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.

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.