digraph beard {
"" -> "A";
"" -> "Given";
"" -> "Consider";
"" -> "For";
"" -> "There";
"" -> "Alice";
"" -> ".";
"shop" -> "or";
"all" -> "possible";
"Based" -> "on";
"they" -> "did";
"they" -> "are";
"chain" -> "There";
"over" -> "all";
"over" -> "the";
"dynamic" -> "programmin";
"What" -> "is";
"area" -> "and";
"accepting" -> "the";
"statistical" -> "significance";
"find" -> "the";
"derive" -> "the";
"system" -> "is";
"parameters" -> "of";
"daily" -> "over";
"solving" -> "this";
"written" -> "down";
"exclusively" -> "by";
"to" -> "evaluate";
"to" -> "guess";
"to" -> "have";
"to" -> "do";
"only" -> "interested";
"interested" -> "in";
"those" -> "are";
"relevance" -> "of";
"hidden" -> "Markov";
"hidden" -> "from";
"has" -> "no";
"local" -> "maximum";
"activities" -> "walking";
"activities" -> "those";
"activities" -> "depending";
"them" -> "directly";
"his" -> "activities";
"his" -> "apartment";
"They" -> "can";
"Bob" -> "is";
"Bob" -> "who";
"Bob" -> "will";
"Bob" -> "lives";
"Bob" -> "likes";
"Bob" -> "tells";
"evaluate" -> "the";
"possible" -> "state";
"choice" -> "of";
"cannot" -> "observe";
"words" -> "the";
"words" -> "derive";
"using" -> "the";
"one" -> "of";
"one" -> "can";
"day" -> "Bob";
"day" -> "there";
"day" -> "Alice";
"apart" -> "from";
"entire" -> "system";
"did" -> "each";
"did" -> "that";
"large" -> "as";
"solved" -> "efficiently";
"either" -> "of";
"each" -> "other";
"each" -> "day";
"output" -> "probabilities";
"output" -> "sequenc";
"output" -> "sequences";
"output" -> "sequence";
"where" -> "Bob";
"likes" -> "to";
"Rainy" -> "and";
"set" -> "of";
"For" -> "either";
"sequence" -> "probability";
"sequence" -> "that";
"sequence" -> "This";
"sequence" -> "When";
"sequence" -> "find";
"sequence" -> "drawn";
"sequence" -> "the";
"sequence" -> "or";
"Since" -> "Bob";
"some" -> "null";
"operates" -> "as";
"likely" -> "to";
"likely" -> "set";
"are" -> "known";
"are" -> "the";
"are" -> "hidden";
"are" -> "three";
"are" -> "two";
"HM" -> ".";
"believes" -> "that";
"special" -> "case";
"canonical" -> "problems";
"what" -> "to";
"what" -> "Bob";
"what" -> "the";
"what" -> "they";
"for" -> "a";
"for" -> "the";
"for" -> "solving";
"discrete" -> "Markov";
"cleaning" -> "his";
"definite" -> "information";
"HMM" -> "are";
"HMM" -> "given";
"HMM" -> "is";
"HMM" -> "probability";
"HMM" -> ".";
"state" -> "sequence";
"state" -> "transition";
"state" -> "sequences";
"On" -> "each";
"drawn" -> "from";
"she" -> "cannot";
"she" -> "knows";
"be" -> "solved";
"be" -> "written";
"be" -> "derived";
"be" -> "done";
"Expectationmaximization" -> "algorith";
"This" -> "requires";
"problems" -> "associated";
"problems" -> "one";
"Viterbi" -> "algorithm";
"Viterbi" -> "algorith";
"guess" -> "what";
"walking" -> "in";
"apartment" -> "The";
"hypothesis" -> "for";
"trends" -> "Based";
"trends" -> "in";
"ask" -> "about";
"BaldiChauvin" -> "algorithm";
"likelihood" -> "estimate";
"likelihood" -> "can";
"by" -> "the";
"on" -> "a";
"on" -> "average";
"on" -> "what";
"on" -> "the";
"about" -> "what";
"about" -> "his";
"about" -> "the";
"about" -> "statistical";
"language" -> ".";
"tractable" -> "algorithm";
"of" -> "a";
"of" -> "what";
"of" -> "dynamic";
"of" -> "state";
"of" -> "output";
"of" -> "such";
"of" -> "the";
"transition" -> "and";
"programming" -> "language";
"tries" -> "to";
"Markov" -> "model";
"Markov" -> "chain";
"must" -> "have";
"or" -> "a";
"or" -> "the";
"or" -> "clean";
"first" -> "two";
"Given" -> "the";
"Given" -> "an";
"probability" -> "of";
"probability" -> "in";
"probability" -> "that";
"No" -> "tractable";
"There" -> "are";
"When" -> "an";
"dataset" -> "of";
"down" -> "in";
"weather" -> "on";
"weather" -> "walk";
"weather" -> "trends";
"weather" -> "operates";
"weather" -> "where";
"weather" -> "must";
"done" -> "efficiently";
"been" -> "lik";
"directly" -> "that";
"sequences" -> "find";
"sequences" -> "but";
"sequences" -> "No";
"summation" -> "over";
"false" -> "positive";
"estimate" -> "of";
"given" -> "a";
"given" -> "day";
"from" -> "some";
"from" -> "her";
"from" -> "each";
"her" -> "On";
"her" -> "he";
"similarly" -> "be";
"probabilities" -> "In";
"positive" -> "rate";
"there" -> "is";
"Sunny" -> "but";
"three" -> "activities";
"three" -> "canonical";
"least" -> "as";
"live" -> "far";
"observations" -> "The";
"forward" -> "algorithm";
"programmin" -> ".";
"shopping" -> "and";
"knows" -> "the";
"knows" -> "general";
"form" -> "of";
"that" -> "a";
"that" -> "Bob";
"that" -> "of";
"that" -> "is";
"that" -> "output";
"that" -> "the";
"that" -> "day";
"exactly" -> "but";
"park" -> "shopping";
"distribution" -> "will";
"but" -> "a";
"but" -> "can";
"but" -> "she";
"observe" -> "them";
"lives" -> "but";
"particular" -> "output";
"known" -> "They";
"known" -> "for";
"general" -> "trends";
"general" -> "weather";
"with" -> "HMM";
"with" -> "accepting";
"algorith" -> ".";
"he" -> "did";
"case" -> "of";
"compute" -> "the";
"Consider" -> "two";
"this" -> "problem";
"rate" -> "associated";
"maximum" -> "over";
"maximum" -> "likelihood";
"maximum" -> "state";
"BaumWelch" -> "algorithm";
"will" -> "perform";
"will" -> "have";
"determined" -> "exclusively";
"can" -> "be";
"can" -> "additionally";
"can" -> "similarly";
"following" -> "activities";
"problem" -> "exactly";
"forwardbackward" -> "algorithm";
"example" -> "of";
"example" -> ".";
"and" -> "a";
"and" -> "what";
"and" -> "is";
"and" -> "who";
"and" -> "Sunny";
"and" -> "cleaning";
"and" -> "output";
"and" -> "Bob";
"associated" -> "with";
"do" -> "on";
"do" -> "is";
"certain" -> "chance";
"is" -> "a";
"is" -> "used";
"is" -> "that";
"is" -> "an";
"is" -> "most";
"is" -> "only";
"is" -> "determined";
"is" -> "they";
"is" -> "known";
"is" -> "the";
"telephone" -> "about";
"an" -> "output";
"an" -> "example";
"an" -> "HMM";
"states" -> "Rainy";
"indicates" -> "the";
"as" -> "large";
"as" -> "a";
"as" -> "that";
"at" -> "least";
"have" -> "generated";
"have" -> "been";
"have" -> "an";
"in" -> "the";
"in" -> "three";
"null" -> "distribution";
"tells" -> "Alice";
"tells" -> "her";
"chance" -> "that";
"information" -> "about";
"no" -> "definite";
"perform" -> "one";
"lik" -> ".";
"walk" -> "shop";
"far" -> "apart";
"other" -> "and";
"other" -> "words";
"which" -> "is";
"significance" -> "indicates";
"significance" -> "What";
"finding" -> "a";
"A" -> "concrete";
"used" -> "to";
"sequenc" -> ".";
"who" -> "live";
"who" -> "talk";
"derived" -> "efficiently";
"Alice" -> "and";
"Alice" -> "about";
"Alice" -> "knows";
"Alice" -> "believes";
"Alice" -> "tries";
"Alice" -> "has";
"most" -> "likely";
"generated" -> "that";
"two" -> "states";
"two" -> "friends";
"two" -> "problems";
"additionally" -> "ask";
"such" -> "sequences";
"The" -> "entire";
"The" -> "choice";
"The" -> "BaumWelch";
"friends" -> "Alice";
"the" -> "false";
"the" -> "probability";
"the" -> "telephone";
"the" -> "general";
"the" -> "weather";
"the" -> "statistical";
"the" -> "parameters";
"the" -> "area";
"the" -> "Python";
"the" -> "HMM";
"the" -> "state";
"the" -> "observations";
"the" -> "relevance";
"the" -> "Expectationmaximization";
"the" -> "Viterbi";
"the" -> "park";
"the" -> "forward";
"the" -> "most";
"the" -> "hypothesis";
"the" -> "BaldiChauvin";
"the" -> "case";
"the" -> "maximum";
"the" -> "BaumWelch";
"the" -> "following";
"the" -> "output";
"the" -> "model";
"the" -> "first";
"efficiently" -> "using";
"efficiently" -> "by";
"a" -> "given";
"a" -> "set";
"a" -> "form";
"a" -> "sequence";
"a" -> "certain";
"a" -> "maximum";
"a" -> "dataset";
"a" -> "discrete";
"a" -> "hypothesis";
"a" -> "particular";
"a" -> "hidden";
"a" -> "forwardbackward";
"a" -> "local";
"a" -> "special";
"Python" -> "programming";
"algorithm" -> "and";
"algorithm" -> "is";
"algorithm" -> "at";
"algorithm" -> "which";
"algorithm" -> "The";
"algorithm" -> "or";
"average" -> "In";
"depending" -> "on";
"together" -> "daily";
"concrete" -> "example";
"clean" -> "Since";
"In" -> "other";
"model" -> "and";
"model" -> "compute";
"model" -> "HM";
"requires" -> "summation";
"requires" -> "finding";
"talk" -> "together";
}