Merging datasets across institutions is a lengthy and costly procedure, especially when it involves private information. Data hosts may therefore want to prospectively gauge which datasets are most beneficial to merge with, without revealing sensitive information. For causal estimation this is particularly challenging as the value of a merge depends not only on reduction in epistemic uncertainty but also on improvement in overlap. To address this challenge, we introduce the first \emph{cryptographically secure} information-theoretic approach for quantifying the value of a merge in the context of heterogeneous treatment effect estimation. We do this by evaluating the \emph{Expected Information Gain} (EIG) using multi-party computation to ensure that no raw data is revealed. We further demonstrate that our approach can be combined with differential privacy (DP) to meet arbitrary privacy requirements whilst preserving more accurate computation compared to DP alone. To the best of our knowledge, this work presents the first privacy-preserving method for dataset acquisition tailored to causal estimation.Code is publicly available: \url{https://github.com/LucileTerminassian/causal_prospective_merge}.

We develop a semi-amortized, policy-based, approach to Bayesian experimental design (BED) called Stepwise Deep Adaptive Design (Step-DAD). Like existing, fully amortized, policy-based BED approaches, Step-DAD trains a design policy upfront before the experiment. However, rather than keeping this policy fixed, Step-DAD periodically updates it as data is gathered, refining it to the particular experimental instance. This test-time adaptation improves both the flexibility and the robustness of the design strategy compared with existing approaches. Empirically, Step-DAD consistently demonstrates superior decision-making and robustness compared with current state-of-the-art BED methods.

We propose a method to improve the efficiency and accuracy of amortized Bayesian inference by leveraging universal symmetries in the joint probabilistic model of parameters and data. In a nutshell, we invert Bayes’ theorem and estimate the marginal likelihood based on approximate representations of the joint model. Upon perfect approximation, the marginal likelihood is constant across all parameter values by definition. However, errors in approximate inference lead to undesirable variance in the marginal likelihood estimates across different parameter values. We penalize violations of this symmetry with a self-consistency loss which significantly improves the quality of approximate inference in low data regimes and can be used to augment the training of popular neural density estimators. We apply our method to a number of synthetic problems and realistic scientific models, discovering notable advantages in the context of both neural posterior and likelihood approximation.

We formalize the problem of contextual optimization through the lens of Bayesian experimental design and propose CO-BED---a general, model-agnostic framework for designing contextual experiments using information-theoretic principles. After formulating a suitable information-based objective, we employ black-box variational methods to simultaneously estimate it and optimize the designs in a single stochastic gradient scheme. In addition, to accommodate discrete actions within our framework, we propose leveraging continuous relaxation schemes, which can naturally be integrated into our variational objective. As a result, CO-BED provides a general and automated solution to a wide range of contextual optimization problems. We illustrate its effectiveness in a number of experiments, where CO-BED demonstrates competitive performance even when compared to bespoke, model-specific alternatives.

We introduce a gradient-based approach for the problem of Bayesian optimal experimental design to learn causal models in a batch setting --- a critical component for causal discovery from finite data where interventions can be costly or risky. Existing methods rely on greedy approximations to construct a batch of experiments while using black-box methods to optimize over a *single target-state* pair to intervene with. In this work, we completely dispose of the black-box optimization techniques and greedy heuristics and instead propose a conceptually simple end-to-end gradient-based optimization procedure to acquire a set of optimal intervention target-value pairs. Such a procedure enables parameterization of the design space to efficiently optimize over a batch of *multi-target-state* interventions, a setting which has hitherto not been explored due to its complexity. We demonstrate that our proposed method outperforms baselines and existing acquisition strategies in both single-target and multi-target settings across a number of synthetic datasets.

We introduce Deep Adaptive Design (DAD), a method for amortizing the cost of adaptive Bayesian experimental design that allows experiments to be run in real-time. Traditional sequential Bayesian optimal experimental design approaches require substantial computation at each stage of the experiment. This makes them unsuitable for most real-world applications, where decisions must typically be made quickly. DAD addresses this restriction by learning an amortized design network upfront and then using this to rapidly run (multiple) adaptive experiments at deployment time. This network represents a design policy which takes as input the data from previous steps, and outputs the next design using a single forward pass; these design decisions can be made in milliseconds during the live experiment. To train the network, we introduce contrastive information bounds that are suitable objectives for the sequential setting, and propose a customized network architecture that exploits key symmetries. We demonstrate that DAD successfully amortizes the process of experimental design, outperforming alternative strategies on a number of problems.

We introduce implicit Deep Adaptive Design (iDAD), a new method for performing adaptive experiments in real-time with implicit models. iDAD amortizes the cost of Bayesian optimal experimental design (BOED) by learning a design policy network upfront, which can then be deployed quickly at the time of the experiment. The iDAD network can be trained on any model which simulates differentiable samples, unlike previous design policy work that requires a closed form likelihood and conditionally independent experiments. At deployment, iDAD allows design decisions to be made in milliseconds, in contrast to traditional BOED approaches that require heavy computation during the experiment itself. We illustrate the applicability of iDAD on a number of experiments, and show that it provides a fast and effective mechanism for performing adaptive design with implicit models.