Bayesian Learning with Random Arrivals

Tho Ngoc Le, Vijay G. Subramanian, Randall A Berry

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We add to a line of work considering the impact of observation imperfections in models of Bayesian observational learning. In particular, we study a discrete-time model in which in each time-slot, an agent may randomly arrive. Agents who arrive have the opportunity to buy a given item. If an agent chooses to buy, this action is recorded for subsequent agents. However, the decisions of agents that choose not to buy are not recorded. Hence, if no one buys in a given slot, agents are unaware if this was due to no agent arriving or an agent choosing not to buy. We study the impact of this uncertainty on the emergence of information cascades. Using a Markov chain based analysis, we show that the probability of incorrect cascades and the expected time until a cascade happens are not monotonic in the arrival probability of a user. We find that adding a small uncertainty in the arrival information from the perfect information setting will make a buy cascade happen with higher probability than a not-buy cascade. However, if the agents' private signals are weak, then a not-buy cascade is more likely to occur for most arrival rates, resulting in wrong cascades dominating when the item is good and vice-versa when the item is bad.

Original languageEnglish (US)
Title of host publication2018 IEEE International Symposium on Information Theory, ISIT 2018
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages926-930
Number of pages5
Volume2018-June
ISBN (Print)9781538647806
DOIs
StatePublished - Aug 15 2018
Event2018 IEEE International Symposium on Information Theory, ISIT 2018 - Vail, United States
Duration: Jun 17 2018Jun 22 2018

Other

Other2018 IEEE International Symposium on Information Theory, ISIT 2018
CountryUnited States
CityVail
Period6/17/186/22/18

Fingerprint

Bayesian Learning
Cascade
Choose
Uncertainty
Discrete-time Model
Imperfections
Monotonic
Markov processes
Markov chain
Likely
Defects

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Information Systems
  • Modeling and Simulation
  • Applied Mathematics

Cite this

Le, T. N., Subramanian, V. G., & Berry, R. A. (2018). Bayesian Learning with Random Arrivals. In 2018 IEEE International Symposium on Information Theory, ISIT 2018 (Vol. 2018-June, pp. 926-930). [8437317] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ISIT.2018.8437317
Le, Tho Ngoc ; Subramanian, Vijay G. ; Berry, Randall A. / Bayesian Learning with Random Arrivals. 2018 IEEE International Symposium on Information Theory, ISIT 2018. Vol. 2018-June Institute of Electrical and Electronics Engineers Inc., 2018. pp. 926-930
@inproceedings{7a5d6c80c1554c058d85e41e39dce697,
title = "Bayesian Learning with Random Arrivals",
abstract = "We add to a line of work considering the impact of observation imperfections in models of Bayesian observational learning. In particular, we study a discrete-time model in which in each time-slot, an agent may randomly arrive. Agents who arrive have the opportunity to buy a given item. If an agent chooses to buy, this action is recorded for subsequent agents. However, the decisions of agents that choose not to buy are not recorded. Hence, if no one buys in a given slot, agents are unaware if this was due to no agent arriving or an agent choosing not to buy. We study the impact of this uncertainty on the emergence of information cascades. Using a Markov chain based analysis, we show that the probability of incorrect cascades and the expected time until a cascade happens are not monotonic in the arrival probability of a user. We find that adding a small uncertainty in the arrival information from the perfect information setting will make a buy cascade happen with higher probability than a not-buy cascade. However, if the agents' private signals are weak, then a not-buy cascade is more likely to occur for most arrival rates, resulting in wrong cascades dominating when the item is good and vice-versa when the item is bad.",
author = "Le, {Tho Ngoc} and Subramanian, {Vijay G.} and Berry, {Randall A}",
year = "2018",
month = "8",
day = "15",
doi = "10.1109/ISIT.2018.8437317",
language = "English (US)",
isbn = "9781538647806",
volume = "2018-June",
pages = "926--930",
booktitle = "2018 IEEE International Symposium on Information Theory, ISIT 2018",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
address = "United States",

}

Le, TN, Subramanian, VG & Berry, RA 2018, Bayesian Learning with Random Arrivals. in 2018 IEEE International Symposium on Information Theory, ISIT 2018. vol. 2018-June, 8437317, Institute of Electrical and Electronics Engineers Inc., pp. 926-930, 2018 IEEE International Symposium on Information Theory, ISIT 2018, Vail, United States, 6/17/18. https://doi.org/10.1109/ISIT.2018.8437317

Bayesian Learning with Random Arrivals. / Le, Tho Ngoc; Subramanian, Vijay G.; Berry, Randall A.

2018 IEEE International Symposium on Information Theory, ISIT 2018. Vol. 2018-June Institute of Electrical and Electronics Engineers Inc., 2018. p. 926-930 8437317.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

TY - GEN

T1 - Bayesian Learning with Random Arrivals

AU - Le, Tho Ngoc

AU - Subramanian, Vijay G.

AU - Berry, Randall A

PY - 2018/8/15

Y1 - 2018/8/15

N2 - We add to a line of work considering the impact of observation imperfections in models of Bayesian observational learning. In particular, we study a discrete-time model in which in each time-slot, an agent may randomly arrive. Agents who arrive have the opportunity to buy a given item. If an agent chooses to buy, this action is recorded for subsequent agents. However, the decisions of agents that choose not to buy are not recorded. Hence, if no one buys in a given slot, agents are unaware if this was due to no agent arriving or an agent choosing not to buy. We study the impact of this uncertainty on the emergence of information cascades. Using a Markov chain based analysis, we show that the probability of incorrect cascades and the expected time until a cascade happens are not monotonic in the arrival probability of a user. We find that adding a small uncertainty in the arrival information from the perfect information setting will make a buy cascade happen with higher probability than a not-buy cascade. However, if the agents' private signals are weak, then a not-buy cascade is more likely to occur for most arrival rates, resulting in wrong cascades dominating when the item is good and vice-versa when the item is bad.

AB - We add to a line of work considering the impact of observation imperfections in models of Bayesian observational learning. In particular, we study a discrete-time model in which in each time-slot, an agent may randomly arrive. Agents who arrive have the opportunity to buy a given item. If an agent chooses to buy, this action is recorded for subsequent agents. However, the decisions of agents that choose not to buy are not recorded. Hence, if no one buys in a given slot, agents are unaware if this was due to no agent arriving or an agent choosing not to buy. We study the impact of this uncertainty on the emergence of information cascades. Using a Markov chain based analysis, we show that the probability of incorrect cascades and the expected time until a cascade happens are not monotonic in the arrival probability of a user. We find that adding a small uncertainty in the arrival information from the perfect information setting will make a buy cascade happen with higher probability than a not-buy cascade. However, if the agents' private signals are weak, then a not-buy cascade is more likely to occur for most arrival rates, resulting in wrong cascades dominating when the item is good and vice-versa when the item is bad.

UR - http://www.scopus.com/inward/record.url?scp=85052468023&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85052468023&partnerID=8YFLogxK

U2 - 10.1109/ISIT.2018.8437317

DO - 10.1109/ISIT.2018.8437317

M3 - Conference contribution

SN - 9781538647806

VL - 2018-June

SP - 926

EP - 930

BT - 2018 IEEE International Symposium on Information Theory, ISIT 2018

PB - Institute of Electrical and Electronics Engineers Inc.

ER -

Le TN, Subramanian VG, Berry RA. Bayesian Learning with Random Arrivals. In 2018 IEEE International Symposium on Information Theory, ISIT 2018. Vol. 2018-June. Institute of Electrical and Electronics Engineers Inc. 2018. p. 926-930. 8437317 https://doi.org/10.1109/ISIT.2018.8437317