A new class of Markov chain Monte Carlo (MCMC) algorithms, based on simulating piecewise deterministic Markov processes (PDMPs), have recently shown great promise: they are non-reversible, can mix better than standard MCMC algorithms, and can use subsampling ideas to speed up computation in big data scenarios. However, current PDMP samplers can only sample from posterior densities that are differentiable almost everywhere, which precludes their use for model choice. Motivated by variable selection problems, we show how to develop reversible jump PDMP samplers that can jointly explore the discrete space of models and the continuous space of parameters. Our framework is general: it takes any existing PDMP sampler, and adds two types of trans-dimensional moves that allow for the addition or removal of a variable from the model. We show how the rates of these trans-dimensional moves can be calculated so that the sampler has the correct invariant distribution. Simulations show that the new samplers can mix better than standard MCMC algorithms. Our empirical results show they are also more efficient than gradient-based samplers that avoid model choice through use of continuous spike-and-slab priors which replace a point mass at zero for each parameter with a density concentrated around zero.

Variational Bayes (VB) is a popular scalable alternative to Markov chain Monte Carlo for Bayesian inference. We study a mean-field spike and slab VB approximation of widely used Bayesian model selection priors in sparse high-dimensional logistic regression. We provide non-asymptotic theoretical guarantees for the VB posterior in both $\ell_2$ and prediction loss for a sparse truth, giving optimal (minimax) convergence rates. Since the VB algorithm does not depend on the unknown truth to achieve optimality, our results shed light on effective prior choices. We confirm the improved performance of our VB algorithm over common sparse VB approaches in a numerical study.

We study high-confidence behavior-agnostic off-policy evaluation in reinforcement learning, where the goal is to estimate a confidence interval on a target policy's value, given only access to a static experience dataset collected by unknown behavior policies. Starting from a function space embedding of the linear program formulation of the $Q$-function, we obtain an optimization problem with generalized estimating equation constraints. By applying the generalized empirical likelihood method to the resulting Lagrangian, we propose CoinDICE, a novel and efficient algorithm for computing confidence intervals. Theoretically, we prove the obtained confidence intervals are valid, in both asymptotic and finite-sample regimes. Empirically, we show in a variety of benchmarks that the confidence interval estimates are tighter and more accurate than existing methods.

Overfitting data is a well-known phenomenon related with the generation of a model that mimics too closely (or exactly) a particular instance of data, and may therefore fail to predict future observations reliably. In practice, this behaviour is controlled by various--sometimes heuristics--regularization techniques, which are motivated by developing upper bounds to the generalization error. In this work, we study the generalization error of classifiers relying on stochastic encodings trained on the cross-entropy loss, which is often used in deep learning for classification problems. We derive bounds to the generalization error showing that there exists a regime where the generalization error is bounded by the mutual information between input features and the corresponding representations in the latent space, which are randomly generated according to the encoding distribution. Our bounds provide an information-theoretic understanding of generalization in the so-called class of variational classifiers, which are regularized by a Kullback-Leibler (KL) divergence term. These results give theoretical grounds for the highly popular KL term in variational inference methods that was already recognized to act effectively as a regularization penalty. We further observe connections with well studied notions such as Variational Autoencoders, Information Dropout, Information Bottleneck and Boltzmann Machines. Finally, we perform numerical experiments on MNIST and CIFAR datasets and show that mutual information is indeed highly representative of the behaviour of the generalization error.

We present a framework to derive bounds on the test loss of randomized learning algorithms for the case of bounded loss functions. This framework leads to bounds that depend on the conditional information density between the the output hypothesis and the choice of the training set, given a larger set of data samples from which the training set is formed. If the conditional information density is bounded uniformly in the sizenof the training set, our bounds decay as1/n, which is referred to as a fast rate. This is in contrast with the tail bounds involving conditional information measures available in the literature, which have a less benign 1/ n dependence. We demonstrate the usefulness of our tail bounds by showing that they lead to estimates of the test loss achievable with several neural network architectures trained on MNIST and Fashion-MNIST that match the state-of-the-art bounds available in the literature. In recent years, there has been a surge of interest in the use of information-theoretic techniques for bounding the loss of learning algorithms. While the first results of this flavor can be traced to the probably approximately correct (PAC)-Bayesian approach (McAllester, 1998; Catoni, 2007) (see also (Guedj, 2019) for a recent review), the connection between loss bounds and classical information-theoretic measures was made explicit in the works of Russo & Zou (2016) and Xu & Raginsky (2017), where bounds on the average population loss were derived in terms of the mutual information between the training data and the output hypothesis. Since then, these average loss bounds have been tightened (Bu et al., 2019; Asadi et al., 2018; Negrea et al., 2019). Furthermore, the information-theoretic framework has also been successfully applied to derive tail probability bounds on the population loss (Bassily et al., 2018; Esposito et al., 2019; Hellström & Durisi, 2020a). Of particular relevance to the present paper is the random-subset setting, introduced by Steinke & Zakynthinou (2020) and further studied in (Hellström & Durisi, 2020b; Haghifam et al., 2020).

Machine learning is increasingly being used to generate prediction models for use in a number of real-world settings, from credit risk assessment to clinical decision support. Recent discussions have highlighted potential problems in the updating of a predictive score for a binary outcome when an existing predictive score forms part of the standard workflow, driving interventions. In this setting, the existing score induces an additional causative pathway which leads to miscalibration when the original score is replaced. We propose a general causal framework to describe and address this problem, and demonstrate an equivalent formulation as a partially observed Markov decision process. We use this model to demonstrate the impact of such `naive updating' when performed repeatedly. Namely, we show that successive predictive scores may converge to a point where they predict their own effect, or may eventually oscillate between two values, and we argue that neither outcome is desirable. Furthermore, we demonstrate that even if model-fitting procedures improve, actual performance may worsen. We complement these findings with a discussion of several potential routes to overcome these problems.

QMIX is a popular $Q$-learning algorithm for cooperative MARL in the centralised training and decentralised execution paradigm. In order to enable easy decentralisation, QMIX restricts the joint action $Q$-values it can represent to be a monotonic mixing of each agent's utilities. However, this restriction prevents it from representing value functions in which an agent's ordering over its actions can depend on other agents' actions. To analyse this representational limitation, we first formalise the objective QMIX optimises, which allows us to view QMIX as an operator that first computes the $Q$-learning targets and then projects them into the space representable by QMIX. This projection returns a representable $Q$-value that minimises the unweighted squared error across all joint actions. We show in particular that this projection can fail to recover the optimal policy even with access to $Q^*$, which primarily stems from the equal weighting placed on each joint action. We rectify this by introducing a weighting into the projection, in order to place more importance on the better joint actions. We propose two weighting schemes and prove that they recover the correct maximal action for any joint action $Q$-values, and therefore for $Q^*$ as well. Based on our analysis and results in the tabular setting, we introduce two scalable versions of our algorithm, Centrally-Weighted (CW) QMIX and Optimistically-Weighted (OW) QMIX and demonstrate improved performance on both predator-prey and challenging multi-agent StarCraft benchmark tasks.

Accurate estimation of aleatoric and epistemic uncertainty is crucial to build safe and reliable systems. Traditional approaches, such as dropout and ensemble methods, estimate uncertainty by sampling probability predictions from different submodels, which leads to slow uncertainty estimation at inference time. Recent works address this drawback by directly predicting parameters of prior distributions over the probability predictions with a neural network. While this approach has demonstrated accurate uncertainty estimation, it requires defining arbitrary target parameters for in-distribution data and makes the unrealistic assumption that out-of-distribution (OOD) data is known at training time. In this work we propose the Posterior Network (PostNet), which uses Normalizing Flows to predict an individual closed-form posterior distribution over predicted probabilites for any input sample. The posterior distributions learned by PostNet accurately reflect uncertainty for in- and out-of-distribution data -- without requiring access to OOD data at training time. PostNet achieves state-of-the art results in OOD detection and in uncertainty calibration under dataset shifts.

Approximate Bayesian computation (ABC) is a likelihood-free inference method that has been employed in various applications. However, ABC is sensitive to outliers, which is caused by an inappropriate choice of the data discrepancy measure. In this paper, we propose to use a nearest-neighbor-based $\gamma$-divergence estimator as a data discrepancy measure. We show that our estimator possesses a suitable robustness property called the redescending property. In addition, our estimator enjoys various desirable properties such as high flexibility, asymptotic unbiasedness, almost sure convergence, and linear time complexity. Through experiments, we demonstrate that our method achieves significantly higher robustness than existing discrepancy measures.

The migration of conversational AI agents across different embodiments in order to maintain the continuity of the task has been recently explored to further improve user experience. However, these migratable agents lack contextual understanding of the user information and the migrated device during the dialog conversations with the user. This opens the question of how an agent might behave when migrated into an embodiment for contextually predicting the next utterance. We collected a dataset from the dialog conversations between crowdsourced workers with the migration context involving personal and non-personal utterances in different settings (public or private) of embodiment into which the agent migrated. We trained the generative and information retrieval models on the dataset using with and without migration context and report the results of both qualitative metrics and human evaluation. We believe that the migration dataset would be useful for training future migratable AI systems.