We consider shared workspace scenarios with humans and robots acting to achieve independent goals, termed as parallel play. We model these as general-sum games and construct a framework that utilizes the Nash equilibrium solution concept to consider the interactive effect of both agents while planning. We find multiple Pareto-optimal equilibria in these tasks. We hypothesize that people act by choosing an equilibrium based on social norms and their personalities. To enable coordination, we infer the equilibrium online using a probabilistic model that includes these two factors and use it to select the robot's action. We apply our approach to a close-proximity pick-and-place task involving a robot and a simulated human with three potential behaviors - defensive, selfish, and norm-following. We showed that using a Bayesian approach to infer the equilibrium enables the robot to complete the task with less than half the number of collisions while also reducing the task execution time as compared to the best baseline. We also performed a study with human participants interacting either with other humans or with different robot agents and observed that our proposed approach performs similar to human-human parallel play interactions. The code is available at https://github.com/shray/bayes-nash

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.

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 present CRISP (COVID-19 Risk Score Prediction), a probabilistic graphical model for COVID-19 infection spread through a population based on the SEIR model where we assume access to (1) mutual contacts between pairs of individuals across time across various channels (e.g., Bluetooth contact traces), as well as (2) test outcomes at given times for infection, exposure and immunity tests. Our micro-level model keeps track of the infection state for each individual at every point in time, ranging from susceptible, exposed, infectious to recovered. We develop a Monte Carlo EM algorithm to infer contact-channel specific infection transmission probabilities. Our algorithm uses Gibbs sampling to draw samples of the latent infection status of each individual over the entire time period of analysis, given the latent infection status of all contacts and test outcome data. Experimental results with simulated data demonstrate our CRISP model can be parametrized by the reproduction factor $R_0$ and exhibits population-level infectiousness and recovery time series similar to those of the classical SEIR model. However, due to the individual contact data, this model allows fine grained control and inference for a wide range of COVID-19 mitigation and suppression policy measures. Moreover, the algorithm is able to support efficient testing in a test-trace-isolate approach to contain COVID-19 infection spread. To the best of our knowledge, this is the first model with efficient inference for COVID-19 infection spread based on individual-level contact data; most epidemic models are macro-level models that reason over entire populations. The implementation of CRISP is available in Python and C++ at https://github.com/zalandoresearch/CRISP.

We detect out-of-training-distribution sentences in Neural Machine Translation using the Bayesian Deep Learning equivalent of Transformer models. For this we develop a new measure of uncertainty designed specifically for long sequences of discrete random variables -- i.e. words in the output sentence. Our new measure of uncertainty solves a major intractability in the naive application of existing approaches on long sentences. We use our new measure on a Transformer model trained with dropout approximate inference. On the task of German-English translation using WMT13 and Europarl, we show that with dropout uncertainty our measure is able to identify when Dutch source sentences, sentences which use the same word types as German, are given to the model instead of German.

In this paper, we employ variational arguments to establish a connection between ensemble methods for Neural Networks and Bayesian inference. We consider an ensemble-based scheme where each model/particle corresponds to a perturbation of the data by means of parametric bootstrap and a perturbation of the prior. We derive conditions under which any optimization steps of the particles makes the associated distribution reduce its divergence to the posterior over model parameters. Such conditions do not require any particular form for the approximation and they are purely geometrical, giving insights on the behavior of the ensemble on a number of interesting models such as Neural Networks with ReLU activations. Experiments confirm that ensemble methods can be a valid alternative to approximate Bayesian inference; the theoretical developments in the paper seek to explain this behavior.