--- title: "Markov" language: "en" type: "Method" summary: "Markov (Machine Learning Method) Method for Classify. Model class probabilities using the n-gram frequencies of the given sequence. In a Markov model, at training time, an n-gram language model is computed for each class. At test time, the probability for each class is computed according to Bayes's theorem, P(class|sequence)\\[Proportional]P(class) P(sequence|class), where P(sequence|class) is given by the language model of the given class and P(class) is class prior. The following options can be given: When Order->n, the method partitions sequences in (n+1)-grams. When Order->0, the method uses unigrams (single tokens). The model can then be called a unigram model or naive Bayes model. The value of AdditiveSmoothing is added to all n-gram counts. It is used to regularize the language model." canonical_url: "https://reference.wolfram.com/language/ref/method/Markov.html" source: "Wolfram Language Documentation" --- # "Markov" (Machine Learning Method) * Method for ``Classify``. * Model class probabilities using the ``n``-gram frequencies of the given sequence. --- ## Details & Suboptions * In a Markov model, at training time, an ``n``-gram language model is computed for each class. At test time, the probability for each class is computed according to Bayes's theorem, $P(\text{class}|\text{sequence})\propto P(\text{class}) P(\text{sequence}|\text{class})$, where $P(\text{sequence}|\text{class})$ is given by the language model of the given class and $P(\text{class})$ is class prior. * The following options can be given: | | | | | -------------------- | --------- | ----------------------------------------------- | | "AdditiveSmoothing" | .1 | the smoothing parameter to use | | "MinimumTokenCount" | Automatic | minimum count for an n-gram to to be considered | | "Order" | Automatic | n-gram length | * When ``"Order" -> n``, the method partitions sequences in (``n``+1)-grams. * When ``"Order" -> 0``, the method uses unigrams (single tokens). The model can then be called a unigram model or naive Bayes model. * The value of ``"AdditiveSmoothing"`` is added to all ``n``-gram counts. It is used to regularize the language model. --- ## Examples (5) ### Basic Examples (1) Train a classifier function on labeled examples: ```wl In[1]:= c = Classify[{{"flour", "butter"}, {"pasta", "tomato"}, {"apple", "ice cream"}, {"salt", "meat"}, {"honey", "sugar", "butter"}} -> {"dessert", "main course", "dessert", "main course", "dessert"}, Method -> "Markov"] Out[1]= ClassifierFunction[Association["ExampleNumber" -> 5, "ClassNumber" -> 2, "Input" -> Association["Preprocessor" -> MachineLearning`MLProcessor["ToMLDataset", Association["Input" -> Association["f1" -> Association["Type" -> "NominalSequence ... "Date" -> DateObject[{2025, 6, 25, 1, 11, 0.2386149`7.130272548300395}, "Instant", "Gregorian", -5.], "ProcessorCount" -> 4, "ProcessorType" -> "x86-64", "OperatingSystem" -> "Windows", "SystemWordLength" -> 64, "Evaluations" -> {}]]] ``` Obtain information about the classifier: ```wl In[2]:= Information[c] Out[2]= MachineLearning`MLInformationObject[ClassifierFunction[Association["ExampleNumber" -> 5, "ClassNumber" -> 2, "Input" -> Association["Preprocessor" -> MachineLearning`MLProcessor[ "ToMLDataset", Association["Input" -> Association[ ... ate" -> DateObject[{2025, 6, 25, 1, 11, 0.2386149`7.130272548300395}, "Instant", "Gregorian", -5.], "ProcessorCount" -> 4, "ProcessorType" -> "x86-64", "OperatingSystem" -> "Windows", "SystemWordLength" -> 64, "Evaluations" -> {}]]]] ``` Classify a new example: ```wl In[3]:= c[{"tomato", "meat", "salt"}] Out[3]= "main course" ``` ### Options (4) #### "AdditiveSmoothing" (2) Train a classifier using the ``"AdditiveSmoothing"`` suboption: ```wl In[1]:= Classify[{{[image], "this is dark red"} -> Red, {[image], "this is blue"} -> Blue, {[image], "this is dark blue"} -> Blue, {[image], "this red is almost orange"} -> Red}, Method -> {"Markov", "AdditiveSmoothing" -> 2}] Out[1]= ClassifierFunction[…] ``` --- Train two classifiers on an imbalanced dataset by varying the value of ``"AdditiveSmoothing"`` : ```wl In[1]:= data = {"aaabb" -> True, "cdfff" -> True, "cdffvvv" -> True, "aaa" -> True, "vvvtul" -> False, "dqedewf" -> True}; In[2]:= c1 = Classify[data, Method -> {"Markov", "AdditiveSmoothing" -> .1}]; c2 = Classify[data, Method -> {"Markov", "AdditiveSmoothing" -> 7}]; ``` Look at the corresponding probabilities for the imbalanced element: ```wl In[3]:= c1["vvvtul", "Probabilities"] Out[3]= <|False -> 0.999999, True -> 6.243717669398518`*^-7|> In[4]:= c2["vvvtul", "Probabilities"] Out[4]= <|False -> 0.636523, True -> 0.363477|> ``` #### "Order" (2) Train a classifier by specifying the ``"Order"`` : ```wl In[1]:= Classify[{{[image], "this is dark red"} -> Red, {[image], "this is blue"} -> Blue, {[image], "this is dark blue"} -> Blue, {[image], "this red is almost orange"} -> Red}, Method -> {"Markov", "Order" -> 2}] Out[1]= ClassifierFunction[…] ``` --- Generate a dataset of real words and random strings: ```wl In[1]:= alphabet = Alphabet[]; randomstrings = RandomChoice[alphabet, RandomInteger[{2, 5}]]; realwords = DictionaryLookup["a" ~~ ___]; trainingset = <|"RealWord" -> RandomSample[realwords, 200], "RandomString" -> Table[StringJoin@@randomstrings, 200]|>; ``` Generate classifiers using different values for the ``"Order"`` : ```wl In[2]:= c0 = Classify[trainingset, Method -> {"Markov" , "Order" -> 0}] Out[2]= ClassifierFunction[Association["ExampleNumber" -> 400, "ClassNumber" -> 2, "Input" -> Association["Preprocessor" -> MachineLearning`MLProcessor["ToMLDataset", Association["Input" -> Association["f1" -> Association["Type" -> "Text"]], ... -> DateObject[{2025, 6, 27, 13, 46, 42.0641526`9.376487018898942}, "Instant", "Gregorian", -5.], "ProcessorCount" -> 4, "ProcessorType" -> "x86-64", "OperatingSystem" -> "Windows", "SystemWordLength" -> 64, "Evaluations" -> {}]]] In[3]:= c2 = Classify[trainingset, Method -> {"Markov", "Order" -> 2}] Out[3]= ClassifierFunction[Association["ExampleNumber" -> 400, "ClassNumber" -> 2, "Input" -> Association["Preprocessor" -> MachineLearning`MLProcessor["ToMLDataset", Association["Input" -> Association["f1" -> Association["Type" -> "Text"]], ... -> DateObject[{2025, 6, 27, 13, 46, 42.3140917`9.379059897496155}, "Instant", "Gregorian", -5.], "ProcessorCount" -> 4, "ProcessorType" -> "x86-64", "OperatingSystem" -> "Windows", "SystemWordLength" -> 64, "Evaluations" -> {}]]] ``` Compare the probabilities of these classifiers on a new real word: ```wl In[4]:= SeedRandom[4] notRandom = RandomSample[DictionaryLookup["a" ~~ ___], 1]; Dataset@<|"Classifier1" -> c0[notRandom, "Probabilities"], "Classifier2" -> c2[notRandom, "Probabilities"]|> Out[4]= RandomGeneratorState[{"ExtendedCA", {80, 4, 0}}, {{RawArray["UnsignedInteger64", {18302116819084061373, 11746481009677376582, 7205648230778544085, 18400895792363088632, 11685717158017383283, 14200862264039299955, 2613688760522993787, ... 3, 3514913594139996632, 10401935623725113395, 57122523875845255, 5247983425652520213, 5354304471328057820, 7321571919780935734}], 0, 20, 20}, {CompressedData["«1415»"], 4, 0}}, RawArray["UnsignedInteger64", {6205802040732621421, 0}]] Out[4]= DynamicModule[«6»] ``` ## See Also * [`Classify`](https://reference.wolfram.com/language/ref/Classify.en.md) * [`ClassifierFunction`](https://reference.wolfram.com/language/ref/ClassifierFunction.en.md) * [`ClassifierMeasurements`](https://reference.wolfram.com/language/ref/ClassifierMeasurements.en.md) * [`Predict`](https://reference.wolfram.com/language/ref/Predict.en.md) * [`SequencePredict`](https://reference.wolfram.com/language/ref/SequencePredict.en.md) * [`ClusterClassify`](https://reference.wolfram.com/language/ref/ClusterClassify.en.md) * [`DecisionTree`](https://reference.wolfram.com/language/ref/method/DecisionTree.en.md) * [`LogisticRegression`](https://reference.wolfram.com/language/ref/method/LogisticRegression.en.md) * [`NearestNeighbors`](https://reference.wolfram.com/language/ref/method/NearestNeighbors.en.md) * [`NeuralNetwork`](https://reference.wolfram.com/language/ref/method/NeuralNetwork.en.md) * [`RandomForest`](https://reference.wolfram.com/language/ref/method/RandomForest.en.md) * [`SupportVectorMachine`](https://reference.wolfram.com/language/ref/method/SupportVectorMachine.en.md) ## Related Links * [An Elementary Introduction to the Wolfram Language: Machine Learning](https://www.wolfram.com/language/elementary-introduction/22-machine-learning.html) ## History * [Introduced in 2014 (10.0)](https://reference.wolfram.com/language/guide/SummaryOfNewFeaturesIn100.en.md)