29:null 2a:["$","title",null,{"children":"Hidden Markov Model (Not completed) | William Pang | Observable"}] 2f:T56e,//From: https://observablehq.com/@tomlarkworthy/vertical-sliders#verticalSliders function verticalSliders(config = {}) { const len = (arr) => arr ? arr.length : undefined; let { n = len(config.values) || len(config.mins) || len(config.maxs) || len(config.values) || len(config.names) || len(config.labels) || 1, mins = Array(n).fill(0), maxs = Array(n).fill(1), steps = Array(n).fill("any"), values = mins.map((min, idx) => (maxs[idx] + min) / 2), names = Array(n).fill(0).map((_, idx) => `${idx}`), labels = Array(n).fill("") } = config; return form(html`

${labels.map(label => html``)} ${Array(n).fill(0).map((_, idx) => html``)}

${label}

`) }30:[{"id":"f08f3ae94cf80c08f66e9a6b56171a945a040e645bf2c86dbabea73d5fc0afb3fd02c6af012adfc967431d5fe0616d75339820a0752db7c6fcea3070ee65292e","href":"https://static.observableusercontent.com/files/f08f3ae94cf80c08f66e9a6b56171a945a040e645bf2c86dbabea73d5fc0afb3fd02c6af012adfc967431d5fe0616d75339820a0752db7c6fcea3070ee65292e","name":"Matrix_Diagram.jpg","type":"image/jpeg","lastModified":1642513416960.103,"size":152955}] 2d:{"id":"c44beb2aa3ad5c08","slug":null,"title":"Hidden Markov Model (Not completed)","thumbnail":"d8091ff0de599aee355a7da32d57f602d9421c506c9ffe0919401c869ca68459","access_level":"public","create_time":"$D2022-01-17T19:02:30.972Z","update_time":"$D2022-01-24T02:00:40.221Z","view_time":null,"first_public_time":"$D2022-01-18T21:01:49.469Z","fork":false,"stars":0,"starred":false,"owner":{"type":"team","id":"88df4b53b2fce8d2","login":"will-pang","name":"William Pang","avatar_url":"https://avatars-next.observableusercontent.com/4e5603477ef111cf1fc74cb0aab0dd58ddab37219e1b2a4e5e9c3d082c5532a0","tier":"starter_2024"},"version":346,"publish_version":null,"role":null,"authored":false,"authors":[{"type":"individual","id":"30424cd7adf510bb","login":"williampangbest1","name":"William Pang","avatar_url":"https://avatars-next.observableusercontent.com/4e5603477ef111cf1fc74cb0aab0dd58ddab37219e1b2a4e5e9c3d082c5532a0","tier":null}],"members":[{"type":"individual","id":"30424cd7adf510bb","login":"williampangbest1","name":"William Pang","avatar_url":"https://avatars-next.observableusercontent.com/4e5603477ef111cf1fc74cb0aab0dd58ddab37219e1b2a4e5e9c3d082c5532a0","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"subscribed":null,"forks":0,"collection":{"id":"346a7806b7ef1030","slug":"half-baked","title":"Half-Baked","owner":{"id":"88df4b53b2fce8d2","login":"will-pang","name":"William Pang"}},"type":"notebook","body":{"title":"Hidden Markov Model (Not completed)","cells":[{"id":0,"value":"# Hidden Markov Model (Not completed)","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined"},{"id":6,"value":"Note: This is an attempt to recreate an interactive version of [ritvikmath's](https://www.youtube.com/watch?v=fX5bYmnHqqE) amazing video explaining the Hidden Markov Model. This is just a half-baked attempt to toy around a bit, and is by no means \"production-ready\".","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined"},{"id":12,"value":"dot `digraph {\n\n S -> Happy[label=\"B\",weight=\"1\"];\n S -> Sad[label=\"A\",weight=\"1\"]; \n\n Sad -> Happy[label=\"C\",weight=\"10\"];\n Sad -> Sad[label=\"D\",weight=\"0.5\"];\n Happy -> Sad[label=\"E\",weight=\"0.3\"];\n Happy -> Happy[label=\"F\",weight=\"0.7\"];\n \n \n Happy -> Red [label=\"G\",weight=\"1\"];\n Happy -> Green [label=\"H\",weight=\"1\"];\n Happy -> Blue [label=\"I\",weight=\"1\"];\n Sad -> Red [label=\"J\",weight=\"1\"];\n Sad -> Green [label=\"K\",weight=\"1\"];\n Sad -> Blue [label=\"L\",weight=\"0.5\"];\n\n {rank=same; S}\n {rank=same; Happy,Sad}\n {rank=same; Red,Green,Blue}\n\n}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":120,"value":"Not a perfect graph, so I'll have to spend more time reading the [graphviz](http://graphviz.org) documentation in the future. *See what I mean by not being production ready?*","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined"},{"id":303,"value":"md`\n## The Scenario\nImagine seeing a professor wearing a ${textcolor('green shirt', 'darkgreen')} on the first day, a ${textcolor('blue shirt', 'blue')} on the second day, and a ${textcolor('red shirt', 'red')} on the third day. Even though the professor is smiling and greeting the class everyday, we know that the pick of color for her attire is not entirely random -- in fact, it's dependent on the *mood* of the professor.\n\nThe colors of the shirt are known as the **observed states** (as this is something you can see), and the mood of the professor is known as **hidden states** (we assume here that the professor does not reveal their emotions easily to the class due to professionalism).\n\n> **Task at hand:** To guess the most likely sequence of moods\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":292,"value":"FileAttachment(\"Matrix_Diagram.jpg\").image()","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":244,"value":"The Transition Matrix is:","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined"},{"id":248,"value":"viewof transitionMatrix = pt(math.matrix([Object.values(H), Object.values(J)]),{ title: \"T=\" })","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":253,"value":"viewof H = verticalSliders({\n labels:[\"D\", \"C\"],\n maxs: [0.9,0.9],\n steps: [0.1,0.1],\n values:[0.1,0.1]\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":256,"value":"viewof J = verticalSliders({\n labels:[\"E\", \"F\"],\n maxs: [0.9,0.9],\n steps: [0.1,0.1],\n values:[0.1,0.1]\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":183,"value":"The Emission Matrix is:","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined"},{"id":168,"value":"viewof emissionMatrix = pt(math.matrix([Object.values(color), Object.values(colore)]),{ title: \"E=\" })","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":187,"value":"viewof color = verticalSliders({\n labels:[\"K\", \"J\", \"L\"],\n maxs: [0.9,0.9,0.9],\n steps: [0.1,0.1,0.1],\n values:[0.1,0.1,0.1]\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":237,"value":"viewof colore = verticalSliders({\n labels:[\"H\", \"G\", \"I\"],\n maxs: [0.9,0.9,0.9],\n steps: [0.1,0.1,0.1],\n values:[0.1,0.1,0.1]\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":328,"value":"md`\n## Approach\nTo guess the most likely moods of the professor, we can think of this as maximizing the probability of seeing the color sequenece (i.e. green \\u279e blue \\u279e red) given a certain sequence of moods. \n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":170,"value":"### Appendix","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined"},{"id":178,"value":"import {pt} from \"@fil/pt\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":174,"value":"math = require(\"https://unpkg.com/mathjs@5.0.1/dist/math.min.js\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":204,"value":"$2f","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":206,"value":"import {form} from \"@tomlarkworthy/mutable-form-input\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":311,"value":"import {textcolor} from \"@observablehq/text-color-annotations-in-markdown\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"}],"files":"$W30","stdlib":"1","titling":"auto"}} 2e:"$2d:body"