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simulations.lisp
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(in-package :kalman-td)
(defun simulate (name) (funcall (symbolicate 'simulate '- name)))
;; A basic demonstration, without using simulations-helper.lisp
(defun simulate-latent-inhibition ()
(let ((*array-element-type* 'single-float))
(let ((control-ktd (default-kalman-td 1))
(experimental-ktd (default-kalman-td 1)))
(loop :for i :from 1 :below 20
:with preex-stimulus
:= (asarray (loop :repeat 10
:appending (list (asarray '((1))) (asarray '((0))))))
:with preex-reward
:= (asarray (loop :repeat 10
:appending (list (asarray '((0))) (asarray '((0))))))
:for expected-reward
:= (predict-reward experimental-ktd
(aref preex-stimulus i)
(aref preex-stimulus (1- i)))
:do (update experimental-ktd
expected-reward
(aref preex-reward i)
(aref preex-stimulus i)
(aref preex-stimulus (1- i))))
(iter (for i from 1 below 20)
(with exp-stimulus = (asarray (loop :repeat 10
:appending (list (asarray '((1))) (asarray '((0)))))))
(with exp-reward = (asarray (loop :repeat 10
:appending (list (asarray '((0))) (asarray '((1)))))))
(for exp-expected-reward = (predict-reward experimental-ktd
(aref exp-stimulus i)
(aref exp-stimulus (1- i))))
(update experimental-ktd
exp-expected-reward
(aref exp-reward i)
(aref exp-stimulus i)
(aref exp-stimulus (1- i)))
(collect exp-expected-reward into exp-expected-rewards)
(for ctrl-expected-reward = (predict-reward control-ktd
(aref exp-stimulus i)
(aref exp-stimulus (1- i))))
(update control-ktd
ctrl-expected-reward
(aref exp-reward i)
(aref exp-stimulus i)
(aref exp-stimulus (1- i)))
(collect ctrl-expected-reward into ctrl-expected-rewards)
(finally
(setq exp-expected-rewards (asarray exp-expected-rewards))
(setq ctrl-expected-rewards (asarray ctrl-expected-rewards))
(plt:plot (alexandria:iota 10 :start 1)
(as-cl-array (aref exp-expected-rewards '(0 :step 2)))
:label "Pre Group")
(plt:plot (alexandria:iota 10 :start 1)
(as-cl-array (aref ctrl-expected-rewards '(0 :step 2)))
:label "No-pre Group")
(plt:title :label "Latent Inhibition aka Preexposure Effect")
(plt:xlabel :xlabel "Stimulus")
(plt:ylabel :ylabel "Expected Reward")
(plt:legend)
(plt:show)
(print (list exp-expected-rewards
ctrl-expected-rewards)))))))
;;; All the functions this point forward rely on simulations-helper.lisp
(defun simulate-latent-inhibition ()
"
Phase 1: X -> - for experimental, none for control
Phase 2: X -> + for both
"
(declare (optimize debug))
(let* ((control-ktd (default-kalman-td 1))
(experimental-ktd (default-kalman-td 1)))
(multiple-value-bind (preex-stimuli preex-rewards)
(prepare-stimuli-rewards '(a) 10 '(a > -))
(process-stimuli-rewards experimental-ktd preex-stimuli preex-rewards))
(multiple-value-bind (exp-stimuli exp-rewards)
(prepare-stimuli-rewards '(a) 10 '(a > +))
(let ((ctrl-expected-rewards
(process-stimuli-rewards experimental-ktd exp-stimuli exp-rewards
:callback (lambda (ktd exp-reward)
(declare (ignore ktd))
exp-reward)))
(exp-expected-rewards
(process-stimuli-rewards control-ktd exp-stimuli exp-rewards
:callback (lambda (ktd exp-reward)
(declare (ignore ktd))
exp-reward))))
(setq exp-expected-rewards (asarray exp-expected-rewards))
(setq ctrl-expected-rewards (asarray ctrl-expected-rewards))
(plt:plot (alexandria:iota 10 :start 1)
(as-cl-array (aref exp-expected-rewards '(0 :step 2)))
:label "Pre Group")
(plt:plot (alexandria:iota 10 :start 1)
(as-cl-array (aref ctrl-expected-rewards '(0 :step 2)))
:label "No-pre Group")
(plt:title :label "Latent Inhibition aka Preexposure Effect")
(plt:xlabel :xlabel "Stimulus")
(plt:ylabel :ylabel "Expected Reward")
(plt:legend)
(plt:show)
(print (list exp-expected-rewards
ctrl-expected-rewards))))))
(defun simulate-overshadowing-and-unovershadowing ()
(bind ((*array-element-type* 'single-float)
(control-ktd (default-kalman-td 2))
(experimental-ktd (default-kalman-td 2))
((:values pre-stimuli pre-rewards) (prepare-stimuli-rewards '(a b) 10 '(a > -)))
((:values p1-stimuli p1-rewards) (prepare-stimuli-rewards '(a b) 10 '(a b > +)))
((:values test-stimuli test-rewards) (prepare-stimuli-rewards '(a b) 01 '(b > +))))
(process-stimuli-rewards experimental-ktd pre-stimuli pre-rewards)
(process-stimuli-rewards experimental-ktd p1-stimuli p1-rewards)
(process-stimuli-rewards control-ktd p1-stimuli p1-rewards)
(bind ((ctrl-test-reward (nth 0 (process-stimuli-rewards control-ktd test-stimuli test-rewards
:callback (lambda (ktd exp-reward)
(declare (ignore ktd))
exp-reward))))
(exp-test-reward (nth 0 (process-stimuli-rewards experimental-ktd test-stimuli test-rewards
:callback (lambda (ktd exp-reward)
(declare (ignore ktd))
exp-reward)))))
(plt:clf)
(plt:bar :x '(1 2)
:height (list ctrl-test-reward exp-test-reward))
(plt:xticks :ticks '(1 2)
:labels '("overshadowed" "unovershadowed"))
(plt:ylabel :ylabel "Reward Expectation")
(plt:title :label "Reversal of overshadowing")
(plt:show))))
(defun simulate-forward-blocking ()
"
Phase 1: A -> +
Phase 2: AB -> +
Phase 3: A -> - (only for unblocking group)
Test : B -> ?
"
(bind ((experimental-ktd (default-kalman-td 2))
(control-ktd (default-kalman-td 2))
((:values p1-stimuli p1-rewards) (prepare-stimuli-rewards '(a b) 10 '(a > +)))
((:values p2-stimuli p2-rewards) (prepare-stimuli-rewards '(a b) 10 '(a b > +)))
((:values p3-stimuli p3-rewards) (prepare-stimuli-rewards '(a b) 10 '(a > -)))
((:values test-stimuli test-rewards) (prepare-stimuli-rewards '(a b) 01 '(b > -))))
(process-stimuli-rewards experimental-ktd p1-stimuli p1-rewards)
(process-stimuli-rewards control-ktd p1-stimuli p1-rewards)
(process-stimuli-rewards experimental-ktd p2-stimuli p2-rewards)
(process-stimuli-rewards control-ktd p2-stimuli p2-rewards)
(process-stimuli-rewards control-ktd p3-stimuli p3-rewards)
(bind ((exp-test-reward (nth 0 (process-stimuli-rewards experimental-ktd test-stimuli test-rewards
:callback (lambda (ktd exp-reward)
(declare (ignore ktd))
exp-reward))))
(ctrl-test-reward (nth 0 (process-stimuli-rewards control-ktd test-stimuli test-rewards
:callback (lambda (ktd exp-reward)
(declare (ignore ktd))
exp-reward)))))
(plt:clf)
(plt:bar :x '(1 2) :height (list exp-test-reward ctrl-test-reward))
(plt:xticks :ticks '(1 2) :labels '("Block" "No-Block"))
(plt:ylabel :ylabel "Value")
(plt:title :label "Forward Blocking")
(plt:show))))
(defun simulate-overexpectation ()
"
Phase 1: A -> + / B -> +
Phase 2: AB -> +
Phase 3: A -> - (only experimental group)
Test : B -> ?
"
(bind ((experimental-ktd (default-kalman-td 2))
(control-ktd (default-kalman-td 2))
((:values p1-stimuli p1-rewards) (prepare-stimuli-rewards '(a b) 10 '(a > + / b > +)))
((:values p2-stimuli p2-rewards) (prepare-stimuli-rewards '(a b) 10 '(a b > +)))
((:values p3-stimuli p3-rewards) (prepare-stimuli-rewards '(a b) 10 '(a > -)))
((:values test-stimuli test-rewards) (prepare-stimuli-rewards '(a b) 01 '(b > -))))
(process-stimuli-rewards experimental-ktd p1-stimuli p1-rewards)
(process-stimuli-rewards control-ktd p1-stimuli p1-rewards)
(process-stimuli-rewards experimental-ktd p2-stimuli p2-rewards)
(process-stimuli-rewards control-ktd p2-stimuli p2-rewards)
(process-stimuli-rewards experimental-ktd p3-stimuli p3-rewards)
(bind ((exp-test-reward (nth 0 (process-stimuli-rewards experimental-ktd test-stimuli test-rewards
:callback (lambda (ktd exp-reward)
(declare (ignore ktd))
exp-reward))))
(ctrl-test-reward (nth 0 (process-stimuli-rewards control-ktd test-stimuli test-rewards
:callback (lambda (ktd exp-reward)
(declare (ignore ktd))
exp-reward)))))
(plt:clf)
(plt:bar :x '(1 2) :height (list ctrl-test-reward exp-test-reward))
(plt:xticks :ticks '(1 2) :labels '("overexpectation" "unoverexpectation"))
(plt:ylabel :ylabel "Reward Expectation")
(plt:title :label "Reversal of overexpectation")
(plt:show))))
(defun simulate-conditioned-inhibition ()
"
Phase 1: A -> +
Phase 2: AB -> -
Phase 3: A -> - (only uninhibition group)
Test : B -> ?
"
(bind ((experimental-ktd (default-kalman-td 2))
(control-ktd (default-kalman-td 2))
((:values p1-stimuli p1-rewards) (prepare-stimuli-rewards '(a b) 10 '(a > +)))
((:values p2-stimuli p2-rewards) (prepare-stimuli-rewards '(a b) 10 '(a b > -)))
((:values p3-stimuli p3-rewards) (prepare-stimuli-rewards '(a b) 10 '(a > -)))
((:values test-stimuli test-rewards) (prepare-stimuli-rewards '(a b) 01 '(b > -))))
(process-stimuli-rewards control-ktd p1-stimuli p1-rewards)
(multiple-value-bind (posterior-variances kalman-gains)
(iter (for (variance gain) in
(process-stimuli-rewards experimental-ktd p1-stimuli p1-rewards
:callback (lambda (ktd expected-reward)
(declare (ignore expected-reward))
(list (aref (slot-value ktd
'weights-covariance)
0 0)
(aref (slot-value ktd 'old-kalman-gain)
0 0)))))
(collect variance into variances)
(collect gain into gains)
(finally (return (values variances gains))))
(plt:clf)
(plt:plot (iota 9 :start 1) (as-cl-array (aref (asarray posterior-variances) '(1 :step 2))))
(plt:xlabel :xlabel "Conditioning Trial")
(plt:ylabel :ylabel "Posterior Variance (A)")
(plt:title :label "Conditioned Inhibition")
(plt:show)
(plt:clf)
(plt:plot (iota 9 :start 1) (as-cl-array (aref (asarray kalman-gains) '(1 :step 2))))
(plt:xlabel :xlabel "Conditioning Trial")
(plt:ylabel :ylabel "Kalman Gain (A)")
(plt:title :label "Conditioned Inhibition")
(plt:show))
(process-stimuli-rewards experimental-ktd p2-stimuli p2-rewards)
(process-stimuli-rewards control-ktd p2-stimuli p2-rewards)
(process-stimuli-rewards control-ktd p3-stimuli p3-rewards)
(bind ((exp-test-reward (nth 0 (process-stimuli-rewards experimental-ktd test-stimuli test-rewards
:callback (lambda (ktd exp-reward)
(declare (ignore ktd))
exp-reward))))
(ctrl-test-reward (nth 0 (process-stimuli-rewards control-ktd test-stimuli test-rewards
:callback (lambda (ktd exp-reward)
(declare (ignore ktd))
exp-reward)))))
(plt:clf)
(plt:bar :x '(1 2) :height (list exp-test-reward ctrl-test-reward))
(plt:xticks :ticks '(1 2) :labels '("CI" "No-CI"))
(plt:ylabel :ylabel "Value")
(plt:title :label "Conditioned Inhibition")
(plt:show))))
(defun simulate-serial-compound-extinction ()
"
Phase 1: Z -> X -> - / X -> +
Phase 2: X -> - (only for experimental group)
Test : Z -> ?
"
(bind ((experimental-ktd (default-kalman-td 2))
(control-ktd (default-kalman-td 2))
((:values p1-stimuli p1-rewards) (prepare-stimuli-rewards '(z x) 10
'(z > x > - / x > +)))
((:values p2-stimuli p2-rewards) (prepare-stimuli-rewards '(z x) 10 '(x > -)))
((:values test-stimuli test-rewards) (prepare-stimuli-rewards '(z x) 01 '(z > -))))
(process-stimuli-rewards control-ktd p1-stimuli p1-rewards)
(process-stimuli-rewards experimental-ktd p1-stimuli p1-rewards)
(process-stimuli-rewards experimental-ktd p2-stimuli p2-rewards)
(bind ((exp-test-reward (nth 0 (process-stimuli-rewards experimental-ktd test-stimuli test-rewards
:callback (lambda (ktd exp-reward)
(declare (ignore ktd))
exp-reward))))
(ctrl-test-reward (nth 0 (process-stimuli-rewards control-ktd test-stimuli test-rewards
:callback (lambda (ktd exp-reward)
(declare (ignore ktd))
exp-reward)))))
(plt:clf)
(plt:bar :x '(1 2) :height (list exp-test-reward ctrl-test-reward))
(plt:xticks :ticks '(1 2) :labels '("Ext" "No-Ext"))
(plt:ylabel :ylabel "Value")
(plt:title :label "Second Order Extinction")
(plt:show))))
(defun simulate-overshadowing-and-second-order-conditioning ()
"
AX->+ /BY->+ ; A->- ; Z->X ; Z->?
AX->+ /BY->+ ; B->- ; Z->X ; Z->?
"
(declare (optimize debug))
(bind ((experimental-ktd (default-kalman-td 5))
(control-ktd (default-kalman-td 5))
((:values p1-stimuli p1-rewards) (prepare-stimuli-rewards '(a x b y z) 10
'(a x > + / b y > +)))
((:values p2a-stimuli p2a-rewards) (prepare-stimuli-rewards '(a x b y z) 10 '(a > -)))
((:values p2b-stimuli p2b-rewards) (prepare-stimuli-rewards '(a x b y z) 10 '(b > -)))
((:values p3-stimuli p3-rewards) (prepare-stimuli-rewards '(a x b y z) 10 '(z > x)))
((:values test-stimuli test-rewards) (prepare-stimuli-rewards '(a x b y z) 01 '(z > -))))
(process-stimuli-rewards control-ktd p1-stimuli p1-rewards)
(multiple-value-bind (covariances gains)
(iter (for (covariance gain)
in (process-stimuli-rewards experimental-ktd p1-stimuli p1-rewards
:callback
(lambda (ktd exp-reward)
(declare (ignore exp-reward))
(list (aref (slot-value ktd 'weights-covariance) 0 1)
(aref (slot-value ktd 'old-kalman-gain) 1 0)))))
(collect covariance into covariances)
(collect gain into gains)
(finally (return (values (asarray covariances) (asarray gains)))))
(plt:clf)
(plt:plot (iota 10 :start 1) (as-cl-array (aref covariances '(0 :step 4))))
(plt:ylabel :ylabel "Posterior Covariance (AX)")
(plt:xlabel :xlabel "Phase 1 Trial")
(plt:title :label "Overshadowing and Second Order Conditioning")
(plt:show)
(plt:clf)
(plt:plot (iota 10 :start 1) (as-cl-array (aref gains '(0 :step 4))))
(plt:ylabel :ylabel "Kalman Gain (X)")
(plt:xlabel :xlabel "Phase 1 Trial")
(plt:title :label "Overshadowing and Second Order Conditioning")
(plt:show))
(bind (((:values cov-ax kalman-gain-x-ctrl)
(iter (for (covariance gain)
in (process-stimuli-rewards control-ktd p2a-stimuli p2a-rewards
:callback
(lambda (ktd exp-reward)
(declare (ignore exp-reward))
(list (aref (slot-value ktd
'weights-covariance)
0 1)
(aref (slot-value ktd
'old-kalman-gain)
1 0)))))
(collect covariance into covariances)
(collect gain into gains)
(finally (return (values (asarray covariances) (asarray gains))))))
(kalman-gain-x-expt
(asarray
(process-stimuli-rewards experimental-ktd p2b-stimuli p2b-rewards
:callback (lambda (ktd exp-reward)
(declare (ignore exp-reward))
(aref (slot-value ktd 'old-kalman-gain) 1 0))))))
(plt:clf)
(plt:plot (iota 10 :start 1) (as-cl-array (aref cov-ax '(0 :step 2))))
(plt:ylabel :ylabel "Posterior Covariance (AX)")
(plt:xlabel :xlabel "Phase 2 Trial")
(plt:title :label "Overshadowing and Second Order Conditioning")
(plt:show)
(plt:clf)
(plt:plot (iota 10 :start 1)
(as-cl-array (aref kalman-gain-x-ctrl '(0 :step 2)))
:label "OV-A")
(plt:plot (iota 10 :start 1)
(as-cl-array (aref kalman-gain-x-expt '(0 :step 2)))
:label "OV-B")
(plt:ylabel :ylabel "Kalman Gain (X)")
(plt:xlabel :xlabel "Phase 2 Trial")
(plt:title :label "Overshadowing and Second Order Conditioning")
(plt:show))
(process-stimuli-rewards control-ktd p3-stimuli p3-rewards)
(process-stimuli-rewards experimental-ktd p3-stimuli p3-rewards)
(bind ((exp-test-reward (nth 0 (process-stimuli-rewards experimental-ktd test-stimuli test-rewards
:callback (lambda (ktd exp-reward)
(declare (ignore ktd))
exp-reward))))
(ctrl-test-reward (nth 0 (process-stimuli-rewards control-ktd test-stimuli test-rewards
:callback (lambda (ktd exp-reward)
(declare (ignore ktd))
exp-reward)))))
(plt:clf)
(plt:bar :x '(1 2) :height (list ctrl-test-reward exp-test-reward))
(plt:xticks :ticks '(1 2) :labels '("OV-A" "OV-B"))
(plt:ylabel :ylabel "Value")
(plt:title :label "Overshadowing and Second Order Conditioning")
(plt:show))))
(defun simulate-serial-compound-extinction ()
"
Phase 1: Z -> X -> +
Phase 2: X -> - (only for extinction group)
Test : Z -> ?
"
(bind ((experimental-ktd (default-kalman-td 2))
(control-ktd (default-kalman-td 2))
((:values p1-stimuli p1-rewards) (prepare-stimuli-rewards '(z x) 10 '(z > x > +)))
((:values p2-stimuli p2-rewards) (prepare-stimuli-rewards '(z x) 10 '(x > -)))
((:values test-stimuli test-rewards) (prepare-stimuli-rewards '(z x) 01 '(z > -))))
(process-stimuli-rewards control-ktd p1-stimuli p1-rewards)
(bind ((posterior-covariances
(cons 0 (process-stimuli-rewards experimental-ktd p1-stimuli p1-rewards
:callback (lambda (ktd expected-reward)
(declare (ignore expected-reward))
(aref (slot-value ktd
'weights-covariance)
0 1))))))
(plt:clf)
(plt:plot (iota 10 :start 1) (as-cl-array (aref (asarray posterior-covariances) '(0 :step 3))))
(plt:xlabel :xlabel "Conditioning Trial")
(plt:ylabel :ylabel "Posterior Covariance (ZX)")
(plt:title :label "Serial Compound Extinction")
(plt:show))
(process-stimuli-rewards experimental-ktd p2-stimuli p2-rewards)
(bind ((exp-test-reward (nth 0 (process-stimuli-rewards experimental-ktd test-stimuli test-rewards
:callback (lambda (ktd exp-reward)
(declare (ignore ktd))
exp-reward))))
(ctrl-test-reward (nth 0 (process-stimuli-rewards control-ktd test-stimuli test-rewards
:callback (lambda (ktd exp-reward)
(declare (ignore ktd))
exp-reward)))))
(plt:clf)
(plt:bar :x '(1 2) :height (list exp-test-reward ctrl-test-reward))
(plt:xticks :ticks '(1 2) :labels '("Ext" "No-Ext"))
(plt:ylabel :ylabel "Value")
(plt:title :label "Serial Compound Extinction")
(plt:show))))
(defun simulate-recovery-from-overshadowing ()
"
Phase 1: Z -> X -> + for experimental ; B -> Y -> + for control
Phase 2: Z -> - for experimental
Test: X -> ? for experimental; Y -> ? for control
"
(declare (optimize debug))
(bind ((control-ktd (default-kalman-td 4))
(experimental-ktd (default-kalman-td 4))
((:values p1e-stimuli p1e-rewards) (prepare-stimuli-rewards '(z x b y) 10 '(z > x > +)))
((:values p1c-stimuli p1c-rewards) (prepare-stimuli-rewards '(z x b y) 10 '(b > y > +)))
((:values p2-stimuli p2-rewards) (prepare-stimuli-rewards '(z x b y) 10 '(z > -)))
((:values test-exp-stimuli) (prepare-stimuli-rewards '(z x b y) 01 '(x > -)))
((:values test-ctrl-stimuli) (prepare-stimuli-rewards '(z x b y) 01 '(y > -))))
(process-stimuli-rewards control-ktd p1c-stimuli p1c-rewards)
(process-stimuli-rewards experimental-ktd p1e-stimuli p1e-rewards)
(process-stimuli-rewards experimental-ktd p2-stimuli p2-rewards)
(bind ((exp-test-reward (predict-reward experimental-ktd
(aref test-exp-stimuli 1)
(aref test-exp-stimuli 0)))
(ctrl-test-reward (predict-reward control-ktd
(aref test-ctrl-stimuli 1)
(aref test-ctrl-stimuli 0))))
(plt:clf)
(plt:bar :x '(1 2)
:height (list exp-test-reward ctrl-test-reward))
(plt:xticks :ticks '(1 2) :labels '("X" "Y"))
(plt:ylabel :ylabel "Value")
(plt:title :label "Recovery from overshadowing")
(plt:show))))