Artificial Intelligence Projects

Artificial Intelligence is a growing domain, where every day new ideas appear and new projects are being built for every day use.

M.sc. eng. Eugen Hristev is the owner of the Artificial Intelligence Portal here, having graduated from the Master of Artificial Intelligence at Polytechnic University of Bucharest, with an Artificial Intelligence master thesis developed in collaboration with the Master of Artificial Intelligence at Polytechnic University of Catalunya, Spain.

Interested persons or companies in having a partner in research or development artificial intelligence projects please send your suggestions to eugenhristev [at] gmail [dot] com.

The owner of this website publicly expresses his interest in collaboration in the field of artificial intelligence, for short or long term, in developing or research activity.

NARX (Nonlinear AutoRegressive with eXogenous inputs) with neural networks

NARX (Nonlinear AutoRegressive with eXogenous inputs) is a model for time series forecasting. It can be modeled with Neural Networks.

The main idea it uses is the following: create an architecture that feeds three types of inputs to the learning algorithm: the past input values of the time series, the past predicted values by the model itself, and exogenous variables - a different time series that indirectly affects the time series we want to predict ( there can be more ).

All the inputs are being fed to a simple neural network architecture that is based on BPTT ( back propagation through time ) and TDNN (time delay neural networks ).

I started working on this subject on my master thesis at Universitat Polytecnica de Catalunya, Barcelona, Spain.

You can visit my project on Sourceforge.

Most important articles about NARX:

T. Lin, B. G. Horne, P. Tino, and C. L. Giles, “Learning long-term dependencies in NARX
recurrent neural networks.,” IEEE transactions on neural networks / a publication of the
IEEE Neural Networks Council, vol. 7, no. 6, pp. 1329-38, Jan. 1996.

H. T. Siegelmann, B. G. Horne, and C. L. Giles, “Computational capabilities of recurrent NARX
neural networks.,” IEEE transactions on systems, man, and cybernetics. Part B,
Cybernetics : a publication of the IEEE Systems, Man, and Cybernetics Society, vol. 27, no.
2, pp. 208-15, Jan. 1997.

J. Menezesjr and G. Barreto, “Long-term time series prediction with the NARX network: An
empirical evaluation,” Neurocomputing, vol. 71, no. 16-18, pp. 3335-3343, Oct. 2008.

E. Diaconescu, “The use of NARX neural networks to predict chaotic time series,” WSEAS
Transactions on Computer Research, vol. 3, no. 3, pp. 182–191, 2008.

Self organizing systems Part 1

A self organizing system is normally a multi-agent system where every agent does a specific action and a structure or pattern appears at the system level, without any specific global action by every agent.

Every agent will perform a specific action, usually each will have the same set of actions, and by doing so, a special global action is performed. This is called the emergent property of the self organizing system.

Let''s give a simple example: self organizing maps. Given a map of pixels, each with a color raging 1-255, which is initially quite indefinite in a shape, can be reorganized by a self organizing agents in order to find parts of the map which have a specific color dominance.

The Kohonen algorithm works in the following way: every agent will randomly pick a certain radius area of the map, and then choose the winning pixel, which is the pixel with the color closest to the area average. Then all the pixels are updated with a certain fixed percentage in order to get closer to the winning pixel.

The radius decreases in time, allowing smoother modifications.

In the end the system will emerge into an organized maps, with colored areas according to the most dominant color of that specific area.

We can observe that after agents that initially did a simple job like modifying colors in a slight matter, the system emerges into a different system having a specific pattern/structure/property, which is organization, in our case delimiting portions of the map having dominant colors.

 

Agent equilibrium

Let''s say we have 2 agents running in a world, each with a set of possible actions ( common for each agent ). Each agent can pick one of the actions ( strategies ) at a time in one round. Depending on his action and the action of the other agent, a reward is given, different for each agent. We can summarize this in the following table:

Reward Action 1 Action 2
Action 1 3, 3 5, 0
Action 2 0, 5 5, 5

For example if Agent 1 and Agent 2 both pick Action 1 then their rewards are respectively 3 and 3.

From this matrix we can see the following : If both agents use Action 2 then they have maximum reward. If the agents choose Action 1, then they have a good reward but not the best. If they choose differently, one of them maximizes its reward but the other has a zero one.

In this situation we call the pair 5,5 the Nash equilibrium pair because if any of the agents change their strategy independently they cannot get a better reward.

The situation 3,3 is Pareto Efficient because any change of strategy could make an agent go better but could make another agent worse.

The social welfare is the sum of the rewards for a given situation. For example the social welfare for Action 2, Action 2 is 10, which is the biggest value for total received reward.

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