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Implicit Weight Uncertainty in Neural Networks

arXiv.org Machine Learning

We interpret HyperNetworks within the framework of variational inference within implicit distributions. Our method, Bayes by Hypernet, is able to model a richer variational distribution than previous methods. Experiments show that it achieves comparable predictive performance on the MNIST classification task while providing higher predictive uncertainties compared to MC-Dropout and regular maximum likelihood training.


Approximate maximum entropy principles via Goemans-Williamson with applications to provable variational methods

Neural Information Processing Systems

The well known maximum-entropy principle due to Jaynes, which states that given mean parameters, the maximum entropy distribution matching them is in an exponential family has been very popular in machine learning due to its "Occam's razor" interpretation. Unfortunately, calculating the potentials in the maximum entropy distribution is intractable [BGS14]. We provide computationally efficient versions of this principle when the mean parameters are pairwise moments: we design distributions that approximately match given pairwise moments, while having entropy which is comparable to the maximum entropy distribution matching those moments. We additionally provide surprising applications of the approximate maximum entropy principle to designing provable variational methods for partition function calculations for Ising models without any assumptions on the potentials of the model. More precisely, we show that we can get approximation guarantees for the log-partition function comparable to those in the low-temperature limit, which is the setting of optimization of quadratic forms over the hypercube.


Approximate maximum entropy principles via Goemans-Williamson with applications to provable variational methods

arXiv.org Machine Learning

The well known maximum-entropy principle due to Jaynes, which states that given mean parameters, the maximum entropy distribution matching them is in an exponential family, has been very popular in machine learning due to its "Occam's razor" interpretation. Unfortunately, calculating the potentials in the maximum-entropy distribution is intractable \cite{bresler2014hardness}. We provide computationally efficient versions of this principle when the mean parameters are pairwise moments: we design distributions that approximately match given pairwise moments, while having entropy which is comparable to the maximum entropy distribution matching those moments. We additionally provide surprising applications of the approximate maximum entropy principle to designing provable variational methods for partition function calculations for Ising models without any assumptions on the potentials of the model. More precisely, we show that in every temperature, we can get approximation guarantees for the log-partition function comparable to those in the low-temperature limit, which is the setting of optimization of quadratic forms over the hypercube. \cite{alon2006approximating}


Approximate maximum entropy principles via Goemans-Williamson with applications to provable variational methods

Neural Information Processing Systems

The well known maximum-entropy principle due to Jaynes, which states that given mean parameters, the maximum entropy distribution matching them is in an exponential family has been very popular in machine learning due to its “Occam’s razor” interpretation. Unfortunately, calculating the potentials in the maximum entropy distribution is intractable [BGS14]. We provide computationally efficient versions of this principle when the mean parameters are pairwise moments: we design distributions that approximately match given pairwise moments, while having entropy which is comparable to the maximum entropy distribution matching those moments. We additionally provide surprising applications of the approximate maximum entropy principle to designing provable variational methods for partition function calculations for Ising models without any assumptions on the potentials of the model. More precisely, we show that we can get approximation guarantees for the log-partition function comparable to those in the low-temperature limit, which is the setting of optimization of quadratic forms over the hypercube. ([AN06])


Trump vows to maintain 'maximum pressure' on North Korea

Al Jazeera

North Korea state media say Friday's summit with South Korea paves the way for a new era of peace and prosperity. But US President Donald Trump is vowing to maintain maximum pressure on Pyongyang until it gives up its nuclear weapons. His comments follow a historic declaration of peace from the North and South Korean leaders on Friday.