A unifying computational framework for teaching and active learning - - PowerPoint PPT Presentation

A unifying computational framework for teaching and active learning

Scott Cheng-Hsin Yang, Wai Keen Vong, Yue Yu & Patrick Shafto

World Learner

Active learning

Teacher

Teaching

World Learner

Self as teacher

Self-teaching

World Learner

World: h* Learner

Active learning

PL(x) x y PL(h|x,y) intervene

• bserve

consequence update belief

h1 h2 h3 h4 h1 h2 h3 h4 step 0 step 1 h1 h2 h3 h4 step 2

active learning strategy

World: h* Learner

Teaching

x,y PL(h|x,y)

Teacher

PT(x,y|h*) PL(x) Shafto et al. 2008, 2014 teaching strategy active learning strategy update belief show Teacher knows y and h*; learner does not.

PL(h|x, y) ∝ PT (x, y|h)PL(h) PT (x, y|h) ∝ PL(h|x, y)PT (x, y)

learner’s inference teacher’s selection

World: h* Learner

Teaching (marginalize out y)

x y PL(h|x,y)

Teacher

PT(x|h*) PL(x) Yang & Shafto 2017 teaching strategy (y marginalized) active learning strategy show

• bserve

consequence update belief

PL(h|x, y) ∝ P(y|x, h)PT (x|h)PL(h) PT (x|h) = X

y∈Y

PT (x, y|h)

learner’s inference teacher’s selection

World: h* Learner

Knowledgeability (marginalize out “h”)

Teacher

Shafto, Eaves, et al. 2012

h1 h2 h3 h4 g1 1/4 1/4 1/4 1/4 g2 1/4 1/4 1/4 1/4 g3 1/4 1/4 1/4 1/4 g4 1/4 1/4 1/4 1/4

δST(g|h) = PL(h): truth learner’s belief

PT (x|h) = X

g∈H

PT (x|g)δ(g|h) PT (x) = X

g∈H

PT (x|g)PL(g)

PT(x|h*)

h1 h2 h3 h4 g1 1 g2 1 g3 1 g4 1

δ(g|h): truth teacher’s belief teaching strategy (y marginalized) PL(x) active learning strategy PT(x) = PL(x) teaching strategy (y & h* marginalized) =

World: h* Learner

Self-teaching

PT(x) = PL(x) x y PL(h|x,y) self-teaching

PL(h|x, y) = P(y|x, h)PT (x)PL(h) P

h02H P (y|x, h0) PT (x)PL (h0)

PT (x) = X

g2H

PT (x|g)PL(g)

learner’s inference self-teacher’s selection

How is the Self-Teaching model different from the most common model of active learning objective —optimizing for expected information gain? Does the Self-Teaching model capture human’s active learning behavior?

• Meta-reasons about oneself

as the teacher

• Reasons about the world

EIG(x) = H(h) − X

y∈Y

PL(y|x)H(h|x, y)

Self-Teaching Expected information gain

PT (x) = X

g∈H

X

y∈Y

PL(g|x, y)PT (x, y) Z(g) PL(g)

• Uses only the rules of

probability

• Also uses entropy and

subtraction

• Hypothesis testing for

distinctive hypothesis

• Overall uncertainty reduction

Self-teaching: confirming distinctive h

A distinctive hypothesis is

• ne that is on average less

likely to be inferred if all interventions and

• bservations are equally

likely to occur.

Z(g) = X

y∈Y

X

x∈X

PL(g|x, y)PT (x, y)

Distinctiveness Learner’s posterior h1 h2 h3 h4 x1 y0 x1 y1 x2 y0 x2 y1 x3 y0 x3 y1 Self-teaching probability x2 x3

*

x1

PT (x) = X

g∈H

PT (x|g)PL(g) = X

g∈H

X

y∈Y

PL(g|x, y)PT (x, y)PL(g)Z(g)−1

How is the Self-Teaching model different from the most common model of active learning objective —optimizing for expected information gain? Does the Self-Teaching model capture human’s active learning behavior?

Boundary game

? ? ? task

Causal graph learning

? ? Coenen et al. 2015 task

Coenen, Rehder, & Gureckis. (2015). Strategies to intervene on causal systems are adaptively selected. Cognitive psychology, 79, 102-133.

Human choices Expected information gain

icti

Self-Teaching model Expected information gain

Collaborators

Wai Keen Vong Yue Yu Patrick Shafto Yang, Vong, Yu & Shafto. (2019). A unifying computational framework for teaching and active learning. Topics in Cognitive Science 11(2): 316-337.

Conclusions

• We derived a Self-Teaching model, a novel form of active learning.
• It depends on only the rules of probability (may have implications for

active machine learning).

• It unifies teaching and active learning under a single learning mechanism.
• It matches human’s active learning behavior in many cases.