Chaotic Time Series Prediction: Run for the Horizon

Vasilii Gromov

International Conference on Software Testing, Machine Learning and Complex Process Analysis (TMPA-2019)
7-9 November 2019, Tbilisi

Video: https://youtu.be/Rh8_sYRr3zA

TMPA Conference website https://tmpaconf.org/
TMPA Conference on Facebook https://www.facebook.com/groups/tmpaconf/

Transcript

1. CHAOTIC TIME SERIES PREDICTION:
   RUN FOR THE HORIZON
   Vasilii A. Gromov
   School of Data Analysis and Artificial Intelligence
   Faculty of Computer Science
   National Research University Higher School of Economics,
   Moscow, Russian Federation
   

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2. -Mobile health (mhealth): How to identify an oncoming heart attack in good
   time?
   EXAMPLES OF CHAOTIC TIME SERIES
   2
   - Smart city: How to balance electricity supply and demand for a city, a
   region, a country?
   

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3. EXAMPLES OF CHAOTIC TIME SERIES
   3
   - Trade systems: How to forecast rates of a national currency, stocks,
   and gold prices?
   - Social media marketing: How to predict explosive growth of popularity for
   social network topic?
   

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4. EXAMPLES OF CHAOTIC TIME SERIES
   4
   - Spot the bot: How to identify bots in social media?
   - Geographic information systems (GIS): How to forecast weather?
   

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5. Emotional paths
   (sentiment analysis)
   1) Each word is
   mapped into its
   sentiment
   characteristics
   2) Average them over
   a sentence
   3) Construct a series,
   which is a sequence
   of such averaged
   characteristics
   Vocabulary
   EXAMPLES OF CHAOTIC TIME SERIES
   - Zoili’s measure for interpreters: How to compare translations of literature
   pieces?
   5
   

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6. Semantic paths
   SVD
   6
   1. Build co-occurrence matrix
   2. Perform SVD decomposition
   3. Map each word into vector
   4. Examine a multi-
   dimensional time series,
   thus constructed
   

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7. Emotional paths
   for original
   pieces and their
   translations
   Charles Dickens
   A Christmas Carol
   (left column)
   David Copperfield
   (right column)
   7
   

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8. PROBLEM STATEMENT
   8
   

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9. PREDICTIVE CLUSTERING
   9
   - Lack of unified prediction model
   - A set of motifs (typical sequences, sub-models)
   - The use of set of similar time series rather than a single
   one
   - Prediction using non-successive observations:
   patterns
   - Non-predictable points
   - Multiple predictions for a single point
   - Quality assessment
   

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10. MOTIFS:
    SET OF TYPICAL SEQUENCES
    10
    

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11. 11
    PREDICTION USING NON-SUCCESSIVE
    OBSERVATIONS: PATTERNS
    

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12. 12 MULTIPLE PREDICTIONS FOR A
    SINGLE POINTS AND
    NON-PREDICTABLE POINTS
    

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13. 13
    QUALITY ASSESSMENT: ESTIMATE
    CLUSTERS, USING THE VALIDATION SET
    A prediction error vs. the
    percentage of dropped-
    out clusters
    

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14. 14
    MULTI-STEP (AHEAD) PREDICTION:
    JUMP FROM TUSSOCK TO TUSSOCK
    For multi-step prediction, we employ a prediction based upon already
    predicted values for intermediate observations
    The more steps ahead we would like to predict, the more is the
    number of non-predictable points , but we succeeded in controlling
    the prediction error for all other points
    The highest Lyapunov exponent and the prediction horizon, which
    depend on it, is an averaged characteristics: for many time series
    sections, the error growth rate appears to be exponential as it
    should be, but with significantly smaller exponent
    

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15. 15
    ATTEMPTS TO
    REVEAL THE
    TUSSOCKS
    Coloured series: points with
    lots of similar prediction
    values, that is points with
    large prediction probability
    

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16. 16 PREDICTION OF CHAOTIC TIME SERIES.
    EXAMPLES
    Blue points denotes original series, red points the respective
    predicted values, green circles non-predictable points.
    Model chaotic series (Lorenz)
    Real-world chaotic series (electricity
    consumption) – multistep ahead
    Plant to produce technical analysis figures:
    predictive clustering algorithm found
    figure ‘crab’, which are popular among
    hashtag popularity prediction community
    (Twitter):
    

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17. The highest
    Lyapunov
    exponents
    David
    Copperfield
    A Christmas
    Carrol
    Anna
    Karenina War and Piece
    Piece
    Translation
    (1)
    Translation
    (2)
    Translation
    (3)
    War and
    Piece
    War and Piece War and Piece War and Piece
    Piece
    Translation
    (1)
    Translation
    (2)
    Translation
    (3)
    The highest Lyapunov exponents for emotional series
    The highest Lyapunov exponents for 10-dimensional semantic series
    17
    

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18. 18
    Gromov V.A. Chaotic time series prediction and clustering methods / V.A.
    Gromov, E.A. Borisenko // Neural Computing and Applications. –
    2015. – №. 2. – P. 307315
    Gromov V.A. Precocious identification of popular topics on Twitter with
    the employment of predictive clustering / Gromov V.A., Konev A.S.
    // Neural Computing and Applications. – 2017. – Vol. 28(11). – P.
    3317-3322. Gromov V.A. A Language as a Self-Organized Critical
    System / Gromov V.A., Migrina A.M. // Complexity. – 2017. – Vol.
    2017(Article ID 9212538). – P. 1-7.
    Obodan N.I. Rapid identification of pre-buckling states: A case of
    cylindrical shell / Obodan N.I., Adlucky V.J., Gromov V.A. // Thin-
    Walled Structures. – 2018. – Vol. 124. – P. 449-457.
    Gromov V.A. Relation Tensors for Chaotic Time Series: between Hidden
    Markov Models and Deep Learning / Gromov V.A., Necheporenko
    A.I. (in press)
    

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