Consider a setting where multiple parties holding sensitive data aim to collaboratively learn population level statistics, but pooling the sensitive data sets is not possible. We propose a framework in which each party shares a differentially private synthetic twin of their data. We study the feasibility of combining such synthetic twin data sets for collaborative learning on real-world health data from the UK Biobank. We discover that parties engaging in the collaborative learning via shared synthetic data obtain more accurate estimates of target statistics compared to using only their local data. This finding extends to the difficult case of small heterogeneous data sets. Furthermore, the more parties participate, the larger and more consistent the improvements become. Finally, we find that data sharing can especially help parties whose data contain underrepresented groups to perform better-adjusted analysis for said groups. Based on our results we conclude that sharing of synthetic twins is a viable method for enabling learning from sensitive data without violating privacy constraints even if individual data sets are small or do not represent the overall population well. The setting of distributed sensitive data is often a bottleneck in biomedical research, which our study shows can be alleviated with privacy-preserving collaborative learning methods.
Conditional Neural Processes (CNPs) are a class of metalearning models popular for combining the runtime efficiency of amortized inference with reliable uncertainty quantification. Many relevant machine learning tasks, such as spatio-temporal modeling, Bayesian Optimization and continuous control, contain equivariances -- for example to translation -- which the model can exploit for maximal performance. However, prior attempts to include equivariances in CNPs do not scale effectively beyond two input dimensions. In this work, we propose Relational Conditional Neural Processes (RCNPs), an effective approach to incorporate equivariances into any neural process model. Our proposed method extends the applicability and impact of equivariant neural processes to higher dimensions. We empirically demonstrate the competitive performance of RCNPs on a large array of tasks naturally containing equivariances.
Deep Ensembles (DEs) demonstrate improved accuracy, calibration and robustness to perturbations over single neural networks partly due to their functional diversity. Particle-based variational inference (ParVI) methods enhance diversity by formalizing a repulsion term based on a network similarity kernel. However, weight-space repulsion is inefficient due to over-parameterization, while direct function-space repulsion has been found to produce little improvement over DEs. To sidestep these difficulties, we propose First-order Repulsive Deep Ensemble (FoRDE), an ensemble learning method based on ParVI, which performs repulsion in the space of first-order input gradients. As input gradients uniquely characterize a function up to translation and are much smaller in dimension than the weights, this method guarantees that ensemble members are functionally different. Intuitively, diversifying the input gradients encourages each network to learn different features, which is expected to improve the robustness of an ensemble. Experiments on image classification datasets show that FoRDE significantly outperforms the gold-standard DEs and other ensemble methods in accuracy and calibration under covariate shift due to input perturbations.
Simulation-based inference (SBI) methods such as approximate Bayesian computation (ABC), synthetic likelihood, and neural posterior estimation (NPE) rely on simulating statistics to infer parameters of intractable likelihood models. However, such methods are known to yield untrustworthy and misleading inference outcomes under model misspecification, thus hindering their widespread applicability. In this work, we propose the first general approach to handle model misspecification that works across different classes of SBI methods. Leveraging the fact that the choice of statistics determines the degree of misspecification in SBI, we introduce a regularized loss function that penalises those statistics that increase the mismatch between the data and the model. Taking NPE and ABC as use cases, we demonstrate the superior performance of our method on high-dimensional time-series models that are artificially misspecified. We also apply our method to real data from the field of radio propagation where the model is known to be misspecified. We show empirically that the method yields robust inference in misspecified scenarios, whilst still being accurate when the model is well-specified.
Contextual Bayesian Optimization (CBO) is a powerful framework for optimizing black-box, expensive-to-evaluate functions with respect to design variables, while simultaneously efficiently integrating relevant contextual information regarding the environment, such as experimental conditions. However, in many practical scenarios, the relevance of contextual variables is not necessarily known beforehand. Moreover, the contextual variables can sometimes be optimized themselves, a setting that current CBO algorithms do not take into account. Optimizing contextual variables may be costly, which raises the question of determining a minimal relevant subset. In this paper, we frame this problem as a cost-aware model selection BO task and address it using a novel method, Sensitivity-Analysis-Driven Contextual BO (SADCBO). We learn the relevance of context variables by sensitivity analysis of the posterior surrogate model at specific input points, whilst minimizing the cost of optimization by leveraging recent developments on early stopping for BO. We empirically evaluate our proposed SADCBO against alternatives on synthetic experiments together with extensive ablation studies, and demonstrate a consistent improvement across examples.
Temporally indexed data are essential in a wide range of fields and of interest to machine learning researchers. Time series data, however, are often scarce or highly sensitive, which precludes the sharing of data between researchers and industrial organizations and the application of existing and new data-intensive ML methods. A possible solution to this bottleneck is to generate synthetic data. In this work, we introduce Time Series Generative Modeling (TSGM), an open-source framework for the generative modeling of synthetic time series. TSGM includes a broad repertoire of machine learning methods: generative models, probabilistic, and simulator-based approaches. The framework enables users to evaluate the quality of the produced data from different angles: similarity, downstream effectiveness, predictive consistency, diversity, and privacy. The framework is extensible, which allows researchers to rapidly implement their own methods and compare them in a shareable environment. TSGM was tested on open datasets and in production and proved to be beneficial in both cases. Additionally to the library, the project allows users to employ command line interfaces for synthetic data generation which lowers the entry threshold for those without a programming background.
The problem of model selection with a limited number of experimental trials has received considerable attention in cognitive science, where the role of experiments is to discriminate between theories expressed as computational models. Research on this subject has mostly been restricted to optimal experiment design with analytically tractable models. However, cognitive models of increasing complexity, with intractable likelihoods, are becoming more commonplace. In this paper, we propose BOSMOS: an approach to experimental design that can select between computational models without tractable likelihoods. It does so in a data-efficient manner, by sequentially and adaptively generating informative experiments. In contrast to previous approaches, we introduce a novel simulator-based utility objective for design selection, and a new approximation of the model likelihood for model selection. In simulated experiments, we demonstrate that the proposed BOSMOS technique can accurately select models in up to 2 orders of magnitude less time than existing LFI alternatives for three cognitive science tasks: memory retention, sequential signal detection and risky choice.
A natural solution concept for many multiagent settings is the Stackelberg equilibrium, under which a ``leader'' agent selects a strategy that maximizes its own payoff assuming the ``follower'' chooses their best response to this strategy. Recent work has presented asymmetric learning updates that can be shown to converge to the \textit{differential} Stackelberg equilibria of two-player differentiable games. These updates are ``coupled'' in the sense that the leader requires some information about the follower's payoff function. Such coupled learning rules cannot be applied to \textit{ad hoc} interactive learning settings, and can be computationally impractical even in centralized training settings where the follower's payoffs are known. In this work, we present an ``uncoupled'' learning process under which each player's learning update only depends on their observations of the other's behavior. We prove that this process converges to a local Stackelberg equilibrium under similar conditions as previous coupled methods. We conclude with a discussion of the potential applications of our approach to human--AI cooperation and multi-agent reinforcement learning.
Likelihood-free inference methods typically make use of a distance between simulated and real data. A common example is the maximum mean discrepancy (MMD), which has previously been used for approximate Bayesian computation, minimum distance estimation, generalised Bayesian inference, and within the nonparametric learning framework. The MMD is commonly estimated at a root-$m$ rate, where $m$ is the number of simulated samples. This can lead to significant computational challenges since a large $m$ is required to obtain an accurate estimate, which is crucial for parameter estimation. In this paper, we propose a novel estimator for the MMD with significantly improved sample complexity. The estimator is particularly well suited for computationally expensive smooth simulators with low- to mid-dimensional inputs. This claim is supported through both theoretical results and an extensive simulation study on benchmark simulators.
Probabilistic user modeling is essential for building collaborative AI systems within probabilistic frameworks. However, modern advanced user models, often designed as cognitive behavior simulators, are computationally prohibitive for interactive use in cooperative AI assistants. In this extended abstract, we address this problem by introducing widely-applicable differentiable surrogates for bypassing this computational bottleneck; the surrogates enable using modern behavioral models with online computational cost which is independent of their original computational cost. We show experimentally that modeling capabilities comparable to likelihood-free inference methods are achievable, with over eight orders of magnitude reduction in computational time. Finally, we demonstrate how AI-assistants can computationally feasibly use cognitive models in a previously studied menu-search task.