Jiang et al. (2021) give empirical evidence that the average test error of deep neural networks can be estimated via the prediction disagreement of two separately trained networks. They also provide a theoretical explanation that this 'Generalization Disagreement Equality' follows from the well-calibrated nature of deep ensembles under the notion of a proposed 'class-aggregated calibration'. In this paper we show that the approach suggested might be impractical because a deep ensemble's calibration deteriorates under distribution shift, which is exactly when the coupling of test error and disagreement would be of practical value. We present both theoretical and experimental evidence, re-deriving the theoretical statements using a simple Bayesian perspective and show them to be straightforward and more generic: they apply to any discriminative model -- not only ensembles whose members output one-hot class predictions. The proposed calibration metrics are also equivalent to two metrics introduced by Nixon et al. (2019): 'ACE' and 'SCE'.

Algorithm configuration (AC) is concerned with the automated search of the most suitable parameter configuration of a parametrized algorithm. There is currently a wide variety of AC problem variants and methods proposed in the literature. Existing reviews do not take into account all derivatives of the AC problem, nor do they offer a complete classification scheme. To this end, we introduce taxonomies to describe the AC problem and features of configuration methods, respectively. We review existing AC literature within the lens of our taxonomies, outline relevant design choices of configuration approaches, contrast methods and problem variants against each other, and describe the state of AC in industry. Finally, our review provides researchers and practitioners with a look at future research directions in the field of AC.

Causal discovery, the learning of causality in a data mining scenario, has been of strong scientific and theoretical interest as a starting point to identify "what causes what?" Contingent on assumptions, it is sometimes possible to identify an exact causal Directed Acyclic Graph (DAG), as opposed to a Markov equivalence class of graphs that gives ambiguity of causal directions. The focus of this paper is on one such case: a linear structural equation model with non-Gaussian noise, a model known as the Linear Non-Gaussian Acyclic Model (LiNGAM). Given a specified parametric noise model, we develop a novel sequential approach to estimate the causal ordering of a DAG. At each step of the procedure, only simple likelihood ratio scores are calculated on regression residuals to decide the next node to append to the current partial ordering. Under mild assumptions, the population version of our procedure provably identifies a true ordering of the underlying causal DAG. We provide extensive numerical evidence to demonstrate that our sequential procedure is scalable to cases with possibly thousands of nodes and works well for high-dimensional data. We also conduct an application to a single-cell gene expression dataset to demonstrate our estimation procedure.

Mean rewards of actions are often correlated. The form of these correlations may be complex and unknown a priori, such as the preferences of a user for recommended products and their categories. To maximize statistical efficiency, it is important to leverage these correlations when learning. We formulate a bandit variant of this problem where the correlations of mean action rewards are represented by a hierarchical Bayesian model with latent variables. Since the hierarchy can have multiple layers, we call it deep. We propose a hierarchical Thompson sampling algorithm (HierTS) for this problem, and show how to implement it efficiently for Gaussian hierarchies. The efficient implementation is possible due to a novel exact hierarchical representation of the posterior, which itself is of independent interest. We use this exact posterior to analyze the Bayes regret of HierTS in Gaussian bandits. Our analysis reflects the structure of the problem, that the regret decreases with the prior width, and also shows that hierarchies reduce the regret by non-constant factors in the number of actions. We confirm these theoretical findings empirically, in both synthetic and real-world experiments.

Weighted knowledge bases for description logics with typicality have been recently considered under a "concept-wise" multipreference semantics (in both the two-valued and fuzzy case), as the basis of a logical semantics of MultiLayer Perceptrons (MLPs). In this paper we consider weighted conditional ALC knowledge bases with typicality in the finitely many-valued case, through three different semantic constructions, based on coherent, faithful and phi-coherent interpretations. For the boolean fragment LC of ALC we exploit ASP and "asprin" for reasoning with the concept-wise multipreference entailment under a phi-coherent semantics, suitable to characterize the stationary states of MLPs. As a proof of concept, we experiment the proposed approach for checking properties of trained MLPs.

We present energy-based generative flow networks (EB-GFN), a novel probabilistic modeling algorithm for high-dimensional discrete data. Building upon the theory of generative flow networks (GFlowNets), we model the generation process by a stochastic data construction policy and thus amortize expensive MCMC exploration into a fixed number of actions sampled from a GFlowNet. We show how GFlowNets can approximately perform large-block Gibbs sampling to mix between modes. We propose a framework to jointly train a GFlowNet with an energy function, so that the GFlowNet learns to sample from the energy distribution, while the energy learns with an approximate MLE objective with negative samples from the GFlowNet. We demonstrate EB-GFN's effectiveness on various probabilistic modeling tasks.

We show how probabilistic numerics can be used to convert an initial value problem into a Gauss--Markov process parametrised by the dynamics of the initial value problem. Consequently, the often difficult problem of parameter estimation in ordinary differential equations is reduced to hyperparameter estimation in Gauss--Markov regression, which tends to be considerably easier. The method's relation and benefits in comparison to classical numerical integration and gradient matching approaches is elucidated. In particular, the method can, in contrast to gradient matching, handle partial observations, and has certain routes for escaping local optima not available to classical numerical integration. Experimental results demonstrate that the method is on par or moderately better than competing approaches.

Fairness and robustness are often considered as orthogonal dimensions when evaluating machine learning models. However, recent work has revealed interactions between fairness and robustness, showing that fairness properties are not necessarily maintained under distribution shift. In healthcare settings, this can result in e.g. a model that performs fairly according to a selected metric in "hospital A" showing unfairness when deployed in "hospital B". While a nascent field has emerged to develop provable fair and robust models, it typically relies on strong assumptions about the shift, limiting its impact for real-world applications. In this work, we explore the settings in which recently proposed mitigation strategies are applicable by referring to a causal framing. Using examples of predictive models in dermatology and electronic health records, we show that real-world applications are complex and often invalidate the assumptions of such methods. Our work hence highlights technical, practical, and engineering gaps that prevent the development of robustly fair machine learning models for real-world applications. Finally, we discuss potential remedies at each step of the machine learning pipeline.

Diffusion models have recently shown great promise for generative modeling, outperforming GANs on perceptual quality and autoregressive models at density estimation. A remaining downside is their slow sampling time: generating high quality samples takes many hundreds or thousands of model evaluations. Here we make two contributions to help eliminate this downside: First, we present new parameterizations of diffusion models that provide increased stability when using few sampling steps. Second, we present a method to distill a trained deterministic diffusion sampler, using many steps, into a new diffusion model that takes half as many sampling steps. We then keep progressively applying this distillation procedure to our model, halving the number of required sampling steps each time. On standard image generation benchmarks like CIFAR-10, ImageNet, and LSUN, we start out with state-of-the-art samplers taking as many as 8192 steps, and are able to distill down to models taking as few as 4 steps without losing much perceptual quality; achieving, for example, a FID of 3.0 on CIFAR-10 in 4 steps. Finally, we show that the full progressive distillation procedure does not take more time than it takes to train the original model, thus representing an efficient solution for generative modeling using diffusion at both train and test time. Diffusion models (Sohl-Dickstein et al., 2015; Song & Ermon, 2019; Ho et al., 2020) are a class of generative models that have recently delivered impressive sample quality and likelihoods on many standard generative modeling benchmarks.

Optimization is a ubiquitous modeling tool and is often deployed in settings which repeatedly solve similar instances of the same problem. Amortized optimization methods use learning to predict the solutions to problems in these settings. This leverages the shared structure between similar problem instances. In this tutorial, we will discuss the key design choices behind amortized optimization, roughly categorizing 1) models into fully-amortized and semi-amortized approaches, and 2) learning methods into regression-based and objectivebased. We then view existing applications through these foundations to draw connections between them, including for manifold optimization, variational inference, sparse coding, meta-learning, control, reinforcement learning, convex optimization, and deep equilibrium networks. This framing enables us easily see, for example, that the amortized inference in variational autoencoders is conceptually identical to value gradients in control and reinforcement learning as they both use fully-amortized models with an objective-based loss.