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.

This paper proposes an online learning method of Gaussian process state-space model (GP-SSM). GP-SSM is a probabilistic representation learning scheme that represents unknown state transition and/or measurement models as Gaussian processes (GPs). While the majority of prior literature on learning of GP-SSM are focused on processing a given set of time series data, data may arrive and accumulate sequentially over time in most dynamical systems. Storing all such sequential data and updating the model over entire data incur large amount of computational resources in space and time. To overcome this difficulty, we propose a practical method, termed \textit{onlineGPSSM}, that incorporates stochastic variational inference (VI) and online VI with novel formulation. The proposed method mitigates the computational complexity without catastrophic forgetting and also support adaptation to changes in a system and/or a real environments. Furthermore, we present application of onlineGPSSM into the reinforcement learning (RL) of partially observable dynamical systems by integrating onlineGPSSM with Bayesian filtering and trajectory optimization algorithms. Numerical examples are presented to demonstrate applicability of the proposed method.

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.

Reliable yet efficient evaluation of generalisation performance of a proposed architecture is crucial to the success of neural architecture search (NAS). Traditional approaches face a variety of limitations: training each architecture to completion is prohibitively expensive, early stopping estimates may correlate poorly with fully trained performance, and model-based estimators require large training sets. Instead, motivated by recent results linking training speed and generalisation with stochastic gradient descent, we propose to estimate the final test performance based on the sum of training losses. Our estimator is inspired by the marginal likelihood, which is used for Bayesian model selection. Our model-free estimator is simple, efficient, and cheap to implement, and does not require hyperparameter-tuning or surrogate training before deployment. We demonstrate empirically that our estimator consistently outperforms other baselines and can achieve a rank correlation of 0.95 with final test accuracy on the NAS-Bench201 dataset within 50 epochs.

Human feedback is widely used to train agents in many domains. However, previous works rarely consider the uncertainty when humans provide feedback, especially in cases that the optimal actions are not obvious to the trainers. For example, the reward of a sub-optimal action can be stochastic and sometimes exceeds that of the optimal action, which is common in games or real-world. Trainers are likely to provide positive feedback to sub-optimal actions, negative feedback to the optimal actions and even do not provide feedback in some confusing situations. Existing works, which utilize the Expectation Maximization (EM) algorithm and treat the feedback model as hidden parameters, do not consider uncertainties in the learning environment and human feedback. To address this challenge, we introduce a novel feedback model that considers the uncertainty of human feedback. However, this incurs intractable calculus in the EM algorithm. To this end, we propose a novel approximate EM algorithm, in which we approximate the expectation step with the Gradient Descent method. Experimental results in both synthetic scenarios and two real-world scenarios with human participants demonstrate the superior performance of our proposed approach.

Active inference offers a first principle account of sentient behaviour, from which special and important cases can be derived, e.g., reinforcement learning, active learning, Bayes optimal inference, Bayes optimal design, etc. Active inference resolves the exploitation-exploration dilemma in relation to prior preferences, by placing information gain on the same footing as reward or value. In brief, active inference replaces value functions with functionals of (Bayesian) beliefs, in the form of an expected (variational) free energy. In this paper, we consider a sophisticated kind of active inference, using a recursive form of expected free energy. Sophistication describes the degree to which an agent has beliefs about beliefs. We consider agents with beliefs about the counterfactual consequences of action for states of affairs and beliefs about those latent states. In other words, we move from simply considering beliefs about "what would happen if I did that" to "what would I believe about what would happen if I did that". The recursive form of the free energy functional effectively implements a deep tree search over actions and outcomes in the future. Crucially, this search is over sequences of belief states, as opposed to states per se. We illustrate the competence of this scheme, using numerical simulations of deep decision problems.

Much of human learning and inference can be framed within the computational problem of relational generalization. In this project, we propose a Bayesian model that generalizes relational knowledge to novel environments by analogically weighting predictions from previously encountered relational structures. First, we show that this learner outperforms a naive, theory-based learner on relational data derived from random- and Wikipedia-based systems when experience with the environment is small. Next, we show how our formalization of analogical similarity translates to the selection and weighting of analogies. Finally, we combine the analogy- and theory-based learners in a single nonparametric Bayesian model, and show that optimal relational generalization transitions from relying on analogies to building a theory of the novel system with increasing experience in it. Beyond predicting unobserved interactions better than either baseline, this formalization gives a computational-level perspective on the formation and abstraction of analogies themselves.

Deep neural networks are often ignorant about what they do not know and overconfident when they make uninformed predictions. Some recent approaches quantify classification uncertainty directly by training the model to output high uncertainty for the data samples close to class boundaries or from the outside of the training distribution. These approaches use an auxiliary data set during training to represent out-of-distribution samples. However, selection or creation of such an auxiliary data set is non-trivial, especially for high dimensional data such as images. In this work we develop a novel neural network model that is able to express both aleatoric and epistemic uncertainty to distinguish decision boundary and out-of-distribution regions of the feature space. To this end, variational autoencoders and generative adversarial networks are incorporated to automatically generate out-of-distribution exemplars for training. Through extensive analysis, we demonstrate that the proposed approach provides better estimates of uncertainty for in- and out-of-distribution samples, and adversarial examples on well-known data sets against state-of-the-art approaches including recent Bayesian approaches for neural networks and anomaly detection methods.

We analyze a sequential decision making model in which decision makers (or, players) take their decisions based on their own private information as well as the actions of previous decision makers. Such decision making processes often lead to what is known as the \emph{information cascade} or \emph{herding} phenomenon. Specifically, a cascade develops when it seems rational for some players to abandon their own private information and imitate the actions of earlier players. The risk, however, is that if the initial decisions were wrong, then the whole cascade will be wrong. Nonetheless, information cascade are known to be fragile: there exists a sequence of \emph{revealing} probabilities $\{p_{\ell}\}_{\ell\geq1}$, such that if with probability $p_{\ell}$ player $\ell$ ignores the decisions of previous players, and rely on his private information only, then wrong cascades can be avoided. Previous related papers which study the fragility of information cascades always assume that the revealing probabilities are known to all players perfectly, which might be unrealistic in practice. Accordingly, in this paper we study a mismatch model where players believe that the revealing probabilities are $\{q_\ell\}_{\ell\in\mathbb{N}}$ when they truly are $\{p_\ell\}_{\ell\in\mathbb{N}}$, and study the effect of this mismatch on information cascades. We consider both adversarial and probabilistic sequential decision making models, and derive closed-form expressions for the optimal learning rates at which the error probability associated with a certain decision maker goes to zero. We prove several novel phase transitions in the behaviour of the asymptotic learning rate.