Introduction to Bioinformatics: Lecture VIII Classification and Supervised Learning
VIII Lecture
description
Transcript of VIII Lecture
![Page 1: VIII Lecture](https://reader036.fdocuments.us/reader036/viewer/2022062315/56816679550346895dda1a0b/html5/thumbnails/1.jpg)
VIII Lecture
Time Preferences
![Page 2: VIII Lecture](https://reader036.fdocuments.us/reader036/viewer/2022062315/56816679550346895dda1a0b/html5/thumbnails/2.jpg)
Wrap up of the previous lecture
• Problem of distinguishing between biasing and shaping effect.
• Evidence for shaping effect in repeated median price selling auctions.
• If preferences form in the course of an interaction, can we intentionally manage them to avoid self-defeating behavior?
![Page 3: VIII Lecture](https://reader036.fdocuments.us/reader036/viewer/2022062315/56816679550346895dda1a0b/html5/thumbnails/3.jpg)
Normative theory and descriptive analysis
• Anomalous behavior of PR, coherent arbitrariness, shaping effect.
• Methodological implications: analysis of experimental methods; relationship between empirical regularities in behavior and the theoretical axiomatic core.
• Epistemological implications: intellectual integration of economic theory and cognitive sciences.
• Anomalous behavior of time preferences.
• Methodological implications: relationship between our actual discount rate of the future and the normative benchmark.
• Epistemological implications: integration between economics and cognitive sciences.
• Ontological implications: it is at issue the characterization of the economic agents.
![Page 4: VIII Lecture](https://reader036.fdocuments.us/reader036/viewer/2022062315/56816679550346895dda1a0b/html5/thumbnails/4.jpg)
Frame of the problem.Why people engage in self-defeating
behaviors?
• A behavior is self-defeating when people prefer a ready at hand utility yielding a long run dis-utility over a long run utility at a delayed point in time (i.e. drug or tobacco addiction).
• If we introduce timing then self-defeating behavior consists of preferring the delayed long run utility when the smaller one is far and reversing preferences when the small reward gets closer in time.
• People devaluate the future and the engagement in self-defeating behavior leads to devaluate it even more.
• Self-defeating behavior is a problem of the discount rate of the future: the more we discount the future the more likely we are to engage in a self-defeating behavior; time preferences is the logical structure of self-defeating behavior.
![Page 5: VIII Lecture](https://reader036.fdocuments.us/reader036/viewer/2022062315/56816679550346895dda1a0b/html5/thumbnails/5.jpg)
• RCT requires to subtract a constant proportion of the utility there would be at any given delay for every additional unit of delay.
• Formula: Value = “Objective” value × (1 − Discount rate) Delay.
• Exponential function of the discount rate: consistency preserving rule in inter-temporal choices.
Standard solution
![Page 6: VIII Lecture](https://reader036.fdocuments.us/reader036/viewer/2022062315/56816679550346895dda1a0b/html5/thumbnails/6.jpg)
Example of drinking
• Immediate utiles of 100; discount rate of 20% per day; costs of 120 utiles for the day after hangover.
• Drinking today: 100 − (120 × 80%) = 4 utiles
• Delay of a day for drinking: (100 × 80%) − 120 × (80%)2 = 3.2 utiles
![Page 7: VIII Lecture](https://reader036.fdocuments.us/reader036/viewer/2022062315/56816679550346895dda1a0b/html5/thumbnails/7.jpg)
Reason why the standard solution is misguided
• The standard solution is an action guiding rule but it does not explain the inconsistency of preferring a long run utility when the short run utility is far and the latter when it is ready at hand.
• Two cases: 1) The exponential discount rate of the future determines always a positive level of utility for a delayed action. 2) The discount rate determines always a negative utility.
• In both cases the standard solution does not explain why people engage self-defeating behaviors: no preferences reversal across time.
• I case: if I have a discount rate of 20%, then I always choose to drink because the level of utility never gets to be zero or negative.
• II case: if I have a discount rate of 10%, then if I choose not to drink from the point of view of some delay then I will not drink even when the occasion is ready at hand.
• Two days of delay: 100 × (90%)2 − 120 × (90%)3 = – 6.48
• Immediate occasion: 100 − 120 × 90% = - 8
![Page 8: VIII Lecture](https://reader036.fdocuments.us/reader036/viewer/2022062315/56816679550346895dda1a0b/html5/thumbnails/8.jpg)
Explanatory lack• The rule does not explain time reversal of preferences
between a short run reward and a long run one when the former is ready at hand.
• This reversal results in a long run disutility (self-defeating behavior).
• According to standard theory (that endorses the exponential discount rule) the explanation of self-defeating behaviors falls out of the economic domain.
![Page 9: VIII Lecture](https://reader036.fdocuments.us/reader036/viewer/2022062315/56816679550346895dda1a0b/html5/thumbnails/9.jpg)
Two alternatives
• I mistakenly calculate the discounted value of a prospect.
• Learning by bad consequences to implement the right calculation.
• My discount rate leads me to always drink.
• I probably need a doctor!
![Page 10: VIII Lecture](https://reader036.fdocuments.us/reader036/viewer/2022062315/56816679550346895dda1a0b/html5/thumbnails/10.jpg)
Relative limitations• Self-defeating behavior can be persistent even if I
learn from bad consequences.
• Time consistent behavior can be forestalled by self-defeating behavior even if I learn the benefits of my consistency.
• Pathological self-defeating behaviors (drug addiction) stand in a continuum relationship with normal ones.
![Page 11: VIII Lecture](https://reader036.fdocuments.us/reader036/viewer/2022062315/56816679550346895dda1a0b/html5/thumbnails/11.jpg)
Hyperbolic discount curve
• The devaluation of rewards is proportional to their delay.
• Ready-at-hand rewards and extremely delayed ones are discounted the same as with the exponential rule.
• The rewards in between the extremes are devaluated more: hyperbolic discount curves are more bowed than the exponential ones.
![Page 12: VIII Lecture](https://reader036.fdocuments.us/reader036/viewer/2022062315/56816679550346895dda1a0b/html5/thumbnails/12.jpg)
Illustration
![Page 13: VIII Lecture](https://reader036.fdocuments.us/reader036/viewer/2022062315/56816679550346895dda1a0b/html5/thumbnails/13.jpg)
Example of the coat• Ms Exponential could buy Ms Hyperbolic’s winter coat
each spring, when Ms H. devaluates it more.
• Ms. E could then sell the coat back to Ms. H every fall when the approach of winter sent Ms. H’s valuation of it into a high spike.
• Only an exponential discount curve will protect a person against exploitation: the hyperbolic discount curve is maladaptive within the economic environment.
![Page 14: VIII Lecture](https://reader036.fdocuments.us/reader036/viewer/2022062315/56816679550346895dda1a0b/html5/thumbnails/14.jpg)
Implications for markets
• An agent with hyperbolic discount curves will be exploited to the point that he will exit the market.
• From a normative point of view a hyperbolic discounter is not an economic agent.
• However hyperbolic discount curves are descriptively relevant.
![Page 15: VIII Lecture](https://reader036.fdocuments.us/reader036/viewer/2022062315/56816679550346895dda1a0b/html5/thumbnails/15.jpg)
Exponential discount curves. Predictive implications
• Offer a choice between a small reward at delay D and a larger reward available at delay D plus a constant lag L.
• Prediction of conventional theory: we consistently choose the larger reward at D + L (i.e. not drinking) even when the smaller reward gets closer in time (i.e. a beer just before me). This means that the respective discount curves stay proportional to each other.
![Page 16: VIII Lecture](https://reader036.fdocuments.us/reader036/viewer/2022062315/56816679550346895dda1a0b/html5/thumbnails/16.jpg)
Illustration of the standard theory prediction
![Page 17: VIII Lecture](https://reader036.fdocuments.us/reader036/viewer/2022062315/56816679550346895dda1a0b/html5/thumbnails/17.jpg)
Hyperbolic discount curves. Predictive implications
• Prediction of hyperbolic discounting: the original choice of the larger reward will be reverted when the smaller reward gets closer in time. This means that the two curves crosses.
![Page 18: VIII Lecture](https://reader036.fdocuments.us/reader036/viewer/2022062315/56816679550346895dda1a0b/html5/thumbnails/18.jpg)
Illustration of hyperbolic discount curves that cross
![Page 19: VIII Lecture](https://reader036.fdocuments.us/reader036/viewer/2022062315/56816679550346895dda1a0b/html5/thumbnails/19.jpg)
Behavioral regularity
• The reward is chosen in direct proportion to his size and in inverse proportion to his delay.
• Value = amount / [Constant 1 + (Constant 2 × Delay)]
• This rule explains how the evaluation of rewards is dependent on their delay such to allow the behavioral phenomenon of time inconsistent preferences.
![Page 20: VIII Lecture](https://reader036.fdocuments.us/reader036/viewer/2022062315/56816679550346895dda1a0b/html5/thumbnails/20.jpg)
Constants
• Constant 1 keeps the value from going to infinity when a reward is immediate; Constant 2 describes how steeply a subject discounts the future.
![Page 21: VIII Lecture](https://reader036.fdocuments.us/reader036/viewer/2022062315/56816679550346895dda1a0b/html5/thumbnails/21.jpg)
Normative theory and descriptive analysis
• We need to take in direct account how individuals assign real value to the prospect.
• We need to understand how much the real value departs from the cognitive benchmark.
• Can we naturalize the normative benchmark?
![Page 22: VIII Lecture](https://reader036.fdocuments.us/reader036/viewer/2022062315/56816679550346895dda1a0b/html5/thumbnails/22.jpg)
Conclusions• Problem of self-defeating behavior: we need to explaining its
occurrence and the possibility of its avoidance.
• Standard exponential discount curves are a normative benchmark not explaining why self-defeating behavior occurs.
• Hyperbolic discount curves are descriptive tools explaining why we engage in self-defeating behavior.
• How do we have to relate the normative and descriptive level?