Two novel methods for Time Series Prediction based on GEP (Gene Expression Programming). The main... more Two novel methods for Time Series Prediction based on GEP (Gene Expression Programming). The main contributions include: (1) GEP-Sliding Window Prediction Method (GEP-SWPM) to mine the relationship between future and historical data directly. (2) GEP-Differential Equation Prediction Method (GEP-DEPM) to mine ordinary differential equations from training data, and predict future trends based on specified initial conditions. (3) A brand new equation mining method, called Differential by Microscope Interpolation (DMI) that boosts the efficiency of our methods. (4) A new, simple and effective GEP-constants generation method called Meta-Constants (MC) is proposed. (5) It is proved that a minimum expression discovered by GEP-MC method with error not exceeding δ/2 uses at most log3(2L/δ) operators and the problem to find δ-accurate expression with fewer operators is NP-hard. Extensive experiments on real data sets for sun spot prediction show that the performance of the new method is 20-900 times higher than existing algorithms.
We present the existence of 2 n stable stationary solutions for a general n-dimensional delayed n... more We present the existence of 2 n stable stationary solutions for a general n-dimensional delayed neural networks with several classes of activation functions. The theory is obtained through formulating parameter conditions motivated by a geometrical observation. Positively invariant regions for the flows generated by the system and basins of attraction for these stationary solutions are established. The theory is also extended to the existence of 2 n limit cycles for the n-dimensional delayed neural networks with time-periodic inputs. It is further confirmed that quasiconvergence is generic for the networks through justifying the strongly order preserving property as the self-feedback time lags are small for the neurons with negative self-connection weights. Our theory on existence of multiple equilibria is then incorporated into this quasiconvergence for the network. Four numerical simulations are presented to illustrate our theory.
Two novel methods for Time Series Prediction based on GEP (Gene Expression Programming). The main... more Two novel methods for Time Series Prediction based on GEP (Gene Expression Programming). The main contributions include: (1) GEP-Sliding Window Prediction Method (GEP-SWPM) to mine the relationship between future and historical data directly. (2) GEP-Differential Equation Prediction Method (GEP-DEPM) to mine ordinary differential equations from training data, and predict future trends based on specified initial conditions. (3) A brand new equation mining method, called Differential by Microscope Interpolation (DMI) that boosts the efficiency of our methods. (4) A new, simple and effective GEP-constants generation method called Meta-Constants (MC) is proposed. (5) It is proved that a minimum expression discovered by GEP-MC method with error not exceeding δ/2 uses at most log3(2L/δ) operators and the problem to find δ-accurate expression with fewer operators is NP-hard. Extensive experiments on real data sets for sun spot prediction show that the performance of the new method is 20-900 times higher than existing algorithms.
We present the existence of 2 n stable stationary solutions for a general n-dimensional delayed n... more We present the existence of 2 n stable stationary solutions for a general n-dimensional delayed neural networks with several classes of activation functions. The theory is obtained through formulating parameter conditions motivated by a geometrical observation. Positively invariant regions for the flows generated by the system and basins of attraction for these stationary solutions are established. The theory is also extended to the existence of 2 n limit cycles for the n-dimensional delayed neural networks with time-periodic inputs. It is further confirmed that quasiconvergence is generic for the networks through justifying the strongly order preserving property as the self-feedback time lags are small for the neurons with negative self-connection weights. Our theory on existence of multiple equilibria is then incorporated into this quasiconvergence for the network. Four numerical simulations are presented to illustrate our theory.
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