README.html 17 KB

123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209210211212213214215216217218219220221222223224225226227228229230231232233234235236237238239240241242243244245246247248249250251252253254255256257258259260261262263264265266267268269270271272273274275276277278279280281282283284285286287288289290291292293294295296297298299300301302303304305306307308309310311312313314315316317318319320321322323324325326327328329330331332333334335336337338339340341342343344345346347348349350351352353354355356357358359360361362363364365366367368369370371372373374375376377378379380381382383384385386387388389390391392393394395396397398399400401402403404405406407408409410411412413414415416417418419420421422423424425426427428429430431432433434435436437438439440441442443444445446447448449450451452453454455456457458459460461462463464465466467468469470471472473474475476477478479480481482483484485486487488489490491492493494495496497498499500501502503504505506507508509510511512513514515516517518519520521522523524525526527528529
  1. <!DOCTYPE html>
  2. <html>
  3. <head>
  4. <meta charset="utf-8" />
  5. <meta name="viewport" content="width=device-width, initial-scale=1.0" />
  6. <title>ssm-book &#8212; State Space Models: A Modern Approach</title>
  7. <link href="_static/css/theme.css" rel="stylesheet">
  8. <link href="_static/css/index.ff1ffe594081f20da1ef19478df9384b.css" rel="stylesheet">
  9. <link rel="stylesheet"
  10. href="_static/vendor/fontawesome/5.13.0/css/all.min.css">
  11. <link rel="preload" as="font" type="font/woff2" crossorigin
  12. href="_static/vendor/fontawesome/5.13.0/webfonts/fa-solid-900.woff2">
  13. <link rel="preload" as="font" type="font/woff2" crossorigin
  14. href="_static/vendor/fontawesome/5.13.0/webfonts/fa-brands-400.woff2">
  15. <link rel="stylesheet" type="text/css" href="_static/pygments.css" />
  16. <link rel="stylesheet" type="text/css" href="_static/sphinx-book-theme.css?digest=c3fdc42140077d1ad13ad2f1588a4309" />
  17. <link rel="stylesheet" type="text/css" href="_static/togglebutton.css" />
  18. <link rel="stylesheet" type="text/css" href="_static/copybutton.css" />
  19. <link rel="stylesheet" type="text/css" href="_static/mystnb.css" />
  20. <link rel="stylesheet" type="text/css" href="_static/sphinx-thebe.css" />
  21. <link rel="stylesheet" type="text/css" href="_static/panels-main.c949a650a448cc0ae9fd3441c0e17fb0.css" />
  22. <link rel="stylesheet" type="text/css" href="_static/panels-variables.06eb56fa6e07937060861dad626602ad.css" />
  23. <link rel="preload" as="script" href="_static/js/index.be7d3bbb2ef33a8344ce.js">
  24. <script data-url_root="./" id="documentation_options" src="_static/documentation_options.js"></script>
  25. <script src="_static/jquery.js"></script>
  26. <script src="_static/underscore.js"></script>
  27. <script src="_static/doctools.js"></script>
  28. <script src="_static/clipboard.min.js"></script>
  29. <script src="_static/copybutton.js"></script>
  30. <script>let toggleHintShow = 'Click to show';</script>
  31. <script>let toggleHintHide = 'Click to hide';</script>
  32. <script>let toggleOpenOnPrint = 'true';</script>
  33. <script src="_static/togglebutton.js"></script>
  34. <script>var togglebuttonSelector = '.toggle, .admonition.dropdown, .tag_hide_input div.cell_input, .tag_hide-input div.cell_input, .tag_hide_output div.cell_output, .tag_hide-output div.cell_output, .tag_hide_cell.cell, .tag_hide-cell.cell';</script>
  35. <script src="_static/sphinx-book-theme.d59cb220de22ca1c485ebbdc042f0030.js"></script>
  36. <script>const THEBE_JS_URL = "https://unpkg.com/thebe@0.8.2/lib/index.js"
  37. const thebe_selector = ".thebe,.cell"
  38. const thebe_selector_input = "pre"
  39. const thebe_selector_output = ".output, .cell_output"
  40. </script>
  41. <script async="async" src="_static/sphinx-thebe.js"></script>
  42. <link rel="index" title="Index" href="genindex.html" />
  43. <link rel="search" title="Search" href="search.html" />
  44. <meta name="viewport" content="width=device-width, initial-scale=1" />
  45. <meta name="docsearch:language" content="None">
  46. <!-- Google Analytics -->
  47. </head>
  48. <body data-spy="scroll" data-target="#bd-toc-nav" data-offset="80">
  49. <div class="container-fluid" id="banner"></div>
  50. <div class="container-xl">
  51. <div class="row">
  52. <div class="col-12 col-md-3 bd-sidebar site-navigation show" id="site-navigation">
  53. <div class="navbar-brand-box">
  54. <a class="navbar-brand text-wrap" href="index.html">
  55. <h1 class="site-logo" id="site-title">State Space Models: A Modern Approach</h1>
  56. </a>
  57. </div><form class="bd-search d-flex align-items-center" action="search.html" method="get">
  58. <i class="icon fas fa-search"></i>
  59. <input type="search" class="form-control" name="q" id="search-input" placeholder="Search this book..." aria-label="Search this book..." autocomplete="off" >
  60. </form><nav class="bd-links" id="bd-docs-nav" aria-label="Main">
  61. <div class="bd-toc-item active">
  62. <ul class="nav bd-sidenav">
  63. <li class="toctree-l1">
  64. <a class="reference internal" href="root.html">
  65. State Space Models: A Modern Approach
  66. </a>
  67. </li>
  68. </ul>
  69. <ul class="nav bd-sidenav">
  70. <li class="toctree-l1">
  71. <a class="reference internal" href="chapters/scratch.html">
  72. Scratchpad
  73. </a>
  74. </li>
  75. <li class="toctree-l1 has-children">
  76. <a class="reference internal" href="chapters/ssm/ssm_index.html">
  77. Introduction
  78. </a>
  79. <input class="toctree-checkbox" id="toctree-checkbox-1" name="toctree-checkbox-1" type="checkbox"/>
  80. <label for="toctree-checkbox-1">
  81. <i class="fas fa-chevron-down">
  82. </i>
  83. </label>
  84. <ul>
  85. <li class="toctree-l2">
  86. <a class="reference internal" href="chapters/ssm/hmm.html">
  87. Hidden Markov Models
  88. </a>
  89. </li>
  90. <li class="toctree-l2">
  91. <a class="reference internal" href="chapters/ssm/hsmm.html">
  92. Hidden Semi-Markov Models
  93. </a>
  94. </li>
  95. <li class="toctree-l2">
  96. <a class="reference internal" href="chapters/ssm/lgssm.html">
  97. Linear Gaussian SSMs
  98. </a>
  99. </li>
  100. <li class="toctree-l2">
  101. <a class="reference internal" href="chapters/ssm/nonlin.html">
  102. Non-Linear Gaussian SSMs
  103. </a>
  104. </li>
  105. <li class="toctree-l2">
  106. <a class="reference internal" href="chapters/ssm/nongauss.html">
  107. Non-Gaussian SSMs
  108. </a>
  109. </li>
  110. <li class="toctree-l2">
  111. <a class="reference internal" href="chapters/ssm/switching.html">
  112. Switching SSMs
  113. </a>
  114. </li>
  115. <li class="toctree-l2">
  116. <a class="reference internal" href="chapters/ssm/deep.html">
  117. Deep SSMs
  118. </a>
  119. </li>
  120. <li class="toctree-l2">
  121. <a class="reference internal" href="chapters/ssm/rnn.html">
  122. Recurrent Neural Networks
  123. </a>
  124. </li>
  125. </ul>
  126. </li>
  127. <li class="toctree-l1 has-children">
  128. <a class="reference internal" href="chapters/hmm/hmm_index.html">
  129. Inference in discrete SSMs
  130. </a>
  131. <input class="toctree-checkbox" id="toctree-checkbox-2" name="toctree-checkbox-2" type="checkbox"/>
  132. <label for="toctree-checkbox-2">
  133. <i class="fas fa-chevron-down">
  134. </i>
  135. </label>
  136. <ul>
  137. <li class="toctree-l2">
  138. <a class="reference internal" href="chapters/hmm/hmm_filter.html">
  139. HMM filtering (forwards algorithm)
  140. </a>
  141. </li>
  142. <li class="toctree-l2">
  143. <a class="reference internal" href="chapters/hmm/hmm_smoother.html">
  144. HMM smoothing (forwards-backwards algorithm)
  145. </a>
  146. </li>
  147. <li class="toctree-l2">
  148. <a class="reference internal" href="chapters/hmm/hmm_viterbi.html">
  149. Viterbi algorithm
  150. </a>
  151. </li>
  152. <li class="toctree-l2">
  153. <a class="reference internal" href="chapters/hmm/hmm_parallel.html">
  154. Parallel HMM smoothing
  155. </a>
  156. </li>
  157. <li class="toctree-l2">
  158. <a class="reference internal" href="chapters/hmm/hmm_sampling.html">
  159. Forwards-filtering backwards-sampling algorithm
  160. </a>
  161. </li>
  162. </ul>
  163. </li>
  164. <li class="toctree-l1 has-children">
  165. <a class="reference internal" href="chapters/lgssm/lgssm_index.html">
  166. Inference in linear-Gaussian SSMs
  167. </a>
  168. <input class="toctree-checkbox" id="toctree-checkbox-3" name="toctree-checkbox-3" type="checkbox"/>
  169. <label for="toctree-checkbox-3">
  170. <i class="fas fa-chevron-down">
  171. </i>
  172. </label>
  173. <ul>
  174. <li class="toctree-l2">
  175. <a class="reference internal" href="chapters/lgssm/kalman_filter.html">
  176. Kalman filtering
  177. </a>
  178. </li>
  179. <li class="toctree-l2">
  180. <a class="reference internal" href="chapters/lgssm/kalman_smoother.html">
  181. Kalman (RTS) smoother
  182. </a>
  183. </li>
  184. <li class="toctree-l2">
  185. <a class="reference internal" href="chapters/lgssm/kalman_parallel.html">
  186. Parallel Kalman Smoother
  187. </a>
  188. </li>
  189. <li class="toctree-l2">
  190. <a class="reference internal" href="chapters/lgssm/kalman_sampling.html">
  191. Forwards-filtering backwards sampling
  192. </a>
  193. </li>
  194. </ul>
  195. </li>
  196. <li class="toctree-l1 has-children">
  197. <a class="reference internal" href="chapters/extended/extended_index.html">
  198. Extended (linearized) methods
  199. </a>
  200. <input class="toctree-checkbox" id="toctree-checkbox-4" name="toctree-checkbox-4" type="checkbox"/>
  201. <label for="toctree-checkbox-4">
  202. <i class="fas fa-chevron-down">
  203. </i>
  204. </label>
  205. <ul>
  206. <li class="toctree-l2">
  207. <a class="reference internal" href="chapters/extended/extended_filter.html">
  208. Extended Kalman filtering
  209. </a>
  210. </li>
  211. <li class="toctree-l2">
  212. <a class="reference internal" href="chapters/extended/extended_smoother.html">
  213. Extended Kalman smoother
  214. </a>
  215. </li>
  216. <li class="toctree-l2">
  217. <a class="reference internal" href="chapters/extended/extended_parallel.html">
  218. Parallel extended Kalman smoothing
  219. </a>
  220. </li>
  221. </ul>
  222. </li>
  223. <li class="toctree-l1 has-children">
  224. <a class="reference internal" href="chapters/unscented/unscented_index.html">
  225. Unscented methods
  226. </a>
  227. <input class="toctree-checkbox" id="toctree-checkbox-5" name="toctree-checkbox-5" type="checkbox"/>
  228. <label for="toctree-checkbox-5">
  229. <i class="fas fa-chevron-down">
  230. </i>
  231. </label>
  232. <ul>
  233. <li class="toctree-l2">
  234. <a class="reference internal" href="chapters/unscented/unscented_filter.html">
  235. Unscented filtering
  236. </a>
  237. </li>
  238. <li class="toctree-l2">
  239. <a class="reference internal" href="chapters/unscented/unscented_smoother.html">
  240. Unscented smoothing
  241. </a>
  242. </li>
  243. </ul>
  244. </li>
  245. <li class="toctree-l1">
  246. <a class="reference internal" href="chapters/quadrature/quadrature_index.html">
  247. Quadrature and cubature methods
  248. </a>
  249. </li>
  250. <li class="toctree-l1">
  251. <a class="reference internal" href="chapters/postlin/postlin_index.html">
  252. Posterior linearization
  253. </a>
  254. </li>
  255. <li class="toctree-l1">
  256. <a class="reference internal" href="chapters/adf/adf_index.html">
  257. Assumed Density Filtering
  258. </a>
  259. </li>
  260. <li class="toctree-l1">
  261. <a class="reference internal" href="chapters/vi/vi_index.html">
  262. Variational inference
  263. </a>
  264. </li>
  265. <li class="toctree-l1">
  266. <a class="reference internal" href="chapters/pf/pf_index.html">
  267. Particle filtering
  268. </a>
  269. </li>
  270. <li class="toctree-l1">
  271. <a class="reference internal" href="chapters/smc/smc_index.html">
  272. Sequential Monte Carlo
  273. </a>
  274. </li>
  275. <li class="toctree-l1 has-children">
  276. <a class="reference internal" href="chapters/learning/learning_index.html">
  277. Offline parameter estimation (learning)
  278. </a>
  279. <input class="toctree-checkbox" id="toctree-checkbox-6" name="toctree-checkbox-6" type="checkbox"/>
  280. <label for="toctree-checkbox-6">
  281. <i class="fas fa-chevron-down">
  282. </i>
  283. </label>
  284. <ul>
  285. <li class="toctree-l2">
  286. <a class="reference internal" href="chapters/learning/em.html">
  287. Expectation Maximization (EM)
  288. </a>
  289. </li>
  290. <li class="toctree-l2">
  291. <a class="reference internal" href="chapters/learning/sgd.html">
  292. Stochastic Gradient Descent (SGD)
  293. </a>
  294. </li>
  295. <li class="toctree-l2">
  296. <a class="reference internal" href="chapters/learning/vb.html">
  297. Variational Bayes (VB)
  298. </a>
  299. </li>
  300. <li class="toctree-l2">
  301. <a class="reference internal" href="chapters/learning/mcmc.html">
  302. Markov Chain Monte Carlo (MCMC)
  303. </a>
  304. </li>
  305. </ul>
  306. </li>
  307. <li class="toctree-l1">
  308. <a class="reference internal" href="chapters/tracking/tracking_index.html">
  309. Multi-target tracking
  310. </a>
  311. </li>
  312. <li class="toctree-l1">
  313. <a class="reference internal" href="chapters/ensemble/ensemble_index.html">
  314. Data assimilation using Ensemble Kalman filter
  315. </a>
  316. </li>
  317. <li class="toctree-l1">
  318. <a class="reference internal" href="chapters/bnp/bnp_index.html">
  319. Bayesian non-parametric SSMs
  320. </a>
  321. </li>
  322. <li class="toctree-l1">
  323. <a class="reference internal" href="chapters/changepoint/changepoint_index.html">
  324. Changepoint detection
  325. </a>
  326. </li>
  327. <li class="toctree-l1">
  328. <a class="reference internal" href="chapters/timeseries/timeseries_index.html">
  329. Timeseries forecasting
  330. </a>
  331. </li>
  332. <li class="toctree-l1">
  333. <a class="reference internal" href="chapters/gp/gp_index.html">
  334. Markovian Gaussian processes
  335. </a>
  336. </li>
  337. <li class="toctree-l1">
  338. <a class="reference internal" href="chapters/ode/ode_index.html">
  339. Differential equations and SSMs
  340. </a>
  341. </li>
  342. <li class="toctree-l1">
  343. <a class="reference internal" href="chapters/control/control_index.html">
  344. Optimal control
  345. </a>
  346. </li>
  347. <li class="toctree-l1">
  348. <a class="reference internal" href="bib.html">
  349. Bibliography
  350. </a>
  351. </li>
  352. </ul>
  353. </div>
  354. </nav> <!-- To handle the deprecated key -->
  355. <div class="navbar_extra_footer">
  356. Powered by <a href="https://jupyterbook.org">Jupyter Book</a>
  357. </div>
  358. </div>
  359. <main class="col py-md-3 pl-md-4 bd-content overflow-auto" role="main">
  360. <div class="topbar container-xl fixed-top">
  361. <div class="topbar-contents row">
  362. <div class="col-12 col-md-3 bd-topbar-whitespace site-navigation show"></div>
  363. <div class="col pl-md-4 topbar-main">
  364. <button id="navbar-toggler" class="navbar-toggler ml-0" type="button" data-toggle="collapse"
  365. data-toggle="tooltip" data-placement="bottom" data-target=".site-navigation" aria-controls="navbar-menu"
  366. aria-expanded="true" aria-label="Toggle navigation" aria-controls="site-navigation"
  367. title="Toggle navigation" data-toggle="tooltip" data-placement="left">
  368. <i class="fas fa-bars"></i>
  369. <i class="fas fa-arrow-left"></i>
  370. <i class="fas fa-arrow-up"></i>
  371. </button>
  372. <div class="dropdown-buttons-trigger">
  373. <button id="dropdown-buttons-trigger" class="btn btn-secondary topbarbtn" aria-label="Download this page"><i
  374. class="fas fa-download"></i></button>
  375. <div class="dropdown-buttons">
  376. <!-- ipynb file if we had a myst markdown file -->
  377. <!-- Download raw file -->
  378. <a class="dropdown-buttons" href="_sources/README.md"><button type="button"
  379. class="btn btn-secondary topbarbtn" title="Download source file" data-toggle="tooltip"
  380. data-placement="left">.md</button></a>
  381. <!-- Download PDF via print -->
  382. <button type="button" id="download-print" class="btn btn-secondary topbarbtn" title="Print to PDF"
  383. onclick="printPdf(this)" data-toggle="tooltip" data-placement="left">.pdf</button>
  384. </div>
  385. </div>
  386. <!-- Source interaction buttons -->
  387. <div class="dropdown-buttons-trigger">
  388. <button id="dropdown-buttons-trigger" class="btn btn-secondary topbarbtn"
  389. aria-label="Connect with source repository"><i class="fab fa-github"></i></button>
  390. <div class="dropdown-buttons sourcebuttons">
  391. <a class="repository-button"
  392. href="https://github.com/ssm-jax/ssm-book"><button type="button" class="btn btn-secondary topbarbtn"
  393. data-toggle="tooltip" data-placement="left" title="Source repository"><i
  394. class="fab fa-github"></i>repository</button></a>
  395. <a class="issues-button"
  396. href="https://github.com/ssm-jax/ssm-book/issues/new?title=Issue%20on%20page%20%2FREADME.html&body=Your%20issue%20content%20here."><button
  397. type="button" class="btn btn-secondary topbarbtn" data-toggle="tooltip" data-placement="left"
  398. title="Open an issue"><i class="fas fa-lightbulb"></i>open issue</button></a>
  399. </div>
  400. </div>
  401. <!-- Full screen (wrap in <a> to have style consistency -->
  402. <a class="full-screen-button"><button type="button" class="btn btn-secondary topbarbtn" data-toggle="tooltip"
  403. data-placement="bottom" onclick="toggleFullScreen()" aria-label="Fullscreen mode"
  404. title="Fullscreen mode"><i
  405. class="fas fa-expand"></i></button></a>
  406. <!-- Launch buttons -->
  407. </div>
  408. <!-- Table of contents -->
  409. <div class="d-none d-md-block col-md-2 bd-toc show noprint">
  410. </div>
  411. </div>
  412. </div>
  413. <div id="main-content" class="row">
  414. <div class="col-12 col-md-9 pl-md-3 pr-md-0">
  415. <!-- Table of contents that is only displayed when printing the page -->
  416. <div id="jb-print-docs-body" class="onlyprint">
  417. <h1>ssm-book</h1>
  418. <!-- Table of contents -->
  419. <div id="print-main-content">
  420. <div id="jb-print-toc">
  421. </div>
  422. </div>
  423. </div>
  424. <div>
  425. <div class="tex2jax_ignore mathjax_ignore section" id="ssm-book">
  426. <h1>ssm-book<a class="headerlink" href="#ssm-book" title="Permalink to this headline">¶</a></h1>
  427. <p>Interactive textbook on state-space models.
  428. The rendered content can be found at <a class="reference external" href="https://probml.github.io/ssm-book/root.html">https://probml.github.io/ssm-book/root.html</a>.</p>
  429. </div>
  430. <script type="text/x-thebe-config">
  431. {
  432. requestKernel: true,
  433. binderOptions: {
  434. repo: "binder-examples/jupyter-stacks-datascience",
  435. ref: "master",
  436. },
  437. codeMirrorConfig: {
  438. theme: "abcdef",
  439. mode: "python"
  440. },
  441. kernelOptions: {
  442. kernelName: "python3",
  443. path: "./."
  444. },
  445. predefinedOutput: true
  446. }
  447. </script>
  448. <script>kernelName = 'python3'</script>
  449. </div>
  450. <!-- Previous / next buttons -->
  451. <div class='prev-next-area'>
  452. </div>
  453. </div>
  454. </div>
  455. <footer class="footer">
  456. <p>
  457. By Kevin Murphy, Scott Linderman, et al.<br/>
  458. &copy; Copyright 2021.<br/>
  459. </p>
  460. </footer>
  461. </main>
  462. </div>
  463. </div>
  464. <script src="_static/js/index.be7d3bbb2ef33a8344ce.js"></script>
  465. </body>
  466. </html>