24,866 research outputs found
Bayesian Learning of Sum-Product Networks
Sum-product networks (SPNs) are flexible density estimators and have received
significant attention due to their attractive inference properties. While
parameter learning in SPNs is well developed, structure learning leaves
something to be desired: Even though there is a plethora of SPN structure
learners, most of them are somewhat ad-hoc and based on intuition rather than a
clear learning principle. In this paper, we introduce a well-principled
Bayesian framework for SPN structure learning. First, we decompose the problem
into i) laying out a computational graph, and ii) learning the so-called scope
function over the graph. The first is rather unproblematic and akin to neural
network architecture validation. The second represents the effective structure
of the SPN and needs to respect the usual structural constraints in SPN, i.e.
completeness and decomposability. While representing and learning the scope
function is somewhat involved in general, in this paper, we propose a natural
parametrisation for an important and widely used special case of SPNs. These
structural parameters are incorporated into a Bayesian model, such that
simultaneous structure and parameter learning is cast into monolithic Bayesian
posterior inference. In various experiments, our Bayesian SPNs often improve
test likelihoods over greedy SPN learners. Further, since the Bayesian
framework protects against overfitting, we can evaluate hyper-parameters
directly on the Bayesian model score, waiving the need for a separate
validation set, which is especially beneficial in low data regimes. Bayesian
SPNs can be applied to heterogeneous domains and can easily be extended to
nonparametric formulations. Moreover, our Bayesian approach is the first, which
consistently and robustly learns SPN structures under missing data.Comment: NeurIPS 2019; See conference page for supplemen
Learning an Approximate Model Predictive Controller with Guarantees
A supervised learning framework is proposed to approximate a model predictive
controller (MPC) with reduced computational complexity and guarantees on
stability and constraint satisfaction. The framework can be used for a wide
class of nonlinear systems. Any standard supervised learning technique (e.g.
neural networks) can be employed to approximate the MPC from samples. In order
to obtain closed-loop guarantees for the learned MPC, a robust MPC design is
combined with statistical learning bounds. The MPC design ensures robustness to
inaccurate inputs within given bounds, and Hoeffding's Inequality is used to
validate that the learned MPC satisfies these bounds with high confidence. The
result is a closed-loop statistical guarantee on stability and constraint
satisfaction for the learned MPC. The proposed learning-based MPC framework is
illustrated on a nonlinear benchmark problem, for which we learn a neural
network controller with guarantees.Comment: 6 pages, 3 figures, to appear in IEEE Control Systems Letter
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