10,584 research outputs found
Optimal classical simulation of state-independent quantum contextuality
Simulating quantum contextuality with classical systems requires memory. A
fundamental yet open question is what is the minimum memory needed and,
therefore, the precise sense in which quantum systems outperform classical
ones. Here, we make rigorous the notion of classically simulating quantum
state-independent contextuality (QSIC) in the case of a single quantum system
submitted to an infinite sequence of measurements randomly chosen from a finite
QSIC set. We obtain the minimum memory needed to simulate arbitrary QSIC sets
via classical systems under the assumption that the simulation should not
contain any oracular information. In particular, we show that, while
classically simulating two qubits tested with the Peres-Mermin set requires
bits, simulating a single qutrit tested with the
Yu-Oh set requires, at least, bits.Comment: 7 pages, 4 figure
Fast Bayesian Optimization of Machine Learning Hyperparameters on Large Datasets
Bayesian optimization has become a successful tool for hyperparameter
optimization of machine learning algorithms, such as support vector machines or
deep neural networks. Despite its success, for large datasets, training and
validating a single configuration often takes hours, days, or even weeks, which
limits the achievable performance. To accelerate hyperparameter optimization,
we propose a generative model for the validation error as a function of
training set size, which is learned during the optimization process and allows
exploration of preliminary configurations on small subsets, by extrapolating to
the full dataset. We construct a Bayesian optimization procedure, dubbed
Fabolas, which models loss and training time as a function of dataset size and
automatically trades off high information gain about the global optimum against
computational cost. Experiments optimizing support vector machines and deep
neural networks show that Fabolas often finds high-quality solutions 10 to 100
times faster than other state-of-the-art Bayesian optimization methods or the
recently proposed bandit strategy Hyperband
Kernel Bayes' rule
A nonparametric kernel-based method for realizing Bayes' rule is proposed,
based on representations of probabilities in reproducing kernel Hilbert spaces.
Probabilities are uniquely characterized by the mean of the canonical map to
the RKHS. The prior and conditional probabilities are expressed in terms of
RKHS functions of an empirical sample: no explicit parametric model is needed
for these quantities. The posterior is likewise an RKHS mean of a weighted
sample. The estimator for the expectation of a function of the posterior is
derived, and rates of consistency are shown. Some representative applications
of the kernel Bayes' rule are presented, including Baysian computation without
likelihood and filtering with a nonparametric state-space model.Comment: 27 pages, 5 figure
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