Markov chain Monte Carlo (MCMC) is one of the main workhorses of probabilistic inference, but it is notoriously hard to measure the quality of approximate posterior samples. This challenge is particularly salient in black box inference methods, which can hide details and obscure inference failures. In this work, we extend the recently introduced bidirectional Monte Carlo [GGA15] technique to evaluate MCMC-based posterior inference algorithms. By running annealed importance sampling (AIS) chains both from prior to posterior and vice versa on simulated data, we upper bound in expectation the symmetrized KL divergence between the true posterior distribution and the distribution of approximate samples. We integrate our method into two probabilistic programming languages, WebPPL [GS] and Stan [CGHL+ p], and validate it on several models and datasets. As an example of how our method be used to guide the design of inference algorithms, we apply it to study the effectiveness of different model representations in WebPPL and Stan.

Many high-stakes applications require machine learning models that protect user privacy and provide well-calibrated, accurate predictions. While Differential Privacy (DP) is the gold standard for protecting user privacy, standard DP mechanisms typically significantly impair performance. One approach to mitigating this issue is pre-training models on simulated data before DP learning on the private data. In this work we go a step further, using simulated data to train a meta-learning model that combines the Convolutional Conditional Neural Process (ConvCNP) with an improved functional DP mechanism of Hall et al. (2013), yielding the DPConvCNP. DPConvCNP learns from simulated data how to map private data to a DP predictive model in one forward pass, and then provides accurate, well-calibrated predictions. We compare DPConvCNP with a DP Gaussian Process (GP) baseline with carefully tuned hyperparameters. The DPConvCNP outperforms the GP baseline, especially on non-Gaussian data, yet is much faster at test time and requires less tuning.

We study the consistency of the $k$-nearest neighbor regressor under complex survey designs. While consistency results for this algorithm are well established for independent and identically distributed data, corresponding results for complex survey data are lacking. We show that the $k$-nearest neighbor regressor is consistent under regularity conditions on the sampling design and the distribution of the data. We derive lower bounds for the rate of convergence and show that these bounds exhibit the curse of dimensionality, as in the independent and identically distributed setting. Empirical studies based on simulated and real data illustrate our theoretical findings.

Neural Information Processing Systems http://nips.cc/

Recently, Sur and Candès [2019] showed that these issues can be corrected by applying a new approximation of the MLE's sampling distribution in this highdimensional regime. Unfortunately, these corrections are difficult to implement in practice, because they require an estimate of thesignal strength, which is a function of the underlying parametersβ of the logistic regression.

Assuming that small spatial structures are more-or-less consistent across these measurements, these methods project to a local low-rank approximation of the data [37,31].

In recent years, model-free reinforcement learning (MFRL) has achieved tremendous success on a wide range of simulated domains, e .

Q1: ...the claim that the algorithm really manages to align the latent distributions of real and simulated data... We will revise the inappropriate statements in the final version. Q2: In the model adaptation phase, are state-action pairs simply sampled randomly from their respective buffers? Do you have results for a single, monolithic model? Q4: Did you investigate the reasons for the slow learning in the 500 steps on InvertedPendulum compared to PETS? Q1: The experiments shown in Figure 2 do not outperform MBPO beyond the confidence bounds.