Hidden Markov Model Algorithms

==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠== You can decompress Drawing data with the command palette: 'Decompress current Excalidraw file'. For more info check in plugin settings under 'Saving' # Excalidraw Data ## Text Elements Q ^Y8OxjSAY The Forward Algorithm ^hhr8b64t t = ^msyTVtpC k-1 ^D1hKbFVE k ^ONt3ZCIO k+1 ^lCfrrnSU k-1 ^hVH4l0QY Q ^ofFNhpiy k ^7MqzdPWE Q ^hHTJBln2 k+1 ^tbDLRjgs O ^apwNWt2F k-1 ^pqBDIO9b O ^65Ql1LM4 k ^V1eXmHIz O ^fM3HAzEX k+1 ^Rtm63eWE ## Embedded Files dd44e156dfe07f3e97d1c3e1ca3259a0e19ebcf3: $\alpha_1(j)=\pi_j \cdot B_j(o_j) \text{, for } 1 \le j \le N$ d3ad13250c22c36435a5e187c16b76bf38236d67: $a_k(j)=\sum^{N}_{i=1}\alpha(i) \times A_{i,j} \times B_j (O_t)$ d1df7f0295d92c8acbd9f0b5903fcf42e935b51d: $N = \text{\# of States}$ b41cba642f9091ffe4acd4345e992a02745327a0: $A_{i \rightarrow j} = \text{Transitions Between States}$ 518bd8caa3e963ede50b15015591008973482e2c: $\alpha_1(j)=\pi_j \cdot B_j(o_j) \text{, for } 1 \le j \le N$ 3438183f93aaaf0834d21face185ba5977c054e7: [[Pasted Image 20241220223307_644.png]] 649dc9109703a61c8ac69366c7049eac0b0d9ac1: [[Pasted Image 20241220223327_533.png]] c16d7cc3e0d7ad27f25abdc7170dac7990179efb: [[Pasted Image 20241220223349_233.png]] %% ## Drawing ```json { "type": "excalidraw", "version": 2, "source": "https://github.com/zsviczian/obsidian-excalidraw-plugin/releases/tag/2.11.1", "elements": [ { "type": "ellipse", "version": 433, "versionNonce": 1414433533, "index": "aFV", "isDeleted": false, "id": "aqdUloxr8LLTcFfsitMie", "fillStyle": "solid", "strokeWidth": 2, "strokeStyle": "solid", "roughness": 1, "opacity": 100, "angle": 0, "x": 216.27077222205503, "y": -1562.761478356307, "strokeColor": "#1e1e1e", "backgroundColor": "transparent", "width": 157.74162194765765, "height": 85.60799232537033, "seed": 288269149, "groupIds": [], "frameId": "hxwpr3x7BIobeQ7MpP945", "roundness": { "type": 2 }, "boundElements": [ { "id": "VvTpNnEK_im2IB4YrMnNG", "type": "arrow" }, { "id": "IPX-XWKukFL9NPwuBEKva", "type": "arrow" }, { "id": "4d-HoYVJELq-3WvRUvDJW", "type": "arrow" } ], "updated": 1729647261021, "link": null, "locked": false }, { "type": 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