2,139 research outputs found
A trust-region method for stochastic variational inference with applications to streaming data
Stochastic variational inference allows for fast posterior inference in
complex Bayesian models. However, the algorithm is prone to local optima which
can make the quality of the posterior approximation sensitive to the choice of
hyperparameters and initialization. We address this problem by replacing the
natural gradient step of stochastic varitional inference with a trust-region
update. We show that this leads to generally better results and reduced
sensitivity to hyperparameters. We also describe a new strategy for variational
inference on streaming data and show that here our trust-region method is
crucial for getting good performance.Comment: in Proceedings of the 32nd International Conference on Machine
Learning, 201
The threshold for integer homology in random d-complexes
Let Y ~ Y_d(n,p) denote the Bernoulli random d-dimensional simplicial
complex. We answer a question of Linial and Meshulam from 2003, showing that
the threshold for vanishing of homology H_{d-1}(Y; Z) is less than 80d log n /
n. This bound is tight, up to a constant factor.Comment: 12 pages, updated to include an additional torsion group boun
Recurrence and transience for the frog model on trees
The frog model is a growing system of random walks where a particle is added
whenever a new site is visited. A longstanding open question is how often the
root is visited on the infinite -ary tree. We prove the model undergoes a
phase transition, finding it recurrent for and transient for .
Simulations suggest strong recurrence for , weak recurrence for , and
transience for . Additionally, we prove a 0-1 law for all -ary
trees, and we exhibit a graph on which a 0-1 law does not hold.
To prove recurrence when , we construct a recursive distributional
equation for the number of visits to the root in a smaller process and show the
unique solution must be infinity a.s. The proof of transience when relies
on computer calculations for the transition probabilities of a large Markov
chain. We also include the proof for , which uses similar techniques
but does not require computer assistance.Comment: 24 pages, 8 figures to appear in Annals of Probabilit
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