Identification of probabilities.

Area of Science:

• Cognitive science
• Computational neuroscience
• Artificial intelligence

Background:

• Increasing interest in the brain's ability to build probabilistic models from sensory and linguistic input.
• Acknowledging practical challenges like limited data and computational resources.

Purpose of the Study:

• To investigate the fundamental possibility of inferring probabilistic models from data.
• To explore the theoretical underpinnings of how the brain learns from samples.

Main Methods:

• Utilizing the strong law of large numbers for independent and identically distributed (i.i.d.) samples.
• Applying Kolmogorov complexity theory for dependent sequences.
• Developing learning algorithms to identify probability distributions and typical sequences.

Main Results:

• Demonstrating that a broad class of probability distributions can be identified in the limit from finite samples.
• Proving that computable measures for typical sequences can be identified for broad classes of dependent sequences.
• Analyzing predictions associated with these learning processes.

Conclusions:

• The inference of probabilistic models from data is possible in principle, even with computational constraints.
• These findings have significant implications for understanding learning in psychology, neuroscience, and artificial intelligence, including language acquisition.