597 research outputs found
Intractability of approximate multi-dimensional nonlinear optimization on independence systems
We consider optimization of nonlinear objective functions that balance
linear criteria over -element independence systems presented by
linear-optimization oracles. For , we have previously shown that an
-best approximate solution can be found in polynomial time. Here, using an
extended Erd\H{o}s-Ko-Rado theorem of Frankl, we show that for , finding a
-best solution requires exponential time
K2-ABC: Approximate Bayesian Computation with Kernel Embeddings
Complicated generative models often result in a situation where computing the
likelihood of observed data is intractable, while simulating from the
conditional density given a parameter value is relatively easy. Approximate
Bayesian Computation (ABC) is a paradigm that enables simulation-based
posterior inference in such cases by measuring the similarity between simulated
and observed data in terms of a chosen set of summary statistics. However,
there is no general rule to construct sufficient summary statistics for complex
models. Insufficient summary statistics will "leak" information, which leads to
ABC algorithms yielding samples from an incorrect (partial) posterior. In this
paper, we propose a fully nonparametric ABC paradigm which circumvents the need
for manually selecting summary statistics. Our approach, K2-ABC, uses maximum
mean discrepancy (MMD) as a dissimilarity measure between the distributions
over observed and simulated data. MMD is easily estimated as the squared
difference between their empirical kernel embeddings. Experiments on a
simulated scenario and a real-world biological problem illustrate the
effectiveness of the proposed algorithm
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