-brackethighlighter-angle:#57606a;--color-prettylights-syntax-invalid-illegal-text:#f6f8fa;--color-prettylights-syntax-invalid-illegal-bg:#82071e;--color-prettylights-syntax-carriage-return-text:#f6f8fa;--color-prettylights-syntax-carriage-return-bg:#cf222e;--color-prettylights-syntax-string-regexp:#116329;--color-prettylights-syntax-markup-list:#3b2300;--color-prettylights-syntax-markup-heading:#0550ae;--color-prettylights-syntax-markup-italic:#24292f;--color-prettylights-syntax-markup-bold:#24292f;--color-prettylights-syntax-markup-deleted-text:#82071e;--color-prettylights-syntax-markup-deleted-bg:#ffebe9;--color-prettylights-syntax-markup-inserted-text:#116329;--color-prettylights-syntax-markup-inserted-bg:#dafbe1;--color-prettylights-syntax-markup-changed-text:#953800;--color-prettylights-syntax-markup-changed-bg:#ffd8b5;--color-prettylights-syntax-markup-ignored-text:#eaeef2;--color-prettylights-syntax-markup-ignored-bg:#0550ae;--color-prettylights-syntax-meta-diff-range:#8250df;--color-prettylights-syntax-sublimelinter-gutter-mark:#8c959f;}div#\:\$p > svg > foreignObject > section [data-theme=dark],div#\:\$p > svg > foreignObject > section:where(.invert){color-scheme:dark;--focus-outlineColor:#1f6feb;--fgColor-default:#e6edf3;--fgColor-muted:#8d96a0;--fgColor-accent:#4493f8;--fgColor-success:#3fb950;--fgColor-attention:#d29922;--fgColor-danger:#f85149;--fgColor-done:#ab7df8;--bgColor-default:#0d1117;--bgColor-muted:#161b22;--bgColor-neutral-muted:#6e768166;--bgColor-attention-muted:#bb800926;--borderColor-default:#30363d;--borderColor-muted:#30363db3;--borderColor-neutral-muted:#6e768166;--borderColor-accent-emphasis:#1f6feb;--borderColor-success-emphasis:#238636;--borderColor-attention-emphasis:#9e6a03;--borderColor-danger-emphasis:#da3633;--borderColor-done-emphasis:#8957e5;--color-prettylights-syntax-comment:#8b949e;--color-prettylights-syntax-constant:#79c0ff;--color-prettylights-syntax-constant-other-reference-link:#a5d6ff;--color-prettylights-syntax-entity:#d2a8ff;--color-prettylights-syntax-storage-modifier-import:#c9d1d9;--color-prettylights-syntax-entity-tag:#7ee787;--color-prettylights-syntax-keyword:#ff7b72;--color-prettylights-syntax-string:#a5d6ff;--color-prettylights-syntax-variable:#ffa657;--color-prettylights-syntax-brackethighlighter-unmatched:#f85149;--color-prettylights-syntax-brackethighlighter-angle:#8b949e;--color-prettylights-syntax-invalid-illegal-text:#f0f6fc;--color-prettylights-syntax-invalid-illegal-bg:#8e1519;--color-prettylights-syntax-carriage-return-text:#f0f6fc;--color-prettylights-syntax-carriage-return-bg:#b62324;--color-prettylights-syntax-string-regexp:#7ee787;--color-prettylights-syntax-markup-list:#f2cc60;--color-prettylights-syntax-markup-heading:#1f6feb;--color-prettylights-syntax-markup-italic:#c9d1d9;--color-prettylights-syntax-markup-bold:#c9d1d9;--color-prettylights-syntax-markup-deleted-text:#ffdcd7;--color-prettylights-syntax-markup-deleted-bg:#67060c;--color-prettylights-syntax-markup-inserted-text:#aff5b4;--color-prettylights-syntax-markup-inserted-bg:#033a16;--color-prettylights-syntax-markup-changed-text:#ffdfb6;--color-prettylights-syntax-markup-changed-bg:#5a1e02;--color-prettylights-syntax-markup-ignored-text:#c9d1d9;--color-prettylights-syntax-markup-ignored-bg:#1158c7;--color-prettylights-syntax-meta-diff-range:#d2a8ff;--color-prettylights-syntax-sublimelinter-gutter-mark:#484f58;}div#\:\$p > svg > foreignObject > section{-ms-text-size-adjust:100%;-webkit-text-size-adjust:100%;background-color:var(--bgColor-default);color:var(--fgColor-default);font-family:-apple-system,BlinkMacSystemFont,Segoe UI,Noto Sans,Helvetica,Arial,sans-serif,Apple Color Emoji,Segoe UI Emoji;font-size:16px;line-height:1.5;margin:0;word-wrap:break-word;scroll-behavior:auto}div#\:\$p > svg > foreignObject > section{--marpit-root-font-size:16px;}div#\:\$p > svg > foreignObject > section :is(h1, marp-h1):hover .anchor .octicon-link:before,div#\:\$p > svg > foreignObject > section :is(h2, marp-h2):hover .anchor .octicon-link:before,div#\:\$p > svg > foreignObject > section :is(h3, marp-h3):hover .anchor .octicon-link:before,div#\:\$p > svg > foreignObject > section :is(h4, marp-h4):hover .anchor .octicon-link:before,div#\:\$p > svg > foreignObject > section :is(h5, marp-h5):hover .anchor .octicon-link:before,div#\:\$p > svg > foreignObject > section :is(h6, marp-h6):hover .anchor .octicon-link:before{background-color:currentColor;content:" ";display:inline-block;height:16px;-webkit-mask-image:url('data:image/svg+xml;charset=utf-8,<svg xmlns="http://www.w3.org/2000/svg" aria-hidden="true" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M7.775 3.275a.75.75 0 0 0 1.06 1.06l1.25-1.25a2 2 0 1 1 2.83 2.83l-2.5 2.5a2 2 0 0 1-2.83 0 .75.75 0 0 0-1.06 1.06 3.5 3.5 0 0 0 4.95 0l2.5-2.5a3.5 3.5 0 0 0-4.95-4.95zm-4.69 9.64a2 2 0 0 1 0-2.83l2.5-2.5a2 2 0 0 1 2.83 0 .75.75 0 0 0 1.06-1.06 3.5 3.5 0 0 0-4.95 0l-2.5 2.5a3.5 3.5 0 0 0 4.95 4.95l1.25-1.25a.75.75 0 0 0-1.06-1.06l-1.25 1.25a2 2 0 0 1-2.83 0"/></svg>');mask-image:url('data:image/svg+xml;charset=utf-8,<svg xmlns="http://www.w3.org/2000/svg" aria-hidden="true" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M7.775 3.275a.75.75 0 0 0 1.06 1.06l1.25-1.25a2 2 0 1 1 2.83 2.83l-2.5 2.5a2 2 0 0 1-2.83 0 .75.75 0 0 0-1.06 1.06 3.5 3.5 0 0 0 4.95 0l2.5-2.5a3.5 3.5 0 0 0-4.95-4.95zm-4.69 9.64a2 2 0 0 1 0-2.83l2.5-2.5a2 2 0 0 1 2.83 0 .75.75 0 0 0 1.06-1.06 3.5 3.5 0 0 0-4.95 0l-2.5 2.5a3.5 3.5 0 0 0 4.95 4.95l1.25-1.25a.75.75 0 0 0-1.06-1.06l-1.25 1.25a2 2 0 0 1-2.83 0"/></svg>');width:16px}div#\:\$p > svg > foreignObject > section details,div#\:\$p > svg > foreignObject > section figcaption,div#\:\$p > svg > foreignObject > section figure{display:block}div#\:\$p > svg > foreignObject > section summary{display:list-item}div#\:\$p > svg > foreignObject > section [hidden]{display:none!important}div#\:\$p > svg > foreignObject > section a{background-color:transparent;color:var(--fgColor-accent);text-decoration:none}div#\:\$p > svg > foreignObject > section abbr[title]{border-bottom:none;-webkit-text-decoration:underline dotted;text-decoration:underline dotted}div#\:\$p > svg > foreignObject > section b,div#\:\$p > svg > foreignObject > section strong{font-weight:var(--base-text-weight-semibold, 600)}div#\:\$p > svg > foreignObject > section dfn{font-style:italic}div#\:\$p > svg > foreignObject > section :is(h1, marp-h1){border-bottom:1px solid var(--borderColor-muted);font-size:2em;font-weight:var(--base-text-weight-semibold, 600);margin:.67em 0;padding-bottom:.3em}div#\:\$p > svg > foreignObject > section mark{background-color:var(--bgColor-attention-muted);color:var(--fgColor-default)}div#\:\$p > svg > foreignObject > section small{font-size:90%}div#\:\$p > svg > foreignObject > section sub,div#\:\$p > svg > foreignObject > section sup{font-size:75%;line-height:0;position:relative;vertical-align:baseline}div#\:\$p > svg > foreignObject > section sub{bottom:-.25em}div#\:\$p > svg > foreignObject > section sup{top:-.5em}div#\:\$p > svg > foreignObject > section img{background-color:var(--bgColor-default);border-style:none;box-sizing:content-box;max-width:100%}div#\:\$p > svg > foreignObject > section code,div#\:\$p > svg > foreignObject > section kbd,div#\:\$p > svg > foreignObject > section :is(pre, marp-pre),div#\:\$p > svg > foreignObject > section samp{font-family:monospace;font-size:1em}div#\:\$p > svg > foreignObject > section figure{margin:1em 40px}div#\:\$p > svg > foreignObject > section hr{background:transparent;background-color:var(--borderColor-default);border:0;box-sizing:content-box;height:.25em;margin:24px 0;overflow:hidden;padding:0}div#\:\$p > svg > foreignObject > section input{font:inherit;font-family:inherit;font-size:inherit;line-height:inherit;margin:0;overflow:visible}div#\:\$p > svg > foreignObject > section [type=button],div#\:\$p > svg > foreignObject > section [type=reset],div#\:\$p > svg > foreignObject > section [type=submit]{-webkit-appearance:button;-moz-appearance:button;appearance:button}div#\:\$p > svg > foreignObject > section [type=checkbox],div#\:\$p > svg > foreignObject > section [type=radio]{box-sizing:border-box;padding:0}div#\:\$p > svg > foreignObject > section [type=number]::-webkit-inner-spin-button,div#\:\$p > svg > foreignObject > section [type=number]::-webkit-outer-spin-button{height:auto}div#\:\$p > svg > foreignObject > section [type=search]::-webkit-search-cancel-button,div#\:\$p > svg > foreignObject > section [type=search]::-webkit-search-decoration{-webkit-appearance:none;appearance:none}div#\:\$p > svg > foreignObject > section ::-webkit-input-placeholder{color:inherit;opacity:.54}div#\:\$p > svg > foreignObject > section ::-webkit-file-upload-button{-webkit-appearance:button;appearance:button;font:inherit}div#\:\$p > svg > foreignObject > section a:hover{text-decoration:underline}div#\:\$p > svg > foreignObject > section ::-moz-placeholder{color:var(--fgColor-muted);opacity:1}div#\:\$p > svg > foreignObject > section ::placeholder{color:var(--fgColor-muted);opacity:1}div#\:\$p > svg > foreignObject > section hr:after,div#\:\$p > svg > foreignObject > section hr:before{content:"";display:table}div#\:\$p > svg > foreignObject > section hr:after{clear:both}div#\:\$p > svg > foreignObject > section table{border-collapse:collapse;border-spacing:0;display:block;max-width:100%;overflow:auto;width:-moz-max-content;width:max-content}div#\:\$p > svg > foreignObject > section td,div#\:\$p > svg > foreignObject > section th{padding:0}div#\:\$p > svg > foreignObject > section details summary{cursor:pointer}div#\:\$p > svg > foreignObject > section details:not([open])>:not(summary){display:none}div#\:\$p > svg > foreignObject > section [role=button]:focus,div#\:\$p > svg > foreignObject > section a:focus,div#\:\$p > svg > foreignObject > section input[type=checkbox]:focus,div#\:\$p > svg > foreignObject > section input[type=radio]:focus{box-shadow:none;outline:2px solid var(--focus-outlineColor);outline-offset:-2px}div#\:\$p > svg > foreignObject > section [role=button]:focus:not(:focus-visible),div#\:\$p > svg > foreignObject > section a:focus:not(:focus-visible),div#\:\$p > svg > foreignObject > section input[type=checkbox]:focus:not(:focus-visible),div#\:\$p > svg > foreignObject > section input[type=radio]:focus:not(:focus-visible){outline:1px solid transparent}div#\:\$p > svg > foreignObject > section [role=button]:focus-visible,div#\:\$p > svg > foreignObject > section a:focus-visible,div#\:\$p > svg > foreignObject > section input[type=checkbox]:focus-visible,div#\:\$p > svg > foreignObject > section input[type=radio]:focus-visible{box-shadow:none;outline:2px solid var(--focus-outlineColor);outline-offset:-2px}div#\:\$p > svg > foreignObject > section a:not([class]):focus,div#\:\$p > svg > foreignObject > section a:not([class]):focus-visible,div#\:\$p > svg > foreignObject > section input[type=checkbox]:focus,div#\:\$p > svg > foreignObject > section input[type=checkbox]:focus-visible,div#\:\$p > svg > foreignObject > section input[type=radio]:focus,div#\:\$p > svg > foreignObject > section input[type=radio]:focus-visible{outline-offset:0}div#\:\$p > svg > foreignObject > section kbd{background-color:var(--bgColor-muted);border-bottom-color:var(--borderColor-neutral-muted);border:1px solid var(--borderColor-neutral-muted);border-radius:6px;box-shadow:inset 0 -1px 0 var(--borderColor-neutral-muted);color:var(--fgColor-default);display:inline-block;font:11px var(--fontStack-monospace, ui-monospace, SFMono-Regular, SF Mono, Menlo, Consolas, Liberation Mono, monospace);line-height:10px;padding:3px 5px;vertical-align:middle}div#\:\$p > svg > foreignObject > section :is(h1, marp-h1),div#\:\$p > svg > foreignObject > section :is(h2, marp-h2),div#\:\$p > svg > foreignObject > section :is(h3, marp-h3),div#\:\$p > svg > foreignObject > section :is(h4, marp-h4),div#\:\$p > svg > foreignObject > section :is(h5, marp-h5),div#\:\$p > svg > foreignObject > section :is(h6, marp-h6){font-weight:var(--base-text-weight-semibold, 600);line-height:1.25;margin-bottom:16px;margin-top:24px}div#\:\$p > svg > foreignObject > section :is(h2, marp-h2){border-bottom:1px solid var(--borderColor-muted);font-size:1.5em;padding-bottom:.3em}div#\:\$p > svg > foreignObject > section :is(h2, marp-h2),div#\:\$p > svg > foreignObject > section :is(h3, marp-h3){font-weight:var(--base-text-weight-semibold, 600)}div#\:\$p > svg > foreignObject > section :is(h3, marp-h3){font-size:1.25em}div#\:\$p > svg > foreignObject > section :is(h4, marp-h4){font-size:1em}div#\:\$p > svg > foreignObject > section :is(h4, marp-h4),div#\:\$p > svg > foreignObject > section :is(h5, marp-h5){font-weight:var(--base-text-weight-semibold, 600)}div#\:\$p > svg > foreignObject > section :is(h5, marp-h5){font-size:.875em}div#\:\$p > svg > foreignObject > section :is(h6, marp-h6){color:var(--fgColor-muted);font-size:.85em;font-weight:var(--base-text-weight-semibold, 600)}div#\:\$p > svg > foreignObject > section p{margin-bottom:10px;margin-top:0}div#\:\$p > svg > foreignObject > section blockquote{border-left:.25em solid var(--borderColor-default);color:var(--fgColor-muted);margin:0;padding:0 1em}div#\:\$p > svg > foreignObject > section ol,div#\:\$p > svg > foreignObject > section ul{margin-bottom:0;margin-top:0;padding-left:2em}div#\:\$p > svg > foreignObject > section ol ol,div#\:\$p > svg > foreignObject > section ul ol{list-style-type:lower-roman}div#\:\$p > svg > foreignObject > section ol ol ol,div#\:\$p > svg > foreignObject > section ol ul ol,div#\:\$p > svg > foreignObject > section ul ol ol,div#\:\$p > svg > foreignObject > section ul ul ol{list-style-type:lower-alpha}div#\:\$p > svg > foreignObject > section dd{margin-left:0}div#\:\$p > svg > foreignObject > section code,div#\:\$p > svg > foreignObject > section :is(pre, marp-pre),div#\:\$p > svg > foreignObject > section samp,div#\:\$p > svg > foreignObject > section tt{font-family:var(--fontStack-monospace, ui-monospace, SFMono-Regular, SF Mono, Menlo, Consolas, Liberation Mono, monospace);font-size:12px}div#\:\$p > svg > foreignObject > section :is(pre, marp-pre){margin-bottom:0;margin-top:0;word-wrap:normal}div#\:\$p > svg > foreignObject > section .octicon{display:inline-block;overflow:visible!important;vertical-align:text-bottom;fill:currentColor}div#\:\$p > svg > foreignObject > section input::-webkit-inner-spin-button,div#\:\$p > svg > foreignObject > section input::-webkit-outer-spin-button{-webkit-appearance:none;appearance:none;margin:0}div#\:\$p > svg > foreignObject > section .mr-2{margin-right:var(--base-size-8, 8px)!important}div#\:\$p > svg > foreignObject > section:after,div#\:\$p > svg > foreignObject > section:before{display:table}div#\:\$p > svg > foreignObject > section:after{clear:both}div#\:\$p > svg > foreignObject > section>:first-child{margin-top:0!important}div#\:\$p > svg > foreignObject > section>:last-child{margin-bottom:0!important}div#\:\$p > svg > foreignObject > section a:not([href]){color:inherit;text-decoration:none}div#\:\$p > svg > foreignObject > section .absent{color:var(--fgColor-danger)}div#\:\$p > svg > foreignObject > section .anchor{float:left;line-height:1;margin-left:-20px;padding-right:4px}div#\:\$p > svg > foreignObject > section .anchor:focus{outline:none}div#\:\$p > svg > foreignObject > section blockquote,div#\:\$p > svg > foreignObject > section details,div#\:\$p > svg > foreignObject > section dl,div#\:\$p > svg > foreignObject > section ol,div#\:\$p > svg > foreignObject > section p,div#\:\$p > svg > foreignObject > section :is(pre, marp-pre),div#\:\$p > svg > foreignObject > section table,div#\:\$p > svg > foreignObject > section ul{margin-bottom:16px;margin-top:0}div#\:\$p > svg > foreignObject > section blockquote>:first-child{margin-top:0}div#\:\$p > svg > foreignObject > section blockquote>:last-child{margin-bottom:0}div#\:\$p > svg > foreignObject > section :is(h1, marp-h1) .octicon-link,div#\:\$p > svg > foreignObject > section :is(h2, marp-h2) .octicon-link,div#\:\$p > svg > foreignObject > section :is(h3, marp-h3) .octicon-link,div#\:\$p > svg > foreignObject > section :is(h4, marp-h4) .octicon-link,div#\:\$p > svg > foreignObject > section :is(h5, marp-h5) .octicon-link,div#\:\$p > svg > foreignObject > section :is(h6, marp-h6) .octicon-link{color:var(--fgColor-default);vertical-align:middle;visibility:hidden}div#\:\$p > svg > foreignObject > section :is(h1, marp-h1):hover .anchor,div#\:\$p > svg > foreignObject > section :is(h2, marp-h2):hover .anchor,div#\:\$p > svg > foreignObject > section :is(h3, marp-h3):hover .anchor,div#\:\$p > svg > foreignObject > section :is(h4, marp-h4):hover .anchor,div#\:\$p > svg > foreignObject > section :is(h5, marp-h5):hover .anchor,div#\:\$p > svg > foreignObject > section :is(h6, marp-h6):hover .anchor{text-decoration:none}div#\:\$p > svg > foreignObject > section :is(h1, marp-h1):hover .anchor .octicon-link,div#\:\$p > svg > foreignObject > section :is(h2, marp-h2):hover .anchor .octicon-link,div#\:\$p > svg > foreignObject > section :is(h3, marp-h3):hover .anchor .octicon-link,div#\:\$p > svg > foreignObject > section :is(h4, marp-h4):hover .anchor .octicon-link,div#\:\$p > svg > foreignObject > section :is(h5, marp-h5):hover .anchor .octicon-link,div#\:\$p > svg > foreignObject > section :is(h6, marp-h6):hover .anchor .octicon-link{visibility:visible}div#\:\$p > svg > foreignObject > section :is(h1, marp-h1) code,div#\:\$p > svg > foreignObject > section :is(h1, marp-h1) tt,div#\:\$p > svg > foreignObject > section :is(h2, marp-h2) code,div#\:\$p > svg > foreignObject > section :is(h2, marp-h2) tt,div#\:\$p > svg > foreignObject > section :is(h3, marp-h3) code,div#\:\$p > svg > foreignObject > section :is(h3, marp-h3) tt,div#\:\$p > svg > foreignObject > section :is(h4, marp-h4) code,div#\:\$p > svg > foreignObject > section :is(h4, marp-h4) tt,div#\:\$p > svg > foreignObject > section :is(h5, marp-h5) code,div#\:\$p > svg > foreignObject > section :is(h5, marp-h5) tt,div#\:\$p > svg > foreignObject > section :is(h6, marp-h6) code,div#\:\$p > svg > foreignObject > section :is(h6, marp-h6) tt{font-size:inherit;padding:0 .2em}div#\:\$p > svg > foreignObject > section summary :is(h1, marp-h1),div#\:\$p > svg > foreignObject > section summary :is(h2, marp-h2),div#\:\$p > svg > foreignObject > section summary :is(h3, marp-h3),div#\:\$p > svg > foreignObject > section summary :is(h4, marp-h4),div#\:\$p > svg > foreignObject > section summary :is(h5, marp-h5),div#\:\$p > svg > foreignObject > section summary :is(h6, marp-h6){display:inline-block}div#\:\$p > svg > foreignObject > section summary :is(h1, marp-h1) .anchor,div#\:\$p > svg > foreignObject > section summary :is(h2, marp-h2) .anchor,div#\:\$p > svg > foreignObject > section summary :is(h3, marp-h3) .anchor,div#\:\$p > svg > foreignObject > section summary :is(h4, marp-h4) .anchor,div#\:\$p > svg > foreignObject > section summary :is(h5, marp-h5) .anchor,div#\:\$p > svg > foreignObject > section summary :is(h6, marp-h6) .anchor{margin-left:-40px}div#\:\$p > svg > foreignObject > section summary :is(h1, marp-h1),div#\:\$p > svg > foreignObject > section summary :is(h2, marp-h2){border-bottom:0;padding-bottom:0}div#\:\$p > svg > foreignObject > section ol.no-list,div#\:\$p > svg > foreignObject > section ul.no-list{list-style-type:none;padding:0}div#\:\$p > svg > foreignObject > section ol[type="a s"]{list-style-type:lower-alpha}div#\:\$p > svg > foreignObject > section ol[type="A s"]{list-style-type:upper-alpha}div#\:\$p > svg > foreignObject > section ol[type="i s"]{list-style-type:lower-roman}div#\:\$p > svg > foreignObject > section ol[type="I s"]{list-style-type:upper-roman}div#\:\$p > svg > foreignObject > section div>ol:not([type]),div#\:\$p > svg > foreignObject > section ol[type="1"]{list-style-type:decimal}div#\:\$p > svg > foreignObject > section ol ol,div#\:\$p > svg > foreignObject > section ol ul,div#\:\$p > svg > foreignObject > section ul ol,div#\:\$p > svg > foreignObject > section ul ul{margin-bottom:0;margin-top:0}div#\:\$p > svg > foreignObject > section li>p{margin-top:16px}div#\:\$p > svg > foreignObject > section li+li{margin-top:.25em}div#\:\$p > svg > foreignObject > section dl{padding:0}div#\:\$p > svg > foreignObject > section dl dt{font-size:1em;font-style:italic;font-weight:var(--base-text-weight-semibold, 600);margin-top:16px;padding:0}div#\:\$p > svg > foreignObject > section dl dd{margin-bottom:16px;padding:0 16px}div#\:\$p > svg > foreignObject > section table th{font-weight:var(--base-text-weight-semibold, 600)}div#\:\$p > svg > foreignObject > section table td,div#\:\$p > svg > foreignObject > section table th{border:1px solid var(--borderColor-default);padding:6px 13px}div#\:\$p > svg > foreignObject > section table td>:last-child{margin-bottom:0}div#\:\$p > svg > foreignObject > section table tr{background-color:var(--bgColor-default);border-top:1px solid var(--borderColor-muted)}div#\:\$p > svg > foreignObject > section table tr:nth-child(2n){background-color:var(--bgColor-muted)}div#\:\$p > svg > foreignObject > section table img{background-color:transparent}div#\:\$p > svg > foreignObject > section img[align=right]{padding-left:20px}div#\:\$p > svg > foreignObject > section img[align=left]{padding-right:20px}div#\:\$p > svg > foreignObject > section .emoji{background-color:transparent;max-width:none;vertical-align:text-top}div#\:\$p > svg > foreignObject > section :is(span, marp-span).frame,div#\:\$p > svg > foreignObject > section :is(span, marp-span).frame>:is(span, marp-span){display:block;overflow:hidden}div#\:\$p > svg > foreignObject > section :is(span, marp-span).frame>:is(span, marp-span){border:1px solid var(--borderColor-default);float:left;margin:13px 0 0;padding:7px;width:auto}div#\:\$p > svg > foreignObject > section :is(span, marp-span).frame :is(span, marp-span) img{display:block;float:left}div#\:\$p > svg > foreignObject > section :is(span, marp-span).frame :is(span, marp-span) :is(span, marp-span){clear:both;color:var(--fgColor-default);display:block;padding:5px 0 0}div#\:\$p > svg > foreignObject > section :is(span, marp-span).align-center{clear:both;display:block;overflow:hidden}div#\:\$p > svg > foreignObject > section :is(span, marp-span).align-center>:is(span, marp-span){display:block;margin:13px auto 0;overflow:hidden;text-align:center}div#\:\$p > svg > foreignObject > section :is(span, marp-span).align-center :is(span, marp-span) img{margin:0 auto;text-align:center}div#\:\$p > svg > foreignObject > section :is(span, marp-span).align-right{clear:both;display:block;overflow:hidden}div#\:\$p > svg > foreignObject > section :is(span, marp-span).align-right>:is(span, marp-span){display:block;margin:13px 0 0;overflow:hidden;text-align:right}div#\:\$p > svg > foreignObject > section :is(span, marp-span).align-right :is(span, marp-span) img{margin:0;text-align:right}div#\:\$p > svg > foreignObject > section :is(span, marp-span).float-left{display:block;float:left;margin-right:13px;overflow:hidden}div#\:\$p > svg > foreignObject > section :is(span, marp-span).float-left :is(span, marp-span){margin:13px 0 0}div#\:\$p > svg > foreignObject > section :is(span, marp-span).float-right{display:block;float:right;margin-left:13px;overflow:hidden}div#\:\$p > svg > foreignObject > section :is(span, marp-span).float-right>:is(span, marp-span){display:block;margin:13px auto 0;overflow:hidden;text-align:right}div#\:\$p > svg > foreignObject > section code,div#\:\$p > svg > foreignObject > section tt{background-color:var(--bgColor-neutral-muted);border-radius:6px;font-size:85%;margin:0;padding:.2em .4em;white-space:break-spaces}div#\:\$p > svg > foreignObject > section code br,div#\:\$p > svg > foreignObject > section tt br{display:none}div#\:\$p > svg > foreignObject > section del code{text-decoration:inherit}div#\:\$p > svg > foreignObject > section samp{font-size:85%}div#\:\$p > svg > foreignObject > section :is(pre, marp-pre) code{font-size:100%}div#\:\$p > svg > foreignObject > section :is(pre, marp-pre)>code{background:transparent;border:0;margin:0;padding:0;white-space:pre;word-break:normal}div#\:\$p > svg > foreignObject > section .highlight{margin-bottom:16px}div#\:\$p > svg > foreignObject > section .highlight :is(pre, marp-pre){margin-bottom:0;word-break:normal}div#\:\$p > svg > foreignObject > section :is(pre, marp-pre){background-color:var(--bgColor-muted);border-radius:6px;color:var(--fgColor-default);font-size:85%;line-height:1.45;overflow:auto;padding:16px}div#\:\$p > svg > foreignObject > section :is(pre, marp-pre) code,div#\:\$p > svg > foreignObject > section :is(pre, marp-pre) tt{display:inline;line-height:inherit;margin:0;max-width:auto;overflow:visible;padding:0;word-wrap:normal;background-color:transparent;border:0}div#\:\$p > svg > foreignObject > section .csv-data td,div#\:\$p > svg > foreignObject > section .csv-data th{font-size:12px;line-height:1;overflow:hidden;padding:5px;text-align:left;white-space:nowrap}div#\:\$p > svg > foreignObject > section .csv-data .blob-num{background:var(--bgColor-default);border:0;padding:10px 8px 9px;text-align:right}div#\:\$p > svg > foreignObject > section .csv-data tr{border-top:0}div#\:\$p > svg > foreignObject > section .csv-data th{background:var(--bgColor-muted);border-top:0;font-weight:var(--base-text-weight-semibold, 600)}div#\:\$p > svg > foreignObject > section [data-footnote-ref]:before{content:"["}div#\:\$p > svg > foreignObject > section [data-footnote-ref]:after{content:"]"}div#\:\$p > svg > foreignObject > section .footnotes{border-top:1px solid var(--borderColor-default);color:var(--fgColor-muted);font-size:12px}div#\:\$p > svg > foreignObject > section div#\:\$p > svg > foreignObject > section section.footnotes{--marpit-root-font-size:12px;}div#\:\$p > svg > foreignObject > section .footnotes ol{padding-left:16px}div#\:\$p > svg > foreignObject > section .footnotes ol ul{display:inline-block;margin-top:16px;padding-left:16px}div#\:\$p > svg > foreignObject > section .footnotes li{position:relative}div#\:\$p > svg > foreignObject > section .footnotes li:target:before{border:2px solid var(--borderColor-accent-emphasis);border-radius:6px;bottom:-8px;content:"";left:-24px;pointer-events:none;position:absolute;right:-8px;top:-8px}div#\:\$p > svg > foreignObject > section .footnotes li:target{color:var(--fgColor-default)}div#\:\$p > svg > foreignObject > section .footnotes .data-footnote-backref g-emoji{font-family:monospace}div#\:\$p > svg > foreignObject > section .pl-c{color:var(--color-prettylights-syntax-comment)}div#\:\$p > svg > foreignObject > section .pl-c1,div#\:\$p > svg > foreignObject > section .pl-s .pl-v{color:var(--color-prettylights-syntax-constant)}div#\:\$p > svg > foreignObject > section .pl-e,div#\:\$p > svg > foreignObject > section .pl-en{color:var(--color-prettylights-syntax-entity)}div#\:\$p > svg > foreignObject > section .pl-s .pl-s1,div#\:\$p > svg > foreignObject > section .pl-smi{color:var(--color-prettylights-syntax-storage-modifier-import)}div#\:\$p > svg > foreignObject > section .pl-ent{color:var(--color-prettylights-syntax-entity-tag)}div#\:\$p > svg > foreignObject > section .pl-k{color:var(--color-prettylights-syntax-keyword)}div#\:\$p > svg > foreignObject > section .pl-pds,div#\:\$p > svg > foreignObject > section .pl-s,div#\:\$p > svg > foreignObject > section .pl-s .pl-pse .pl-s1,div#\:\$p > svg > foreignObject > section .pl-sr,div#\:\$p > svg > foreignObject > section .pl-sr .pl-cce,div#\:\$p > svg > foreignObject > section .pl-sr .pl-sra,div#\:\$p > svg > foreignObject > section .pl-sr .pl-sre{color:var(--color-prettylights-syntax-string)}div#\:\$p > svg > foreignObject > section .pl-smw,div#\:\$p > svg > foreignObject > section .pl-v{color:var(--color-prettylights-syntax-variable)}div#\:\$p > svg > foreignObject > section .pl-bu{color:var(--color-prettylights-syntax-brackethighlighter-unmatched)}div#\:\$p > svg > foreignObject > section .pl-ii{background-color:var(--color-prettylights-syntax-invalid-illegal-bg);color:var(--color-prettylights-syntax-invalid-illegal-text)}div#\:\$p > svg > foreignObject > section .pl-c2{background-color:var(--color-prettylights-syntax-carriage-return-bg);color:var(--color-prettylights-syntax-carriage-return-text)}div#\:\$p > svg > foreignObject > section .pl-sr .pl-cce{color:var(--color-prettylights-syntax-string-regexp);font-weight:700}div#\:\$p > svg > foreignObject > section .pl-ml{color:var(--color-prettylights-syntax-markup-list)}div#\:\$p > svg > foreignObject > section .pl-mh,div#\:\$p > svg > foreignObject > section .pl-mh .pl-en,div#\:\$p > svg > foreignObject > section .pl-ms{color:var(--color-prettylights-syntax-markup-heading);font-weight:700}div#\:\$p > svg > foreignObject > section .pl-mi{color:var(--color-prettylights-syntax-markup-italic);font-style:italic}div#\:\$p > svg > foreignObject > section .pl-mb{color:var(--color-prettylights-syntax-markup-bold);font-weight:700}div#\:\$p > svg > foreignObject > section .pl-md{background-color:var(--color-prettylights-syntax-markup-deleted-bg);color:var(--color-prettylights-syntax-markup-deleted-text)}div#\:\$p > svg > foreignObject > section .pl-mi1{background-color:var(--color-prettylights-syntax-markup-inserted-bg);color:var(--color-prettylights-syntax-markup-inserted-text)}div#\:\$p > svg > foreignObject > section .pl-mc{background-color:var(--color-prettylights-syntax-markup-changed-bg);color:var(--color-prettylights-syntax-markup-changed-text)}div#\:\$p > svg > foreignObject > section .pl-mi2{background-color:var(--color-prettylights-syntax-markup-ignored-bg);color:var(--color-prettylights-syntax-markup-ignored-text)}div#\:\$p > svg > foreignObject > section .pl-mdr{color:var(--color-prettylights-syntax-meta-diff-range);font-weight:700}div#\:\$p > svg > foreignObject > section .pl-ba{color:var(--color-prettylights-syntax-brackethighlighter-angle)}div#\:\$p > svg > foreignObject > section .pl-sg{color:var(--color-prettylights-syntax-sublimelinter-gutter-mark)}div#\:\$p > svg > foreignObject > section .pl-corl{color:var(--color-prettylights-syntax-constant-other-reference-link);text-decoration:underline}div#\:\$p > svg > foreignObject > section [role=button]:focus:not(:focus-visible),div#\:\$p > svg > foreignObject > section [role=tabpanel][tabindex="0"]:focus:not(:focus-visible),div#\:\$p > svg > foreignObject > section a:focus:not(:focus-visible),div#\:\$p > svg > foreignObject > section button:focus:not(:focus-visible),div#\:\$p > svg > foreignObject > section summary:focus:not(:focus-visible){box-shadow:none;outline:none}div#\:\$p > svg > foreignObject > section [tabindex="0"]:focus:not(:focus-visible),div#\:\$p > svg > foreignObject > section details-dialog:focus:not(:focus-visible){outline:none}div#\:\$p > svg > foreignObject > section g-emoji{display:inline-block;font-family:Apple Color Emoji,Segoe UI Emoji,Segoe UI Symbol;font-size:1em;font-style:normal!important;font-weight:var(--base-text-weight-normal, 400);line-height:1;min-width:1ch;vertical-align:-.075em}div#\:\$p > svg > foreignObject > section g-emoji img{height:1em;width:1em}div#\:\$p > svg > foreignObject > section .task-list-item{list-style-type:none}div#\:\$p > svg > foreignObject > section .task-list-item label{font-weight:var(--base-text-weight-normal, 400)}div#\:\$p > svg > foreignObject > section .task-list-item.enabled label{cursor:pointer}div#\:\$p > svg > foreignObject > section .task-list-item+.task-list-item{margin-top:var(--base-size-4)}div#\:\$p > svg > foreignObject > section .task-list-item .handle{display:none}div#\:\$p > svg > foreignObject > section .task-list-item-checkbox{margin:0 .2em .25em -1.4em;vertical-align:middle}div#\:\$p > svg > foreignObject > section .contains-task-list:dir(rtl) .task-list-item-checkbox{margin:0 -1.6em .25em .2em}div#\:\$p > svg > foreignObject > section .contains-task-list{position:relative}div#\:\$p > svg > foreignObject > section .contains-task-list:focus-within .task-list-item-convert-container,div#\:\$p > svg > foreignObject > section .contains-task-list:hover .task-list-item-convert-container{display:block;height:24px;overflow:visible;width:auto;clip:auto}div#\:\$p > svg > foreignObject > section ::-webkit-calendar-picker-indicator{filter:invert(50%)}div#\:\$p > svg > foreignObject > section .markdown-alert{border-left:.25em solid var(--borderColor-default);color:inherit;margin-bottom:var(--base-size-16);padding:var(--base-size-8) var(--base-size-16)}div#\:\$p > svg > foreignObject > section .markdown-alert>:first-child{margin-top:0}div#\:\$p > svg > foreignObject > section .markdown-alert>:last-child{margin-bottom:0}div#\:\$p > svg > foreignObject > section .markdown-alert .markdown-alert-title{align-items:center;display:flex;font-weight:var(--base-text-weight-medium, 500);line-height:1}div#\:\$p > svg > foreignObject > section .markdown-alert.markdown-alert-note{border-left-color:var(--borderColor-accent-emphasis)}div#\:\$p > svg > foreignObject > section .markdown-alert.markdown-alert-note .markdown-alert-title{color:var(--fgColor-accent)}div#\:\$p > svg > foreignObject > section .markdown-alert.markdown-alert-important{border-left-color:var(--borderColor-done-emphasis)}div#\:\$p > svg > foreignObject > section .markdown-alert.markdown-alert-important .markdown-alert-title{color:var(--fgColor-done)}div#\:\$p > svg > foreignObject > section .markdown-alert.markdown-alert-warning{border-left-color:var(--borderColor-attention-emphasis)}div#\:\$p > svg > foreignObject > section .markdown-alert.markdown-alert-warning .markdown-alert-title{color:var(--fgColor-attention)}div#\:\$p > svg > foreignObject > section .markdown-alert.markdown-alert-tip{border-left-color:var(--borderColor-success-emphasis)}div#\:\$p > svg > foreignObject > section .markdown-alert.markdown-alert-tip .markdown-alert-title{color:var(--fgColor-success)}div#\:\$p > svg > foreignObject > section .markdown-alert.markdown-alert-caution{border-left-color:var(--borderColor-danger-emphasis)}div#\:\$p > svg > foreignObject > section .markdown-alert.markdown-alert-caution .markdown-alert-title{color:var(--fgColor-danger)}div#\:\$p > svg > foreignObject > section>:first-child>.heading-element:first-child{margin-top:0!important}div#\:\$p > svg > foreignObject > section :is(h1, marp-h1){color:var(--h1-color);font-size:1.6em}div#\:\$p > svg > foreignObject > section :is(h1, marp-h1),div#\:\$p > svg > foreignObject > section :is(h2, marp-h2){border-bottom:none}div#\:\$p > svg > foreignObject > section :is(h2, marp-h2){font-size:1.3em}div#\:\$p > svg > foreignObject > section :is(h3, marp-h3){font-size:1.1em}div#\:\$p > svg > foreignObject > section :is(h4, marp-h4){font-size:1.05em}div#\:\$p > svg > foreignObject > section :is(h5, marp-h5){font-size:1em}div#\:\$p > svg > foreignObject > section :is(h6, marp-h6){font-size:.9em}div#\:\$p > svg > foreignObject > section :is(h1, marp-h1) strong,div#\:\$p > svg > foreignObject > section :is(h2, marp-h2) strong,div#\:\$p > svg > foreignObject > section :is(h3, marp-h3) strong,div#\:\$p > svg > foreignObject > section :is(h4, marp-h4) strong,div#\:\$p > svg > foreignObject > section :is(h5, marp-h5) strong,div#\:\$p > svg > foreignObject > section :is(h6, marp-h6) strong{color:var(--heading-strong-color);font-weight:inherit}div#\:\$p > svg > foreignObject > section :is(h1, marp-h1)::part(auto-scaling),div#\:\$p > svg > foreignObject > section :is(h2, marp-h2)::part(auto-scaling),div#\:\$p > svg > foreignObject > section :is(h3, marp-h3)::part(auto-scaling),div#\:\$p > svg > foreignObject > section :is(h4, marp-h4)::part(auto-scaling),div#\:\$p > svg > foreignObject > section :is(h5, marp-h5)::part(auto-scaling),div#\:\$p > svg > foreignObject > section :is(h6, marp-h6)::part(auto-scaling){max-height:563px}div#\:\$p > svg > foreignObject > section hr{height:0;padding-top:.25em}div#\:\$p > svg > foreignObject > section img{background-color:transparent}div#\:\$p > svg > foreignObject > section :is(pre, marp-pre){border:1px solid var(--borderColor-default);line-height:1.15;overflow:visible}div#\:\$p > svg > foreignObject > section :is(pre, marp-pre)::part(auto-scaling){max-height:529px}div#\:\$p > svg > foreignObject > section :is(pre, marp-pre) :where(.hljs){color:var(--color-prettylights-syntax-storage-modifier-import)}div#\:\$p > svg > foreignObject > section :is(pre, marp-pre) :where(.hljs-doctag),div#\:\$p > svg > foreignObject > section :is(pre, marp-pre) :where(.hljs-keyword),div#\:\$p > svg > foreignObject > section :is(pre, marp-pre) :where(.hljs-meta .hljs-keyword),div#\:\$p > svg > foreignObject > section :is(pre, marp-pre) :where(.hljs-template-tag),div#\:\$p > svg > foreignObject > section :is(pre, marp-pre) :where(.hljs-template-variable),div#\:\$p > svg > foreignObject > section :is(pre, marp-pre) :where(.hljs-type),div#\:\$p > svg > foreignObject > section :is(pre, marp-pre) :where(.hljs-variable.language_){color:var(--color-prettylights-syntax-keyword)}div#\:\$p > svg > foreignObject > section :is(pre, marp-pre) :where(.hljs-title),div#\:\$p > svg > foreignObject > section :is(pre, marp-pre) :where(.hljs-title.class_),div#\:\$p > svg > foreignObject > section :is(pre, marp-pre) :where(.hljs-title.class_.inherited__),div#\:\$p > svg > foreignObject > section :is(pre, marp-pre) :where(.hljs-title.function_){color:var(--color-prettylights-syntax-entity)}div#\:\$p > svg > foreignObject > section :is(pre, marp-pre) :where(.hljs-attr),div#\:\$p > svg > foreignObject > section :is(pre, marp-pre) :where(.hljs-attribute),div#\:\$p > svg > foreignObject > section :is(pre, marp-pre) :where(.hljs-literal),div#\:\$p > svg > foreignObject > section :is(pre, marp-pre) :where(.hljs-meta),div#\:\$p > svg > foreignObject > section :is(pre, marp-pre) :where(.hljs-number),div#\:\$p > svg > foreignObject > section :is(pre, marp-pre) :where(.hljs-operator),div#\:\$p > svg > foreignObject > section :is(pre, marp-pre) :where(.hljs-selector-attr),div#\:\$p > svg > foreignObject > section :is(pre, marp-pre) :where(.hljs-selector-class),div#\:\$p > svg > foreignObject > section :is(pre, marp-pre) :where(.hljs-selector-id),div#\:\$p > svg > foreignObject > section :is(pre, marp-pre) :where(.hljs-variable){color:var(--color-prettylights-syntax-constant)}div#\:\$p > svg > foreignObject > section :is(pre, marp-pre) :where(.hljs-meta .hljs-string),div#\:\$p > svg > foreignObject > section :is(pre, marp-pre) :where(.hljs-regexp),div#\:\$p > svg > foreignObject > section :is(pre, marp-pre) :where(.hljs-string){color:var(--color-prettylights-syntax-string)}div#\:\$p > svg > foreignObject > section :is(pre, marp-pre) :where(.hljs-built_in),div#\:\$p > svg > foreignObject > section :is(pre, marp-pre) :where(.hljs-symbol){color:var(--color-prettylights-syntax-variable)}div#\:\$p > svg > foreignObject > section :is(pre, marp-pre) :where(.hljs-code),div#\:\$p > svg > foreignObject > section :is(pre, marp-pre) :where(.hljs-comment),div#\:\$p > svg > foreignObject > section :is(pre, marp-pre) :where(.hljs-formula){color:var(--color-prettylights-syntax-comment)}div#\:\$p > svg > foreignObject > section :is(pre, marp-pre) :where(.hljs-name),div#\:\$p > svg > foreignObject > section :is(pre, marp-pre) :where(.hljs-quote),div#\:\$p > svg > foreignObject > section :is(pre, marp-pre) :where(.hljs-selector-pseudo),div#\:\$p > svg > foreignObject > section :is(pre, marp-pre) :where(.hljs-selector-tag){color:var(--color-prettylights-syntax-entity-tag)}div#\:\$p > svg > foreignObject > section :is(pre, marp-pre) :where(.hljs-subst){color:var(--color-prettylights-syntax-storage-modifier-import)}div#\:\$p > svg > foreignObject > section :is(pre, marp-pre) :where(.hljs-section){color:var(--color-prettylights-syntax-markup-heading);font-weight:700}div#\:\$p > svg > foreignObject > section :is(pre, marp-pre) :where(.hljs-bullet){color:var(--color-prettylights-syntax-markup-list)}div#\:\$p > svg > foreignObject > section :is(pre, marp-pre) :where(.hljs-emphasis){color:var(--color-prettylights-syntax-markup-italic);font-style:italic}div#\:\$p > svg > foreignObject > section :is(pre, marp-pre) :where(.hljs-strong){color:var(--color-prettylights-syntax-markup-bold);font-weight:700}div#\:\$p > svg > foreignObject > section :is(pre, marp-pre) :where(.hljs-addition){background-color:var(--color-prettylights-syntax-markup-inserted-bg);color:var(--color-prettylights-syntax-markup-inserted-text)}div#\:\$p > svg > foreignObject > section :is(pre, marp-pre) :where(.hljs-deletion){background-color:var(--color-prettylights-syntax-markup-deleted-bg);color:var(--color-prettylights-syntax-markup-deleted-text)}div#\:\$p > svg > foreignObject > section footer,div#\:\$p > svg > foreignObject > section header{color:var(--header-footer-color);font-size:18px;left:30px;margin:0;position:absolute}div#\:\$p > svg > foreignObject > section header{top:21px}div#\:\$p > svg > foreignObject > section footer{bottom:21px}div#\:\$p > svg > foreignObject > section{--h1-color:#246;--header-footer-color:hsla(0,0%,40%,.75);--heading-strong-color:#48c;--paginate-color:#777;align-items:stretch;display:block;flex-flow:column nowrap;font-size:29px;height:720px;padding:78.5px;place-content:safe center center;width:1280px}div#\:\$p > svg > foreignObject > section{--marpit-root-font-size:29px;}div#\:\$p > svg > foreignObject > section:where(.invert){--h1-color:#cee7ff;--header-footer-color:hsla(0,0%,60%,.75);--heading-strong-color:#7bf;--paginate-color:#999;}div#\:\$p > svg > foreignObject > section>:last-child,div#\:\$p > svg > foreignObject > section[data-footer]>:nth-last-child(2){margin-bottom:0}div#\:\$p > svg > foreignObject > section>:first-child,div#\:\$p > svg > foreignObject > section>header:first-child+*{margin-top:0}div#\:\$p > svg > foreignObject > section:after{bottom:21px;color:var(--paginate-color);font-size:24px;padding:0;position:absolute;right:30px}div#\:\$p > svg > foreignObject > section:after{--marpit-root-font-size:24px;}div#\:\$p > svg > foreignObject > section[data-color] :is(h1, marp-h1),div#\:\$p > svg > foreignObject > section[data-color] :is(h2, marp-h2),div#\:\$p > svg > foreignObject > section[data-color] :is(h3, marp-h3),div#\:\$p > svg > foreignObject > section[data-color] :is(h4, marp-h4),div#\:\$p > svg > foreignObject > section[data-color] :is(h5, marp-h5),div#\:\$p > svg > foreignObject > section[data-color] :is(h6, marp-h6){color:currentcolor}div#\:\$p > svg > foreignObject > 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</style></head><body><div class="bespoke-marp-osc"><button data-bespoke-marp-osc="prev" tabindex="-1" title="Previous slide">Previous slide</button><span data-bespoke-marp-osc="page"></span><button data-bespoke-marp-osc="next" tabindex="-1" title="Next slide">Next slide</button><button data-bespoke-marp-osc="fullscreen" tabindex="-1" title="Toggle fullscreen (f)">Toggle fullscreen</button><button data-bespoke-marp-osc="presenter" tabindex="-1" title="Open presenter view (p)">Open presenter view</button></div><div id=":$p"><svg data-marpit-svg="" viewBox="0 0 1280 720"><foreignObject width="1280" height="720"><section data-paginate="true" data-header="ODISSEI 2024, PreFer data challenge" data-footer="Simone Meneghello, Alessio Piraccini, Gianluca Ivo Tori" data-theme="default" data-style="section {
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<header>ODISSEI 2024, PreFer data challenge</header>
<h1 id="odissei-2024-prefer-data-challenge">ODISSEI 2024, PreFer data challenge</h1>
<p><em>Simone Meneghello, Alessio Piraccini, Gianluca Ivo Tori</em></p>
<footer>Simone Meneghello, Alessio Piraccini, Gianluca Ivo Tori</footer>
</section>
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<header>ODISSEI 2024, PreFer data challenge</header>
<h2 id="initial-considerations">Initial considerations</h2>
<ul>
<li>
<p><strong>Recent data priority</strong>: Key insights for predicting fertility (2021-2023) likely stem from surveys around 2021. Focus on recent surveys, supplemented by relevant past data.</p>
</li>
<li>
<p><strong>Feature selection</strong>: Despite numerous survey questions, only a few features may be crucial. Identifying and selecting these key features is essential to streamline the dataset.</p>
</li>
<li>
<p><strong>Handling missing values</strong>: Missing data might not be random and could hold valuable information. Some missing responses result from survey branching logic. Longitudinal data may allow filling gaps with past information.</p>
</li>
<li>
<p><strong>Key predictors</strong>: Likely predictors include age, relationship status, economic situation, and existing children. However, the dataset's breadth may reveal unexpected patterns.</p>
</li>
</ul>
<footer>Simone Meneghello, Alessio Piraccini, Gianluca Ivo Tori</footer>
</section>
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<header>ODISSEI 2024, PreFer data challenge</header>
<h2 id="data-exploration">Data exploration</h2>
<ul>
<li>
<p><strong>Task Overview</strong>: classify if a person will have a child within 2021-2023 using 2020 data.</p>
</li>
<li>
<p><strong>Dataset Details</strong>:</p>
<ul>
<li>Initial dataset: 6,418 rows, 31,634 columns.</li>
<li>Cleaned dataset: 987 rows, 25,868 columns (removed rows with missing outcomes and columns with all missing values).</li>
</ul>
</li>
<li>
<p><strong>Background Dataset</strong>:</p>
<ul>
<li>Longitudinal format with repeated entries per subject across years.</li>
<li>Filtered to include subjects with available outcomes.</li>
<li>Contains key predictive features (e.g., age, income, civil status).</li>
</ul>
</li>
</ul>
<footer>Simone Meneghello, Alessio Piraccini, Gianluca Ivo Tori</footer>
</section>
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<header>ODISSEI 2024, PreFer data challenge</header>
<h2 id="tree-selection">Tree selection</h2>
<ul>
<li>Used a univariate decision tree with stratified 5-fold cross-validation for feature evaluation.</li>
<li>Performance decreases over time, supporting the <em>relevance of recent surveys</em>.</li>
</ul>
<footer>Simone Meneghello, Alessio Piraccini, Gianluca Ivo Tori</footer>
</section>
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<header>ODISSEI 2024, PreFer data challenge</header>
<h2 id="tree-selection-1">Tree selection</h2>
<ul>
<li>Most surveys show limited key variables.</li>
<li>Key variables are desire for children, income, age, civil status, gynecologist visits</li>
</ul>
<footer>Simone Meneghello, Alessio Piraccini, Gianluca Ivo Tori</footer>
</section>
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<header>ODISSEI 2024, PreFer data challenge</header>
<h2 id="missing-values">Missing values</h2>
<p><strong>Key considerations</strong>:</p>
<ul>
<li>missing data can often be attributed to <em>survey logic</em> or <em>non-participation</em></li>
<li>missing data in key variables, like <em>future child plans</em>, often correlates with not having a child</li>
</ul>
<p>We used a <strong>longitudinal</strong> approach for imputation, filling gaps with the most recent past responses.<br />
<br /></p>
<table>
<thead>
<tr>
<th>quest2015</th>
<th>quest2016</th>
<th>quest2017</th>
<th>quest2018</th>
<th>quest2019</th>
<th>quest2020</th>
<th>quest2020_imp</th>
</tr>
</thead>
<tbody>
<tr>
<td>4</td>
<td>--</td>
<td>4</td>
<td>--</td>
<td>5</td>
<td>5</td>
<td>5</td>
</tr>
<tr>
<td>--</td>
<td>--</td>
<td>5</td>
<td>3</td>
<td>--</td>
<td>--</td>
<td>3</td>
</tr>
<tr>
<td>2</td>
<td>--</td>
<td>--</td>
<td>--</td>
<td>--</td>
<td>--</td>
<td>2</td>
</tr>
</tbody>
</table>
<footer>Simone Meneghello, Alessio Piraccini, Gianluca Ivo Tori</footer>
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<header>ODISSEI 2024, PreFer data challenge</header>
<h2 id="exploratory-data-analysis">Exploratory data analysis</h2>
<ul>
<li><em>Propensity to have a child</em> is the strongest predictor.</li>
<li>Income, relationship status, and Big Five traits are significant.</li>
</ul>
<footer>Simone Meneghello, Alessio Piraccini, Gianluca Ivo Tori</footer>
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<header>ODISSEI 2024, PreFer data challenge</header>
<h2 id="exploratory-data-analysis-1">Exploratory data analysis</h2>
<footer>Simone Meneghello, Alessio Piraccini, Gianluca Ivo Tori</footer>
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<header>ODISSEI 2024, PreFer data challenge</header>
<h2 id="exploratory-data-analysis-2">Exploratory data analysis</h2>
<ul>
<li>Immediate plans for children and desire for children correlate with having children.</li>
<li>Recent cohabitation and individuals in their thirties are more likely to have children.</li>
<li>Mostly married or never married have children.</li>
<li>Income shows no clear difference between groups.</li>
</ul>
<footer>Simone Meneghello, Alessio Piraccini, Gianluca Ivo Tori</footer>
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<header>ODISSEI 2024, PreFer data challenge</header>
<h2 id="modeling">Modeling</h2>
<ul>
<li>Used stratified shuffle split (k=10, 30% validation) for validation to improve test performance alignment.</li>
<li>Focused on tree-based models: Random Forest, Extra Trees, and Gradient Boosting (CatBoost, LightGBM, XGBoost).</li>
<li>Employed Bayesian hyperparameter tuning.</li>
<li>Combined CatBoost, LightGBM, Extra Trees using weighted voting (CatBoost weight: 0.5).</li>
<li>Final model: weighted voting of CatBoost, LightGBM, Extra Trees; CatBoost is the best standalone model.</li>
</ul>
<footer>Simone Meneghello, Alessio Piraccini, Gianluca Ivo Tori</footer>
</section>
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<header>ODISSEI 2024, PreFer data challenge</header>
<h2 id="modeling-1">Modeling</h2>
<ul>
<li><em>Intention of having a child</em> and related features.</li>
<li><em>Relationship status</em>: start year of cohabitation, civil status, and marriage flag are significant.</li>
<li><em>Age</em> is the third most important feature.</li>
<li>Additional predictors include <em>"Go to the gynecologist"</em> and <em>Big Five</em> personality traits (agreeableness, conscientiousness).</li>
</ul>
<footer>Simone Meneghello, Alessio Piraccini, Gianluca Ivo Tori</footer>
</section>
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<header>ODISSEI 2024, PreFer data challenge</header>
<footer>Simone Meneghello, Alessio Piraccini, Gianluca Ivo Tori</footer>
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<header>ODISSEI 2024, PreFer data challenge</header>
<h2 id="modeling-2">Modeling</h2>
<ul>
<li>Higher <strong>SHAP values</strong> for <em>individuals desiring children, especially older subjects</em>.</li>
<li>Increased predicted probability for people in their thirties planning another child soon.</li>
<li>Married individuals, particularly those marrying young, show higher predicted probabilities.</li>
<li>Recent cohabitation (within ten years) and age 28-38 correlate with higher SHAP values.</li>
<li>Visiting a gynecologist indicates a higher expected probability, supporting its role in identifying pregnant women.</li>
</ul>
<footer>Simone Meneghello, Alessio Piraccini, Gianluca Ivo Tori</footer>
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<header>ODISSEI 2024, PreFer data challenge</header>
<h2 id="final-considerations">Final considerations</h2>
<ul>
<li>Achieved <strong>~90% accuracy</strong> with the final model; sophisticated techniques offer slight performance improvements but aren't essential.</li>
<li>Key predictors of fertility are intention to have a child and relationship status, as expected.</li>
<li>Personality traits, analyzed via factor analysis, can enhance prediction accuracy.</li>
</ul>
<footer>Simone Meneghello, Alessio Piraccini, Gianluca Ivo Tori</footer>
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<header>ODISSEI 2024, PreFer data challenge</header>
<h2 id="appendix-big-five">Appendix: Big five</h2>
<ul>
<li>Focused on investigating how Big Five personality traits affect childbearing propensity.</li>
<li>According to this model the personality traits are Extraversion, Agreeableness, Conscientiousness, Emotional Stability, and Openness; viewed as spectrums. It's based on factor analysis of psychometric data, validated across cultures.</li>
<li>Survey questions are rated on a 5-point scale, missing values are imputed using previous year data due to trait stability.</li>
<li>Used Factor Analysis on survey questions to obtain five traits to be used as features for the final model.</li>
</ul>
<footer>Simone Meneghello, Alessio Piraccini, Gianluca Ivo Tori</footer>
</section>
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<header>ODISSEI 2024, PreFer data challenge</header>
<h2 id="appendix-big-five-1">Appendix: Big five</h2>
<table>
<thead>
<tr>
<th></th>
<th>Neuroticism</th>
<th>Extraversion</th>
<th>Agreeableness</th>
<th>Conscientiousness</th>
<th>Openness</th>
</tr>
</thead>
<tbody>
<tr>
<td></td>
<td>(+) Get upset easily.</td>
<td>(-) Keep in the background.</td>
<td>(+) Sympathize with others’ feelings.</td>
<td>(+) Like order.</td>
<td>(+) Have excellent ideas.</td>
</tr>
<tr>
<td></td>
<td>(+) Have frequent mood swings.</td>
<td>(-) Am quiet around strangers.</td>
<td>(-) Am not really interested in others.</td>
<td>(-) Often forget to put things back in their proper place.</td>
<td>(+) Am full of ideas.</td>
</tr>
<tr>
<td></td>
<td>(+) Get stressed out easily.</td>
<td>(-) Don’t talk a lot.</td>
<td>(+) Am interested in people.</td>
<td>(-) Leave my belongings around.</td>
<td>(+) Have a rich vocabulary.</td>
</tr>
</tbody>