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Adaptively Setting Path Lengths in Hamiltonian Monte Carlo Hamiltonian Monte Carlo (HMC) is a Markov Chain Monte Carlo (MCMC) algorithm that avoids the random walk behavior and sensitivity to correlations that plague many MCMC methods by taking a series of steps informed by first-order gradient information. These features allow it to converge to high-dimensional target distributions much more quickly than popular methods such as random walk Metropolis or Gibbs sampling. However, HMC's performance is highly sensitive to two user-specified parameters: a step size $\epsilon$ and a desired number of steps $L$. In particular, if $L$ is too small then the algorithm exhibits undesirable random walk behavior, while if $L$ is too large the algorithm wastes computation. We present the No-U-Turn Sampler (NUTS), an extension to HMC that eliminates the need to set a number of steps $L$. NUTS uses a recursive algorithm to build a set of likely candidate points that spans a wide swath of the target distribution, stopping automatically when it starts to double back and retrace its steps. NUTS is able to achieve similar performance to a well tuned standard HMC method, without requiring user intervention or costly tuning runs. NUTS can thus be used in applications such as BUGS-style automatic inference engines that require efficient "turnkey'' sampling algorithms.
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