Efficient and Robust High-Dimensional Linear Contextual Bandits
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The linear contextual bandits is a sequential decision-making problem where an agent decides among sequential actions given their corresponding contexts. Since large-scale data sets become more and more common, we study the linear contextual bandits in high-dimensional situations. Recent works focus on employing matrix sketching methods to accelerating contextual bandits. However, the matrix approximation error will bring additional terms to the regret bound. In this paper we first propose a novel matrix sketching method which is called Spectral Compensation Frequent Directions (SCFD). Then we propose an efficient approach for contextual bandits by adopting SCFD to approximate the covariance matrices. By maintaining and manipulating sketched matrices, our method only needs O(md) space and O(md) updating time in each round, where d is the dimensionality of the data and m is the sketching size. Theoretical analysis reveals that our method has better regret bounds than previous methods in high-dimensional cases. Experimental results demonstrate the effectiveness of our algorithm and verify our theoretical guarantees.Keywords:
Matrix (chemical analysis)
This paper investigates the interplay among anticipated regret, experienced regret and satisfaction in a service retention context. Results from an online service patronization decision making experiment show that the higher consumers' anticipated regret before a service visit, the lower their visit intention for the same alternative when they experience regret after the decision. Furthermore, a forward looking perspective in regret context has been advocated, in specific, the impact of experienced regret on next visit intention is partially through adjusting anticipated regret and partially mediated through satisfaction.
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<p>Regret is an emotion closely related to people's daily life. This paper summarizes the research results on regret, including the definition of regret, the influencing factors of regret and the research status of regret.</p>
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Regret and regret regulation were studied using a weeklong web-based diary method. 108 participants aged 19 to 89 years reported regret for a decision made and a decision to be made. They also reported the extent to which they used strategies to prevent or regulate decision regret. Older adults reported both less experienced and anticipated regret compared to younger adults. The lower level of experienced regret in older adults was mediated by reappraisal of the decision. The lower level of anticipated regret was mediated by delaying the decision, and expecting regret in older adults. It is suggested that the lower level of regret observed in older adults is partly explained by regret prevention and regulation strategies.
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Extended Kalman filter (EKF) is prevailing for cooperative localization, where the cross-covariance (representing the correlation of estimated position) determines the benefit quantity from the local measurement. In this paper, the covariance factor set is adopted for cross-covariance maintaining in distributed architecture. During two exteroceptive measurements, the covariance factor set is propagated independently in each agent. When the updating information from the measuring agent is received by the other agents, a temporary relative master-slave relationship is determined between them. The updated correlation is retained in the receiver (slave) agent as a covariance factor. Meanwhile, the counterpart in the measuring (master) agent is set as identify matrix. The operation of matrix decomposition and the feedback for covariance update from slave to master is saved. Thus, the computational consumption and communication burden are reduced. It is significant for real-time cooperative localization.
Master/slave
Position (finance)
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Decisions were sampled from 108 participants during 8 days using a web-based diary method. Each day participants rated experienced regret for a decision made, as well as forecasted regret for a decision to be made. Participants also indicated to what extent they used different strategies to prevent or regulate regret. Participants regretted 30% of decisions and forecasted regret in 70% of future decisions, indicating both that regret is relatively prevalent in daily decisions but also that experienced regret was less frequent than forecasted regret. In addition, a number of decision-specific regulation and prevention strategies were successfully used by the participants to minimize regret and negative emotions in daily decision making. Overall, these results suggest that regulation and prevention of regret are important strategies in many of our daily decisions.
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This study examines the influence of regret experience and anticipation regret in deciding order
aggressiveness when investors buy and sell. This study is an experimental research design with a mix
between and within subjects (Experienced Regret-due to act versus Experienced Regret-due to not act) X
(Anticipated Regret versus No anticipated regret). This study involved 40 undergraduate students. The
results showed that experienced regret and anticipated regret impact order aggressiveness. Investors
respond to the experience of regret and anticipation of the same emotions by showing risk averse behavior
(low aggressiveness) and risk seeking behavior (high aggressiveness) when selling and buying.
Anticipation (artificial intelligence)
Risk-seeking
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This empirical research introduces and validates the need for assessing regret from both the decision-making process and the product concurrently, subsequent to an unfavorable decision outcome during post-purchase assessment. Prior regret research in marketing has investigated the experience of regret either from the decision-making process or from the product, but not simultaneously. The research posits and shows that not examining the sources of the regret emotion simultaneously leads to a lop-sided assessment and is likely to inhibit future learning. Results from the study indicate that a differential regret experience is reflected when regret is measured from the decision-making process, however, the same is not revealed when regret is measured from the product.
Empirical Research
Decision-making
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ABSTRACT The relative efficiency of maximum likelihood estimates is studied when taking advantage of underlying linear patterns in the covariances or correlations when estimating covariance matrices. We compare the variances of estimates of the covariance matrix obtained under two nested patterns with the assumption that the more restricted pattern is the true state. Formulas for the asymptotic variances are given which are exact for linear covariance patterns when explicit maximum likelihood estimates exist. Several specific examples are given using complete symmetry, circular symmetry and general covariance patterns as well as an example involving a covariance matrix with a linear pattern in the correlations.
General Covariance
Covariance mapping
Analysis of covariance
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This chapter briefly reviews the concept of post-purchase regret (both anticipated regret and post-decision regret) and compares it to dissatisfaction and anger. Consumers may believe that a purchase decision was right at the time of purchase, they later may regret it. Dissatisfaction is distinguished from regret in that it directly affects both repurchase intention and complaint intention, whereas regret directly affects only repurchase intention. The distinction between anticipated regret and post-decision regret is also explained.
Complaint
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Covariance matrix estimation is a persistent challenge for cosmology. We focus on a class of model covariance matrices that can be generated with high accuracy and precision, using a tiny fraction of the computational resources that would be required to achieve comparably precise covariance matrices using mock catalogues. In previous work, the free parameters in these models were determined using sample covariance matrices computed using a large number of mocks, but we demonstrate that those parameters can be estimated consistently and with good precision by applying jackknife methods to a single survey volume. This enables model covariance matrices that are calibrated from data alone, with no reference to mocks.
Jackknife resampling
General Covariance
Covariance mapping
Matérn covariance function
Analysis of covariance
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