This work considers variational Bayesian inference as an inexpensive and scalable alternative to a fully Bayesian approach in the context of sparsity-promoting priors. In particular, the priors considered arise from scale mixtures of Normal distributions with a generalized inverse Gaussian mixing distribution. This includes the variational Bayesian LASSO as an inexpensive and scalable alternative to the Bayesian LASSO introduced in [56]. It also includes priors which more strongly promote sparsity. For linear models the method requires only the iterative solution of deterministic least squares problems. Furthermore, for $n\rightarrow \infty$ data points and p unknown covariates the method can be implemented exactly online with a cost of O(p$^3$) in computation and O(p$^2$) in memory. For large p an approximation is able to achieve promising results for a cost of O(p) in both computation and memory. Strategies for hyper-parameter tuning are also considered. The method is implemented for real and simulated data. It is shown that the performance in terms of variable selection and uncertainty quantification of the variational Bayesian LASSO can be comparable to the Bayesian LASSO for problems which are tractable with that method, and for a fraction of the cost. The present method comfortably handles n = p = 131,073 on a laptop in minutes, and n = 10$^5$, p = 10$^6$ overnight.

Classification with abstention has gained a lot of attention in recent years as it allows to incorporate human decision-makers in the process. Yet, abstention can potentially amplify disparities and lead to discriminatory predictions. The goal of this work is to build a general purpose classification algorithm, which is able to abstain from prediction, while avoiding disparate impact. We formalize this problem as risk minimization under fairness and abstention constraints for which we derive the form of the optimal classifier. Building on this result, we propose a post-processing classification algorithm, which is able to modify any off-the-shelf score-based classifier using only unlabeled sample. We establish finite sample risk, fairness, and abstention guarantees for the proposed algorithm. In particular, it is shown that fairness and abstention constraints can be achieved independently from the initial classifier as long as sufficiently many unlabeled data is available. The risk guarantee is established in terms of the quality of the initial classifier. Our post-processing scheme reduces to a sparse linear program allowing for an efficient implementation, which we provide. Finally, we validate our method empirically showing that moderate abstention rates allow to bypass the risk-fairness trade-off.

Deep kernel learning and related techniques promise to combine the representational power of neural networks with the reliable uncertainty estimates of Gaussian processes. One crucial aspect of these models is an expectation that, because they are treated as Gaussian process models optimized using the marginal likelihood, they are protected from overfitting. However, we identify pathological behavior, including overfitting, on a simple toy example. We explore this pathology, explaining its origins and considering how it applies to real datasets. Through careful experimentation on UCI datasets, CIFAR-10, and the UTKFace dataset, we find that the overfitting from overparameterized deep kernel learning, in which the model is "somewhat Bayesian", can in certain scenarios be worse than that from not being Bayesian at all. However, we find that a fully Bayesian treatment of deep kernel learning can rectify this overfitting and obtain the desired performance improvements over standard neural networks and Gaussian processes.

We address the problem of uncertainty calibration and introduce a novel calibration method, Parametrized Temperature Scaling (PTS). Standard deep neural networks typically yield uncalibrated predictions, which can be transformed into calibrated confidence scores using post-hoc calibration methods. In this contribution, we demonstrate that the performance of accuracy-preserving state-of-the-art post-hoc calibrators is limited by their intrinsic expressive power. We generalize temperature scaling by computing prediction-specific temperatures, parameterized by a neural network. We show with extensive experiments that our novel accuracy-preserving approach consistently outperforms existing algorithms across a large number of model architectures, datasets and metrics.

Quantum machine learning is an emerging field at the intersection of machine learning and quantum computing. Classical cross entropy plays a central role in machine learning. We define its quantum generalization, the quantum cross entropy, and investigate its relations with the quantum fidelity and the maximum likelihood principle. We also discuss its physical implications on quantum measurements.

Maximum likelihood estimation is widely used in training Energy-based models (EBMs). Training requires samples from an unnormalized distribution, which is usually intractable, and in practice, these are obtained by MCMC algorithms such as Langevin dynamics. However, since MCMC in high-dimensional space converges extremely slowly, the current understanding of maximum likelihood training, which assumes approximate samples from the model can be drawn, is problematic. In this paper, we try to understand this training procedure by replacing Langevin dynamics with deterministic solutions of the associated gradient descent ODE. Doing so allows us to study the density induced by the dynamics (if the dynamics are invertible), and connect with GANs by treating the dynamics as generator models, the initial values as latent variables and the loss as optimizing a critic defined by the very same energy that determines the generator through its gradient. Hence the term - self-adversarial loss. We show that reintroducing the noise in the dynamics does not lead to a qualitative change in the behavior, and merely reduces the quality of the generator. We thus show that EBM training is effectively a self-adversarial procedure rather than maximum likelihood estimation.

We show that a single softmax neural net with minimal changes can beat the uncertainty predictions of Deep Ensembles and other more complex single-forward-pass uncertainty approaches. Softmax neural nets cannot capture epistemic uncertainty reliably because for OoD points they extrapolate arbitrarily and suffer from feature collapse. This results in arbitrary softmax entropies for OoD points which can have high entropy, low, or anything in between. We study why, and show that with the right inductive biases, softmax neural nets trained with maximum likelihood reliably capture epistemic uncertainty through the feature-space density. This density is obtained using Gaussian Discriminant Analysis, but it cannot disentangle uncertainties. We show that it is necessary to combine this density with the softmax entropy to disentangle aleatoric and epistemic uncertainty -- crucial e.g. for active learning. We examine the quality of epistemic uncertainty on active learning and OoD detection, where we obtain SOTA ~0.98 AUROC on CIFAR-10 vs SVHN.

We consider image completion from the perspective of amortized inference in an image generative model. We leverage recent state of the art variational auto-encoder architectures that have been shown to produce photo-realistic natural images at non-trivial resolutions. Through amortized inference in such a model we can train neural artifacts that produce diverse, realistic image completions even when the vast majority of an image is missing. We demonstrate superior sample quality and diversity compared to prior art on the CIFAR-10 and FFHQ-256 datasets. We conclude by describing and demonstrating an application that requires an in-painting model with the capabilities ours exhibits: the use of Bayesian optimal experimental design to select the most informative sequence of small field of view x-rays for chest pathology detection.

Recent approaches to goal recognition have leveraged planning landmarks to achieve high-accuracy with low runtime cost. These approaches, however, lack a probabilistic interpretation. Furthermore, while most probabilistic models to goal recognition assume that the recognizer has access to a prior probability representing, for example, an agent's preferences, virtually no goal recognition approach actually uses the prior in practice, simply assuming a uniform prior. In this paper, we provide a model to both extend landmark-based goal recognition with a probabilistic interpretation and allow the estimation of such prior probability and its usage to compute posterior probabilities after repeated interactions of observed agents. We empirically show that our model can not only recognize goals effectively but also successfully infer the correct prior probability distribution representing an agent's preferences.

This paper introduces a procedure for testing the identifiability of Bayesian models for causal inference. Although the do-calculus is sound and complete given a causal graph, many practical assumptions cannot be expressed in terms of graph structure alone, such as the assumptions required by instrumental variable designs, regression discontinuity designs, and within-subjects designs. We present simulation-based identifiability (SBI), a fully automated identification test based on a particle optimization scheme with simulated observations. This approach expresses causal assumptions as priors over functions in a structural causal model, including flexible priors using Gaussian processes. We prove that SBI is asymptotically sound and complete, and produces practical finite-sample bounds. We also show empirically that SBI agrees with known results in graph-based identification as well as with widely-held intuitions for designs in which graph-based methods are inconclusive.