68,251 research outputs found
Bayesian Generalized Network Design
We study network coordination problems, as captured by the setting of generalized network design (Emek et al., STOC 2018), in the face of uncertainty resulting from partial information that the network users hold regarding the actions of their peers. This uncertainty is formalized using Alon et al.\u27s Bayesian ignorance framework (TCS 2012). While the approach of Alon et al. is purely combinatorial, the current paper takes into account computational considerations: Our main technical contribution is the development of (strongly) polynomial time algorithms for local decision making in the face of Bayesian uncertainty
Comparison between Suitable Priors for Additive Bayesian Networks
Additive Bayesian networks are types of graphical models that extend the
usual Bayesian generalized linear model to multiple dependent variables through
the factorisation of the joint probability distribution of the underlying
variables. When fitting an ABN model, the choice of the prior of the parameters
is of crucial importance. If an inadequate prior - like a too weakly
informative one - is used, data separation and data sparsity lead to issues in
the model selection process. In this work a simulation study between two weakly
and a strongly informative priors is presented. As weakly informative prior we
use a zero mean Gaussian prior with a large variance, currently implemented in
the R-package abn. The second prior belongs to the Student's t-distribution,
specifically designed for logistic regressions and, finally, the strongly
informative prior is again Gaussian with mean equal to true parameter value and
a small variance. We compare the impact of these priors on the accuracy of the
learned additive Bayesian network in function of different parameters. We
create a simulation study to illustrate Lindley's paradox based on the prior
choice. We then conclude by highlighting the good performance of the
informative Student's t-prior and the limited impact of the Lindley's paradox.
Finally, suggestions for further developments are provided.Comment: 8 pages, 4 figure
Multi-level Gated Bayesian Recurrent Neural Network for State Estimation
The optimality of Bayesian filtering relies on the completeness of prior
models, while deep learning holds a distinct advantage in learning models from
offline data. Nevertheless, the current fusion of these two methodologies
remains largely ad hoc, lacking a theoretical foundation. This paper presents a
novel solution, namely a multi-level gated Bayesian recurrent neural network
specifically designed to state estimation under model mismatches. Firstly, we
transform the non-Markov state-space model into an equivalent first-order
Markov model with memory. It is a generalized transformation that overcomes the
limitations of the first-order Markov property and enables recursive filtering.
Secondly, by deriving a data-assisted joint state-memory-mismatch Bayesian
filtering, we design a Bayesian multi-level gated framework that includes a
memory update gate for capturing the temporal regularities in state evolution,
a state prediction gate with the evolution mismatch compensation, and a state
update gate with the observation mismatch compensation. The Gaussian
approximation implementation of the filtering process within the gated
framework is derived, taking into account the computational efficiency.
Finally, the corresponding internal neural network structures and end-to-end
training methods are designed. The Bayesian filtering theory enhances the
interpretability of the proposed gated network, enabling the effective
integration of offline data and prior models within functionally explicit gated
units. In comprehensive experiments, including simulations and real-world
datasets, the proposed gated network demonstrates superior estimation
performance compared to benchmark filters and state-of-the-art deep learning
filtering methods
Bayesian networks and decision trees in the diagnosis of female urinary incontinence
This study compares the effectiveness of Bayesian networks versus Decision Trees in modeling the Integral Theory of Female Urinary Incontinence diagnostic algorithm. Bayesian networks and Decision Trees were developed and trained using data from 58 adult women presenting with urinary incontinence symptoms. A Bayesian Network was developed in collaboration with an expert specialist who regularly utilizes a non-automated diagnostic algorithm in clinical practice. The original Bayesian network was later refined using a more connected approach. Diagnoses determined from all automated approaches were compared with the diagnoses of a single human expert. In most cases, Bayesian networks were found to be at least as accurate as the Decision Tree approach. The refined Connected Bayesian Network was found to be more accurate than the Original Bayesian Network accurately discriminated between diagnoses despite the small sample size. In contrast, the Connected and Decision Tree approaches were less able to discriminate between diagnoses. The Original Bayesian Network was found to provide an excellent basis for graphically communicating the correlation between symptoms and laxity defects in a given anatomical zone. Performance measures in both networks indicate that Bayesian networks could provide a potentially useful tool in the management of female pelvic floor dysfunction. Before the technique can be utilized in practice, well-established learning algorithms should be applied to improve network structure. A larger training data set should also improve network accuracy, sensitivity, and specificity
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