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SequencePredict
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SequencePredict

[Experimental]

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SequencePredict[{seq1,seq2,…}]

generates a SequencePredictorFunction[…] based on the sequences given.

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SequencePredict[training,seq]

attempts to predict the next element in the sequence seq from the training sequences given.

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SequencePredict[training,{seq1,seq2,…}]

gives predictions for each of the sequences seqi.

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SequencePredict["name",seq]

uses the built-in sequence predictor represented by "name".

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SequencePredict[…,seq,prop]

give the specified property of the prediction associated with seq.

Details and Options

  • The sequences seqi can be lists of either tokens or strings.
  • Sequences seqi are assumed to be unordered subsequences of an underlying infinite sequence.
  • In SequencePredict[…,seq,prop], properties are as given in SequencePredictorFunction[…]; they include:
  • "NextElement"most likely next element
    "NextElement"nindividually most likely next n elements
    "NextSequence"nmost likely next length-n sequence of elements
    "RandomNextElement"random sample from the next-element distribution
    "RandomNextElement"nrandom sample from the next-sequence distribution
    "Probabilities"association of probabilities for all possible next elements
    "SequenceProbability"probability for the predictor to generate the given sequence
    "SequenceLogProbability"log probability for the predictor to generate the sequence
    "Properties"list of all properties available
  • Examples of built-in sequence predictors include:
  • "Chinese"character-based Chinese-language text
    "English"character-based English-language text
    "French"character-based French-language text
    "German"character-based German-language text
    "Portuguese"character-based Portuguese-language text
    "Russian"character-based Russian-language text
    "Spanish"character-based Spanish-language text
  • The following options can be given:
  • FeatureExtractor Automatichow to preprocess sequences
    Method Automaticwhich prediction algorithm to use
    PerformanceGoal Automaticaspects of performance to try to optimize
    RandomSeeding1234what seeding of pseudorandom generators should be done internally
  • Typical settings for FeatureExtractor for strings include:
  • "SegmentedCharacters"string interpreted as a sequence of characters (default)
    "SegmentedWords"string interpreted as a sequence of words
  • Possible settings for PerformanceGoal include:
  • "Memory"minimize storage requirements of the predictor
    "Quality"maximize accuracy of the predictor
    "Speed"maximize speed of the predictor
    "TrainingSpeed"minimize time spent producing the predictor
    Automaticautomatic tradeoff among speed, accuracy and memory
  • PerformanceGoal{goal1,goal2,…} will automatically combine goal1, goal2, etc.
  • Possible settings for RandomSeeding include:
  • Automaticautomatically reseed every time the function is called
    Inheriteduse externally seeded random numbers
    seeduse an explicit integer or strings as a seed
  • Possible settings for Method include:
  • "Markov"Markov model
  • In SequencePredict[…,Method{"Markov","Order"order}], order corresponds to Markov process memory size.
  • In SequencePredict[…,"SequenceProbability"], some probability mass is kept for unknown elements.
  • In SequencePredict[training,{},prop], {} is interpreted as an empty list of sequences rather than an empty sequence.

Examples

open allclose all

Basic Examples  (1)Summary of the most common use cases

Train a sequence predictor on a set of sequences:

In[1]:=1
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https://wolfram.com/xid/05e4dew1xz-lnu020
Out[1]=1

Predict the next element of a new sequence:

In[2]:=2
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https://wolfram.com/xid/05e4dew1xz-oatr7j
Out[2]=2

Obtain the probabilities of the next element given the sequence:

In[3]:=3
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https://wolfram.com/xid/05e4dew1xz-serypb
Out[3]=3

Obtain a random next element according to the preceding distribution:

In[4]:=4
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https://wolfram.com/xid/05e4dew1xz-k54pti
Out[4]=4

Obtain multiple predictions at a time:

In[5]:=5
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https://wolfram.com/xid/05e4dew1xz-u85bu5
Out[5]=5

Predict the most likely next element and reuse this intermediate guess to predict the following element:

In[6]:=6
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https://wolfram.com/xid/05e4dew1xz-qkskkl
Out[6]=6

Predict the most likely following sequence:

In[7]:=7
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https://wolfram.com/xid/05e4dew1xz-n5n77h
Out[7]=7

Compare the probabilities for the preceding sequences:

In[8]:=8
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https://wolfram.com/xid/05e4dew1xz-t1bu2t
Out[8]=8

Scope  (4)Survey of the scope of standard use cases

Custom Sequence Predictors  (3)

Train a sequence predictor on a list of strings:

In[1]:=1
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https://wolfram.com/xid/05e4dew1xz-6sez10
Out[1]=1

Predict the next character following a given string:

In[2]:=2
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https://wolfram.com/xid/05e4dew1xz-l22s5c
Out[2]=2

Predict the next four characters:

In[3]:=3
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https://wolfram.com/xid/05e4dew1xz-rxtxgj
Out[3]=3

Obtain the probabilities for each character to follow the given string:

In[4]:=4
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https://wolfram.com/xid/05e4dew1xz-id78on
Out[4]=4

Train a sequence predictor on the list of common English words, each word treated as a sequence of characters:

In[1]:=1
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https://wolfram.com/xid/05e4dew1xz-k0b3xh
Out[1]=1

Predict the most likely next character from a given sequence:

In[2]:=2
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https://wolfram.com/xid/05e4dew1xz-8h9wld
Out[2]=2

In the previous example, each word is considered as a subsequence of an infinite sequence. Use the character | to mark boundaries between words:

In[3]:=3
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https://wolfram.com/xid/05e4dew1xz-5nicwp

Build a new sequence predictor aware of word boundaries:

In[4]:=4
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https://wolfram.com/xid/05e4dew1xz-n8cvau
Out[4]=4

Generate the beginning of an English-like word:

In[5]:=5
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https://wolfram.com/xid/05e4dew1xz-hi4e3b
Out[5]=5

Load a book from ExampleData:

In[1]:=1
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https://wolfram.com/xid/05e4dew1xz-x7jn6t

Train a sequence predictor on this book:

In[2]:=2
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https://wolfram.com/xid/05e4dew1xz-f9ehi6
Out[2]=2

Sample a random string in the book style:

In[3]:=3
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https://wolfram.com/xid/05e4dew1xz-heh36n
Out[3]=3

Train another sequence predictor, interpreting strings as word sequences rather than character sequences:

In[4]:=4
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https://wolfram.com/xid/05e4dew1xz-gvbc7m
Out[4]=4

Complete the preceding string with 10 consecutive words (spaces and punctuation marks are considered as words):

In[5]:=5
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https://wolfram.com/xid/05e4dew1xz-5ei7cf
Out[5]=5

Built-in Sequence Predictors  (1)

Download the "English" built-in sequence predictor:

In[1]:=1
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https://wolfram.com/xid/05e4dew1xz-v5n1n
Out[1]=1

Obtain the log-probability of the given string:

In[2]:=2
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https://wolfram.com/xid/05e4dew1xz-r3uk4w
Out[2]=2

Options  (5)Common values & functionality for each option

FeatureExtractor  (2)

Preprocess the training text to predict on words rather than at the character level:

In[1]:=1
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https://wolfram.com/xid/05e4dew1xz-p8j69j
Out[1]=1

Complete the preceding string with 10 consecutive words (spaces and punctuation marks are considered as words):

In[2]:=2
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https://wolfram.com/xid/05e4dew1xz-rqx153
Out[2]=2

Preprocess the training text to lowercase to obtain a better statistic with higher letter counts:

In[1]:=1
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https://wolfram.com/xid/05e4dew1xz-4z0cco
Out[1]=1

PerformanceGoal  (2)

Train a classifier with an emphasis on the resulting model memory footprint:

In[1]:=1
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https://wolfram.com/xid/05e4dew1xz-cm5rc6
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/05e4dew1xz-n8wuhu
Out[2]=2

Compare with the automatically generated model size:

In[3]:=3
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https://wolfram.com/xid/05e4dew1xz-4tbp3n
Out[3]=3

Tune the computation time and precision when exploring the full sequence probability space:

In[1]:=1
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https://wolfram.com/xid/05e4dew1xz-vlrrop
Out[1]=1

Favor fast and approximated exploration:

In[2]:=2
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https://wolfram.com/xid/05e4dew1xz-lhupqt
Out[2]=2

Favor more in-depth exploration taking longer computation time:

In[3]:=3
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https://wolfram.com/xid/05e4dew1xz-xhc8jh
Out[3]=3

Compare the results:

In[4]:=4
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https://wolfram.com/xid/05e4dew1xz-vqh6zu
Out[4]=4

Method  (1)

Specify a memory size of 3 for the Markov process trained on the training subsequences:

In[1]:=1
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https://wolfram.com/xid/05e4dew1xz-2nf7iq
Out[1]=1

Possible Issues  (1)Common pitfalls and unexpected behavior

An empty list is parsed as the list with no sequences inside and will return an empty list:

In[1]:=1
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https://wolfram.com/xid/05e4dew1xz-tjzlqh
Out[1]=1

To obtain the most likely next element completing an empty sequence, nest it in a second list for disambiguation:

In[2]:=2
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https://wolfram.com/xid/05e4dew1xz-v31l1l
Out[2]=2
Wolfram Research (2017), SequencePredict, Wolfram Language function, https://reference.wolfram.com/language/ref/SequencePredict.html (updated 2017).
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Wolfram Research (2017), SequencePredict, Wolfram Language function, https://reference.wolfram.com/language/ref/SequencePredict.html (updated 2017).

Text

Wolfram Research (2017), SequencePredict, Wolfram Language function, https://reference.wolfram.com/language/ref/SequencePredict.html (updated 2017).

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Wolfram Research (2017), SequencePredict, Wolfram Language function, https://reference.wolfram.com/language/ref/SequencePredict.html (updated 2017).

CMS

Wolfram Language. 2017. "SequencePredict." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2017. https://reference.wolfram.com/language/ref/SequencePredict.html.

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Wolfram Language. 2017. "SequencePredict." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2017. https://reference.wolfram.com/language/ref/SequencePredict.html.

APA

Wolfram Language. (2017). SequencePredict. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/SequencePredict.html

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Wolfram Language. (2017). SequencePredict. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/SequencePredict.html

BibTeX

@misc{reference.wolfram_2025_sequencepredict, author="Wolfram Research", title="{SequencePredict}", year="2017", howpublished="\url{https://reference.wolfram.com/language/ref/SequencePredict.html}", note=[Accessed: 25-March-2025 ]}

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@misc{reference.wolfram_2025_sequencepredict, author="Wolfram Research", title="{SequencePredict}", year="2017", howpublished="\url{https://reference.wolfram.com/language/ref/SequencePredict.html}", note=[Accessed: 25-March-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_sequencepredict, organization={Wolfram Research}, title={SequencePredict}, year={2017}, url={https://reference.wolfram.com/language/ref/SequencePredict.html}, note=[Accessed: 25-March-2025 ]}

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@online{reference.wolfram_2025_sequencepredict, organization={Wolfram Research}, title={SequencePredict}, year={2017}, url={https://reference.wolfram.com/language/ref/SequencePredict.html}, note=[Accessed: 25-March-2025 ]}