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

-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?

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?

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

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

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

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

PROBLEM STATEMENT 8

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

MOTIFS: SET OF TYPICAL SEQUENCES 10

11 PREDICTION USING NON-SUCCESSIVE OBSERVATIONS: PATTERNS

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

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

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

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

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):

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

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)