A fundamental difficulty of causal learning is that causal models can generally not be fully identified based on observational data only. Interventional data, that is, data originating from different experimental environments, improves identifiability. However, the improvement depends critically on the target and nature of the interventions carried out in each experiment. Since in real applications experiments tend to be costly, there is a need to perform the right interventions such that as few as possible are required. In this work we propose a new active learning (i.e. experiment selection) framework (A-ICP) based on Invariant Causal Prediction (ICP) (Peters et al., 2016). For general structural causal models, we characterize the effect of interventions on so-called stable sets, a notion introduced by (Pfister et al., 2019). We leverage these results to propose several intervention selection policies for A-ICP which quickly reveal the direct causes of a response variable in the causal graph while maintaining the error control inherent in ICP. Empirically, we analyze the performance of the proposed policies in both population and finite-regime experiments.

When modelling real-valued sequences, a typical approach in current RNN architectures is to use a Gaussian mixture model to describe the conditional output distribution. In this paper, we argue that mixture-based distributions could exhibit structural limitations when faced with highly complex data distributions such as for spatial densities. To address this issue, we introduce recurrent flow networks which combine deterministic and stochastic recurrent hidden states with conditional normalizing flows to form a probabilistic neural generative model capable of describing the kind of variability observed in highly structured spatio-temporal data. Inspired by the model's factorization, we further devise a structured variational inference network to approximate the intractable posterior distribution by exploiting a spatial representation of the data. We empirically evaluate our model against other generative models for sequential data on three real-world datasets for the task of spatio-temporal transportation demand modelling. Results show how the added flexibility allows our model to generate distributions matching potentially complex urban topologies.

Continual Learning (CL) algorithms incrementally learn a predictor or representation across multiple sequentially observed tasks. Designing CL algorithms that perform reliably and avoid so-called catastrophic forgetting has proven a persistent challenge. The current paper develops a theoretical approach that explains why. In particular, we derive the computational properties which CL algorithms would have to possess in order to avoid catastrophic forgetting. Our main finding is that such optimal CL algorithms generally solve an NP-hard problem and will require perfect memory to do so. The findings are of theoretical interest, but also explain the excellent performance of CL algorithms using experience replay, episodic memory and core sets relative to regularization-based approaches.

In this paper, we focus on the problem of stable prediction across unknown test data, where the test distribution is agnostic and might be totally different from the training one. In such a case, previous machine learning methods might exploit subtly spurious correlations in training data induced by non-causal variables for prediction. Those spurious correlations are changeable across data, leading to instability of prediction across data. By assuming the relationships between causal variables and response variable are invariant across data, to address this problem, we propose a conditional independence test based algorithm to separate those causal variables with a seed variable as priori, and adopt them for stable prediction. By assuming the independence between causal and non-causal variables, we show, both theoretically and with empirical experiments, that our algorithm can precisely separate causal and non-causal variables for stable prediction across test data. Extensive experiments on both synthetic and real-world datasets demonstrate that our algorithm outperforms state-of-the-art methods for stable prediction.

Canonical Correlation Analysis (CCA) is a statistical technique used to extract common information from multiple data sources or views. It has been used in various representation learning problems, such as dimensionality reduction, word embedding, and clustering. Recent work has given CCA probabilistic footing in a deep learning context and uses a variational lower bound for the data log likelihood to estimate model parameters. Alternatively, adversarial techniques have arisen in recent years as a powerful alternative to variational Bayesian methods in autoencoders. In this work, we explore straightforward adversarial alternatives to recent work in Deep Variational CCA (VCCA and VCCA-Private) we call ACCA and ACCA-Private and show how these approaches offer a stronger and more flexible way to match the approximate posteriors coming from encoders to much larger classes of priors than the VCCA and VCCA-Private models. This allows new priors for what constitutes a good representation, such as disentangling underlying factors of variation, to be more directly pursued. We offer further analysis on the multi-level disentangling properties of VCCA-Private and ACCA-Private through the use of a newly designed dataset we call Tangled MNIST. We also design a validation criteria for these models that is theoretically grounded, task-agnostic, and works well in practice. Lastly, we fill a minor research gap by deriving an additional variational lower bound for VCCA that allows the representation to use view-specific information from both input views.

Loss-based clustering methods, such as k-means and its variants, are standard tools for finding groups in data. However, the lack of quantification of uncertainty in the estimated clusters is a disadvantage. Model-based clustering based on mixture models provides an alternative, but such methods face computational problems and large sensitivity to the choice of kernel. This article proposes a generalized Bayes framework that bridges between these two paradigms through the use of Gibbs posteriors. In conducting Bayesian updating, the log likelihood is replaced by a loss function for clustering, leading to a rich family of clustering methods. The Gibbs posterior represents a coherent updating of Bayesian beliefs without needing to specify a likelihood for the data, and can be used for characterizing uncertainty in clustering. We consider losses based on Bregman divergence and pairwise similarities, and develop efficient deterministic algorithms for point estimation along with sampling algorithms for uncertainty quantification. Several existing clustering algorithms, including k-means, can be interpreted as generalized Bayes estimators under our framework, and hence we provide a method of uncertainty quantification for these approaches.

Learning theory mostly addresses the standard learning paradigm, assuming the availability of complete and correct supervision signals for large amounts of data. However, in practice, machine learning researchers and practitioners acquire and make use of a range of {\em incidental supervision} signals that only have statistical associations with the gold supervision. This paper addresses the question: {\em Can one quantify models' performance when learning with such supervision signals, without going through an exhaustive experimentation process with various supervision signals and learning protocols?} To quantify the benefits of various incidental supervision signals, we propose a unified PAC-Bayesian Informativeness measure (PABI), characterizing the reduction in uncertainty that incidental supervision signals provide. We then demonstrate PABI's use in quantifying various types of incidental signals such as partial labels, noisy labels, constraints, cross-domain signals, and some combinations of these. Experiments on named entity recognition and question answering show that PABI correlates well with learning performance, providing a promising way to determine, ahead of learning, which supervision signals would be beneficial.

This paper proposes Variational Auto-Regressive Gaussian Process (VAR-GP), a principled Bayesian updating mechanism to incorporate new data for sequential tasks in the context of continual learning. It relies on a novel auto-regressive characterization of the variational distribution and inference is made scalable using sparse inducing point approximations. Experiments on standard continual learning benchmarks demonstrate the ability of VAR-GPs to perform well at new tasks without compromising performance on old ones, yielding competitive results to state-of-the-art methods. In addition, we qualitatively show how VAR-GP improves the predictive entropy estimates as we train on new tasks. Further, we conduct a thorough ablation study to verify the effectiveness of inferential choices.

Small disturbances can trigger functional breakdowns in complex systems. A challenging task is to infer the structural cause of a disturbance in a networked system, soon enough to prevent a catastrophe. We present a graph neural network approach, borrowed from the deep learning paradigm, to infer structural perturbations from functional time series. We show our data-driven approach outperforms typical reconstruction methods while meeting the accuracy of Bayesian inference. We validate the versatility and performance of our approach with epidemic spreading, population dynamics, and neural dynamics, on various network structures: random networks, scale-free networks, 25 real food-web systems, and the C. Elegans connectome. Moreover, we report that our approach is robust to data corruption. This work uncovers a practical avenue to study the resilience of real-world complex systems.

We study a contextual bandit setting where the learning agent has access to sampled bandit instances from an unknown prior distribution $\mathcal{P}$. The goal of the agent is to achieve high reward on average over the instances drawn from $\mathcal{P}$. This setting is of a particular importance because it formalizes the offline optimization of bandit policies, to perform well on average over anticipated bandit instances. The main idea in our work is to optimize differentiable bandit policies by policy gradients. We derive reward gradients that reflect the structure of our problem, and propose contextual policies that are parameterized in a differentiable way and have low regret. Our algorithmic and theoretical contributions are supported by extensive experiments that show the importance of baseline subtraction, learned biases, and the practicality of our approach on a range of classification tasks.