Lecture 2: Receiver-operating characteristics

Neurons act as if they were performing reinforcement learning.

Neural Encoding

How does the brain encode the sensory stimuli?

from Stimulus: $s$ to ⟶ Response: $r$

⟹ We try to guess $P(r \mid s)$

⟶ but: it’s a hard problem

so instead, we compute backward probability:

from $r$ to ⟶ $p(s \mid r)$

Psychophysical threshold curves: experiences with light flashes ⟹ how the stimulus relates to the behavior

Based on the output of the cell, what would an ideal observer decide?

  • $p(r \mid -)$: no flash
  • $p(r \mid +)$: flash

from histogram distributions

There are two types of wrong answers: false positives and false negatives (miss)

Then: we identify a discrimination threshold to separate the distributions

Sometimes:

  • you want a tight threshold (to absolutely avoid misses (to don’t want to miss the presence of a tiger!))

  • you want a loose threshold (to avoid false positives (to don’t want to begin the race in advance not to get disqualified!))

Then you can plot the evolution of the threshold: receiver-operating characteristics

Motion discrimination task

Have a monkey try to guess where a bunch of moving points is heading: to the right or to the left?

Neurons in area V5 have a space receptive field

Weird paradox: if we can tell what the monkey will do, what do the other neurons do?

Even more surprising: a single neuron can perform better than the monkey itself!

Hemodynamics

How neural activities encode the link between stimulus and behavioral response?

Can we understand what happens between neural responses and behavior?

$r$ ⟶ $p(\underbrace{a}_{\text{action}} \mid r)$

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