Sequential Kernelized Stein Discrepancy

We present a sequential version of the kernelized Stein discrepancy, which allows for conducting goodness-of-fit tests for unnormalized densities that are continuously monitored and adaptively stopped. That is, the sample size need not be fixed prior to data collection; the practitioner can choose whether to stop the test or continue to gather evidence at any time while controlling the false discovery rate. In stark contrast to related literature, we do not impose uniform boundedness on the Stein kernel. Instead, we exploit the potential boundedness of the Stein kernel at arbitrary point evaluations to define test martingales, that give way to the subsequent novel sequential tests. We prove the validity of the test, as well as an asymptotic lower bound for the logarithmic growth of the wealth process under the alternative. We further illustrate the empirical performance of the test with a variety of distributions, including restricted Boltzmann machines.

An Efficient Doubly-Robust Test for the Kernel Treatment Effect

The average treatment effect, which is the difference in expectation of the counterfactuals, is probably the most popular target effect in causal inference with binary treatments. However, treatments may have effects beyond the mean, for instance decreasing or increasing the variance. We propose a new kernel-based test for distributional effects of the treatment. It is, to the best of our knowledge, the first kernel-based, doubly-robust test with provably valid type-I error. Furthermore, our proposed algorithm is efficient, avoiding the use of permutations.

Bayesian Counterfactual Mean Embeddings and Off-Policy Evaluation

The counterfactual distribution models the effect of the treatment in the untreated group. While most of the work focuses on the expected values of the treatment effect, one may be interested in the whole counterfactual distribution or other quantities associated to it. Building on the framework of Bayesian conditional mean embeddings, we propose a Bayesian approach for modeling the counterfactual distribution, which leads to quantifying the epistemic uncertainty about the distribution. The framework naturally extends to the setting where one observes multiple treatment effects (e.g. an intermediate effect after an interim period, and an ultimate treatment effect which is of main interest) and allows for additionally modelling uncertainty about the relationship of these effects. For such goal, we present three novel Bayesian methods to estimate the expectation of the ultimate treatment effect, when only noisy samples of the dependence between intermediate and ultimate effects are provided. These methods differ on the source of uncertainty considered and allow for combining two sources of data. Moreover, we generalize these ideas to the off-policy evaluation framework, which can be seen as an extension of the counterfactual estimation problem. We empirically explore the calibration of the algorithms in two different experimental settings which require data fusion, and illustrate the value of considering the uncertainty stemming from the two sources of data.

Sequential Decision Making on Unmatched Data using Bayesian Kernel Embeddings

The problem of sequentially maximizing the expectation of a function seeks to maximize the expected value of a function of interest without having direct control on its features. Instead, the distribution of such features depends on a given context and an action taken by an agent. In contrast to Bayesian optimization, the arguments of the function are not under agent's control, but are indirectly determined by the agent's action based on a given context. If the information of the features is to be included in the maximization problem, the full conditional distribution of such features, rather than its expectation only, needs to be accounted for. Furthermore, the function is itself unknown, only counting with noisy observations of such function, and potentially requiring the use of unmatched data sets. We propose a novel algorithm for the aforementioned problem which takes into consideration the uncertainty derived from the estimation of both the conditional distribution of the features and the unknown function, by modeling the former as a Bayesian conditional mean embedding and the latter as a Gaussian process. Our algorithm empirically outperforms the current state-of-the-art algorithm in the experiments conducted.