6-Probabilistic Inference

1. Computational Theory - defines the problem

   whats the goal of computation?

   why is it appropiate?

   what is the logic of strategy?

2. Representation and Algorithm - steps to solve the problem

   How can it be implemented?

   What is represenation for input and output?

   What is the algorithm for transformation?

3. Hardware Implementation - realizes algorithm

   How can implementaiton and algorithm be realized?

—> provide framework to analyze brain function at different abstraction levels

brain integrates prior expectations (experience) and likelihoods (current sensory evidence) to estimate most probable interpretation of environment

e.g. contextial information (shadows and patterns) with prior knowledge to perceive same physical color (A and B) differently

sensory data: brightness

prior knowledge: shadows dim obejcts

when sensory input can be interpreted in multiple ways, leading to uncertainty

• Sound Source Position in Neurons

  single neurons use interaural time differences (ITD) to localize sound

• Heading Direction in Flies

  ellipsoid body encodes heading direction based on sensory input, integrating environmental cues probabilistically

—> neural systems across species employ inference mechanisms to process sensory information for adaptive behavior

Perceptual priors are shaped by regularities in environment

e.g. visual perception: humans perceive more likely continous patterns due to prior experiences

left: random, unconnected segments

right: emergent structure, influenced by perceptual priors to infer patterns and meanings

rely on probabilistic internal models to make motor control decisions

—> integrating prior knowledge with sensory feedback

e.g. experiment: participants aim to align cursor with a target despite a lateral shift in cursor path (Verschiebung im Pfad)

prior: expected shift based on previous experience

likelhood: sensory feedback estimate of shift during the task

posterior: integration of prior and likelihood, refines final estimate of shift for accurate motor control

by processing sensory information in a structured, layered manner

1. Sensory Input Processing: visual inputs are detected and encoded in lower-level neurons (edges or orientation)

2. Integratoin of Information: higher-level neurons forming more abstract representations (e.g patterns and shapes)

3. Prediction and Feedback: hierachical structure allows predictions made at higher levels, then sent back to lower levels as feedback

4. Bayesian Framework: each level combines sensory evidence with prior knowledge to generate posterior belief about environment

—> brain’s ability to interpret complex stimuli in probabilistic manner, utilizing bottom-up data and top-down expectations

Sound Source Localization

brain infers position of sound source using

• interaural time differences (ITD)

• interaural level difference (ILD)

1. Sensory Cues: auditory system measures slight differences in time (ITD) and intensity (ILD) of arriving sound

2. Noise in System: due environmental and neural noise —> cues not perfectly reliable

3. Inference: brain integrates cues probabilistically, combining with prior knowledge about typical sound sources

4. Solution: brain estimates most probable location of sound source

Bayesian inference

integrates prior knowledge (priors) with sensory evidence (likelihood) to compute posterior belief

widely used for tasks like:

• Perception (visual illusions based on priors about lighting and shadows)

• Motor control (adjusting movements based in prior expectations of errors)

• Decision-making (evaluating uncertain outcomes in probabilistic manner)

—> handles uncertainty efficientyl

• complexity of real-world environments

• lack of complete understanding of neural mechanisms

• dificulty in measuring and modeling brain processes at necessary levels of detail