# Predicting The Future Of Discrete Sequences From Fractal Representations Of The Past

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### UNIVERSITY OF TOKYO

[4] P. Tino and G. Dorffner, Predicting the future of discrete sequences from fractal representations of the past, Machine Learning, 45(2), pp. 187-218, 2001. [5] R. G. Krishnan, D. Liang, and M. D. Hoffman, On the challenges of learning with inference networks on sparse,

### arXiv:1702.08565v1 [cond-mat.stat-mech] 27 Feb 2017

mined by the fractal dimensions of a process mixed-state distribution. These results, in turn, show how widely-used nite-order Markov models can fail as predictors and that mixed-state predictive features o er a substantial improvement. PACS numbers: 02.50.-r 89.70.+c 05.45.Tp 02.50.Ga

### Reservoir Computing Approaches - e-learning

Fractal Prediction Machines P. Tino, G. Dorffner (2001) Contractive Iterated Function Systems Fractal Analysis 12 Tino, P., Dor®ner, G.: Predicting the future of discrete sequences from fractal representations of the past. Machine Learning 45 (2001) 187-218

### Trajectory Indexing Using Movement Constraints*

5/4/2004 are typically represented as trajectories, sequences of connected line segments. In certain cases, movement is restricted; specifically, in this paper, we aim at exploiting that movements occur in transportation networks to reduce the dimensionality of the data. Briefly, the idea is to reduce movements to occur in one spatial dimen-sion.

### Complexity Sciences Center and Physics Department, arXiv

predict the future using information from the past. At root, a prediction is probabilistic, speciﬁed by a distri-bution of possible futures → X given a particular past ←−x: Pr(→ X ←−x). At a minimum, a good predictor needs to capture all of the information I shared between past and future: E = I[←− X; → X] the process s excess entropy [16,

### Prediction, Retrodiction, and the Amount of Information

Our goal is also simply stated: We wish to predict the future using information from the past. At root, a prediction is probabilistic, speciﬁed by a distribution of possible futures −→ X given a particular past ←−x:Pr(−→ X ←−x) At a minimum, a good predictor needs to capture all of the information I shared between the past and future: E =I

### Reservoir Computing Methods - unipi.it

Fractal Prediction Machines}P. Tino, G. Dorffner(2001)} Contractive Iterated Function Systems} Fractal Analysis 8 Tino, P., Dor®ner, G.: Predicting the future of discrete sequences from fractal representations of the past. Machine Learning 45 (2001) 187-218