Learning without Recall: A Case for Log-Linear Learning

We analyze a model of learning and belief formation in networks in which agents follow Bayes rule yet they do not recall their history of past observations and cannot reason about how other agents' beliefs are formed. They do so by making rational inferences about their observations which include a sequence of independent and identically distributed private signals as well as the beliefs of their neighboring agents at each time. Fully rational agents would successively apply Bayes rule to the entire history of observations. This leads to forebodingly complex inferences due to lack of knowledge about the global network structure that causes those observations. To address these complexities, we consider a Learning without Recall model, which in addition to providing a tractable framework for analyzing the behavior of rational agents in social networks, can also provide a behavioral foundation for the variety of non-Bayesian update rules in the literature. We present the implications of various choices for time-varying priors of such agents and how this choice affects learning and its rate.Comment: in 5th IFAC Workshop on Distributed Estimation and Control in Networked Systems, (NecSys 2015

Learning without Recall by Random Walks on Directed Graphs

We consider a network of agents that aim to learn some unknown state of the world using private observations and exchange of beliefs. At each time, agents observe private signals generated based on the true unknown state. Each agent might not be able to distinguish the true state based only on her private observations. This occurs when some other states are observationally equivalent to the true state from the agent's perspective. To overcome this shortcoming, agents must communicate with each other to benefit from local observations. We propose a model where each agent selects one of her neighbors randomly at each time. Then, she refines her opinion using her private signal and the prior of that particular neighbor. The proposed rule can be thought of as a Bayesian agent who cannot recall the priors based on which other agents make inferences. This learning without recall approach preserves some aspects of the Bayesian inference while being computationally tractable. By establishing a correspondence with a random walk on the network graph, we prove that under the described protocol, agents learn the truth exponentially fast in the almost sure sense. The asymptotic rate is expressed as the sum of the relative entropies between the signal structures of every agent weighted by the stationary distribution of the random walk.Comment: 6 pages, To Appear in Conference on Decision and Control 201

Controllability and Fraction of Leaders in Infinite Network

In this paper, we study controllability of a network of linear single-integrator agents when the network size goes to infinity. We first investigate the effect of increasing size by injecting an input at every node and requiring that network controllability Gramian remain well-conditioned with the increasing dimension. We provide theoretical justification to the intuition that high degree nodes pose a challenge to network controllability. In particular, the controllability Gramian for the networks with bounded maximum degrees is shown to remain well-conditioned even as the network size goes to infinity. In the canonical cases of star, chain and ring networks, we also provide closed-form expressions which bound the condition number of the controllability Gramian in terms of the network size. We next consider the effect of the choice and number of leader nodes by actuating only a subset of nodes and considering the least eigenvalue of the Gramian as the network size increases. Accordingly, while a directed star topology can never be made controllable for all sizes by injecting an input just at a fraction $f<1$ of nodes; for path or cycle networks, the designer can actuate a non-zero fraction of nodes and spread them throughout the network in such way that the least eigenvalue of the Gramians remain bounded away from zero with the increasing size. The results offer interesting insights on the challenges of control in large networks and with high-degree nodes.Comment: 6 pages, 3 figures, to appear in 2014 IEEE CD

Minimal Actuator Placement with Optimal Control Constraints

We introduce the problem of minimal actuator placement in a linear control system so that a bound on the minimum control effort for a given state transfer is satisfied while controllability is ensured. We first show that this is an NP-hard problem following the recent work of Olshevsky. Next, we prove that this problem has a supermodular structure. Afterwards, we provide an efficient algorithm that approximates up to a multiplicative factor of O(logn), where n is the size of the multi-agent network, any optimal actuator set that meets the specified energy criterion. Moreover, we show that this is the best approximation factor one can achieve in polynomial-time for the worst case. Finally, we test this algorithm over large Erdos-Renyi random networks to further demonstrate its efficiency.Comment: This version includes all the omitted proofs from the one to appear in the American Control Conference (ACC) 2015 proceeding

Bayesian Heuristics for Group Decisions

We propose a model of inference and heuristic decision-making in groups that is rooted in the Bayes rule but avoids the complexities of rational inference in partially observed environments with incomplete information, which are characteristic of group interactions. Our model is also consistent with a dual-process psychological theory of thinking: the group members behave rationally at the initiation of their interactions with each other (the slow and deliberative mode); however, in the ensuing decision epochs, they rely on a heuristic that replicates their experiences from the first stage (the fast automatic mode). We specialize this model to a group decision scenario where private observations are received at the beginning, and agents aim to take the best action given the aggregate observations of all group members. We study the implications of the information structure together with the properties of the probability distributions which determine the structure of the so-called "Bayesian heuristics" that the agents follow in our model. We also analyze the group decision outcomes in two classes of linear action updates and log-linear belief updates and show that many inefficiencies arise in group decisions as a result of repeated interactions between individuals, leading to overconfident beliefs as well as choice-shifts toward extremes. Nevertheless, balanced regular structures demonstrate a measure of efficiency in terms of aggregating the initial information of individuals. These results not only verify some well-known insights about group decision-making but also complement these insights by revealing additional mechanistic interpretations for the group declension-process, as well as psychological and cognitive intuitions about the group interaction model

Risk Factors for Ulcerative Colitis in Shahrekord, Iran: A Case-Control Study

Background and aims: Ulcerative colitis (UC) is a chronic inflammatory bowel disease (IBD) which involves the rectum and colonic mucosa, and is often constantly expanding. Few data are available on risk factors in Chaharmahal and Bakhtiari province. Therefore, the aim of this study was to investigate the association between potential risk factors and UC in Shahrekord. Methods: A case-control study was conducted on patients diagnosed with UC. Overall, 27 new cases of UC and 54 healthy controls in the age range of 20–80 years were studied. Participants were recruited from Pathologic Centers in Shahrekord in 2018. Chi-square test and t test and were used. Logistic regression model was employed to analyze the association between risk factors and UC disease. Results: The mean age at diagnosis was 41.74 years (SD: 7.16 years) and 44.94 years (SD: 6.67 years) for case and control subjects, respectively. Moreover, univariate and multiple odds ratio (OR) showed that there was no significant association between UC and any of the risk factors including gender, marital status, education, diastolic blood pressure, history of diabetes, history of hypertension, permanent use of piped water, night shift work, history of thyroid diseases, depression, history of fatty liver disease, history of kidney stones, and sleep time and wake-up time in the morning. Conclusion: Generally, no significant association was observed between UC and the variables in the present study. Thus, further studies with larger sample size are necessary to better understand the other risk factors and environmental determinants of UC. Keywords: Ulcerative colitis Inflammatory bowel disease Risk factors Case-contro

Early Maladjustment Schemas in Individuals with and without Type 2 Diabetes Mellitus

Objective. This study explored Early Maladjustment Schemas (EMSs) among individuals with and without type 2 diabetes mellitus and examined potential moderating roles for gender, level of education, and occupation. Methods. The sample included 371 adult participants (120 patients with diabetes and 251 individuals without diabetes), from Shiraz City, Fars province; Iran. The Young Schema Questionnaire-Short Form (YSQ-SF) was used to assess early maladjustment schemas. Results. Findings showed that patients with type 2 diabetes had significantly higher scores than controls on a number of EMSs, including abandonment, failure, vulnerability, enmeshment, self-sacrifice, entitlement, and insufficient self-control schemas as well as the over-vigilance and inhibition schematic domains. However, results did not support roles for gender, the level of education, and occupation on any of EMSs and schematic domains. Conclusions. Medical and health professionals may find these results helpful for assessment, treatment, and prevention goals in patients with type 2 diabetes