9 resultados para NONPARAMETRIC PROBLEMS
em Duke University
Resumo:
Bayesian nonparametric models, such as the Gaussian process and the Dirichlet process, have been extensively applied for target kinematics modeling in various applications including environmental monitoring, traffic planning, endangered species tracking, dynamic scene analysis, autonomous robot navigation, and human motion modeling. As shown by these successful applications, Bayesian nonparametric models are able to adjust their complexities adaptively from data as necessary, and are resistant to overfitting or underfitting. However, most existing works assume that the sensor measurements used to learn the Bayesian nonparametric target kinematics models are obtained a priori or that the target kinematics can be measured by the sensor at any given time throughout the task. Little work has been done for controlling the sensor with bounded field of view to obtain measurements of mobile targets that are most informative for reducing the uncertainty of the Bayesian nonparametric models. To present the systematic sensor planning approach to leaning Bayesian nonparametric models, the Gaussian process target kinematics model is introduced at first, which is capable of describing time-invariant spatial phenomena, such as ocean currents, temperature distributions and wind velocity fields. The Dirichlet process-Gaussian process target kinematics model is subsequently discussed for modeling mixture of mobile targets, such as pedestrian motion patterns.
Novel information theoretic functions are developed for these introduced Bayesian nonparametric target kinematics models to represent the expected utility of measurements as a function of sensor control inputs and random environmental variables. A Gaussian process expected Kullback Leibler divergence is developed as the expectation of the KL divergence between the current (prior) and posterior Gaussian process target kinematics models with respect to the future measurements. Then, this approach is extended to develop a new information value function that can be used to estimate target kinematics described by a Dirichlet process-Gaussian process mixture model. A theorem is proposed that shows the novel information theoretic functions are bounded. Based on this theorem, efficient estimators of the new information theoretic functions are designed, which are proved to be unbiased with the variance of the resultant approximation error decreasing linearly as the number of samples increases. Computational complexities for optimizing the novel information theoretic functions under sensor dynamics constraints are studied, and are proved to be NP-hard. A cumulative lower bound is then proposed to reduce the computational complexity to polynomial time.
Three sensor planning algorithms are developed according to the assumptions on the target kinematics and the sensor dynamics. For problems where the control space of the sensor is discrete, a greedy algorithm is proposed. The efficiency of the greedy algorithm is demonstrated by a numerical experiment with data of ocean currents obtained by moored buoys. A sweep line algorithm is developed for applications where the sensor control space is continuous and unconstrained. Synthetic simulations as well as physical experiments with ground robots and a surveillance camera are conducted to evaluate the performance of the sweep line algorithm. Moreover, a lexicographic algorithm is designed based on the cumulative lower bound of the novel information theoretic functions, for the scenario where the sensor dynamics are constrained. Numerical experiments with real data collected from indoor pedestrians by a commercial pan-tilt camera are performed to examine the lexicographic algorithm. Results from both the numerical simulations and the physical experiments show that the three sensor planning algorithms proposed in this dissertation based on the novel information theoretic functions are superior at learning the target kinematics with
little or no prior knowledge
Resumo:
Empirical modeling of high-frequency currency market data reveals substantial evidence for nonnormality, stochastic volatility, and other nonlinearities. This paper investigates whether an equilibrium monetary model can account for nonlinearities in weekly data. The model incorporates time-nonseparable preferences and a transaction cost technology. Simulated sample paths are generated using Marcet's parameterized expectations procedure. The paper also develops a new method for estimation of structural economic models. The method forces the model to match (under a GMM criterion) the score function of a nonparametric estimate of the conditional density of observed data. The estimation uses weekly U.S.-German currency market data, 1975-90. © 1995.
Resumo:
The relation between social rejection and growth in antisocial behavior was investigated. In Study 1,259 boys and girls (34% African American) were followed from Grades 1 to 3 (ages 6-8 years) to Grades 5 to 7 (ages 10-12 years). Early peer rejection predicted growth in aggression. In Study 2,585 boys and girls (16% African American) were followed from kindergarten to Grade 3 (ages 5-8 years), and findings were replicated. Furthermore, early aggression moderated the effect of rejection, such that rejection exacerbated antisocial development only among children initially disposed toward aggression. In Study 3, social information-processing patterns measured in Study 1 were found to mediate partially the effect of early rejection on later aggression. In Study 4, processing patterns measured in Study 2 replicated the mediation effect. Findings are integrated into a recursive model of antisocial development.
Resumo:
Externalizing behavior problems of 124 adolescents were assessed across Grades 7-11. In Grade 9, participants were also assessed across social-cognitive domains after imagining themselves as the object of provocations portrayed in six videotaped vignettes. Participants responded to vignette-based questions representing multiple processes of the response decision step of social information processing. Phase 1 of our investigation supported a two-factor model of the response evaluation process of response decision (response valuation and outcome expectancy). Phase 2 showed significant relations between the set of these response decision processes, as well as response selection, measured in Grade 9 and (a) externalizing behavior in Grade 9 and (b) externalizing behavior in Grades 10-11, even after controlling externalizing behavior in Grades 7-8. These findings suggest that on-line behavioral judgments about aggression play a crucial role in the maintenance and growth of aggressive response tendencies in adolescence.