Bayesian optimization (BO) is a popular method for efficiently inferring optima of an expensive black-box function via a sequence of queries. Existing informationtheoretic BO procedures aim to make queries that most reduce the uncertainty about optima, where the uncertainty is captured by Shannon entropy. However, an optimal measure of uncertainty would, ideally, factor in how we intend to use the inferred quantity in some downstream procedure. In this paper, we instead consider a generalization of Shannon entropy from work in statistical decision theory [13, 39], which contains a broad class of uncertainty measures parameterized by a problem-specific loss function corresponding to a downstream task. We first show that special cases of this entropy lead to popular acquisition functions used in BO procedures such as knowledge gradient, expected improvement, and entropy search. We then show how alternative choices for the loss yield a flexible family of acquisition functions that can be customized for use in novel optimization settings.

Sequences of events, such as crashes in the stock market or outages in a network, contain strong temporal dependencies, whose understanding is crucial to react to and influence future events. In this paper, we study the problem of discovering the underlying causal structure from event sequences. To this end, we introduce a new causal model, where individual events of the cause trigger events of the effect with dynamic delays. We show that in contrast to existing methods based on Granger causality, our model is identifiable for both instant and delayed effects. We base our approach on the Algorithmic Markov Condition, by which we identify the true causal network as the one that minimizes the Kolmogorov complexity. As the Kolmogorov complexity is not computable, we instantiate our model using Minimum Description Length and show that the resulting score identifies the causal direction.

We present theoretical results to show that K-priors with limited memory can achieve low gradientreconstruction error. We will discuss the optimal K-prior which can theoretically achieve perfect reconstruction error. Note that the prior is difficult to realize in practice since it requires all past training-data inputs X. Our goal here is to establish a theoretical limit, not to give practical choices. Our key idea is to choose a few input locations that provide a good representation of the training-data inputs X.

Real-world classification problems must contend with domain shift, the (potential) mismatch between the domain where a model is deployed and the domain(s) where the training data was gathered. Methods to handle such problems must specify what structure is common between the domains and what varies. A natural assumption is that causal (structural) relationships are invariant in all domains. Then, it is tempting to learn a predictor for label Y that depends only on its causal parents. However, many real-world problems are "anti-causal" in the sense that Y is a cause of the covariates X--in this case, Y has no causal parents and the naive causal invariance is useless.

Generative Adversarial Networks (GANs) are a widely-used tool for generative modeling of complex data. Despite their empirical success, the training of GANs is not fully understood due to the min-max optimization of the generator and discriminator. This paper analyzes these joint dynamics when the true samples as well as the generated samples are discrete, finite sets, and the discriminator is kernel-based. A simple yet expressive framework for analyzing training called the Isolated Points Model is introduced. In the proposed model, the distance between true samples greatly exceeds the kernel width, so each generated point is influenced by at most one true point. Our model enables precise characterization of the conditions for convergence, both to good and bad minima. In particular, the analysis explains two common failure modes: (i) an approximate mode collapse and (ii) divergence. Numerical simulations are provided that predictably replicate these behaviors.

For all authors... (a) Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope? If you used crowdsourcing or conducted research with human subjects... (a) Did you include the full text of instructions given to participants and screenshots, if applicable? [N/A] (b) Did you describe any potential participant risks, with links to Institutional Review Board (IRB) approvals, if applicable? [N/A] (c) Did you include the estimated hourly wage paid to participants and the total amount spent on participant compensation? Our method proposes to learn efficient data structure for accurate prediction in large-output space. It helps existing large-scale retrieval systems used in various online applications to efficiently produce more accurate results. To the best of our knowledge, this poses no negative impacts on society.

Recently, AutoRegressive (AR) models for the whole image generation empowered by transformers have achieved comparable or even better performance compared to Generative Adversarial Networks (GANs). Unfortunately, directly applying such AR models to edit/change local image regions, may suffer from the problems of missing global information, slow inference speed, and information leakage of local guidance. To address these limitations, we propose a novel model - image Local Autoregressive Transformer (iLAT), to better facilitate the locally guided image synthesis. Our iLAT learns the novel local discrete representations, by the newly proposed local autoregressive (LA) transformer of the attention mask and convolution mechanism. Thus iLAT can efficiently synthesize the local image regions by key guidance information. Our iLAT is evaluated on various locally guided image syntheses, such as pose-guided person image synthesis and face editing. Both quantitative and qualitative results show the efficacy of our model.

We study the regularisation induced in neural networks by Gaussian noise injections (GNIs). Though such injections have been extensively studied when applied to data, there have been few studies on understanding the regularising effect they induce when applied to network activations. Here we derive the explicit regulariser of GNIs, obtained by marginalising out the injected noise, and show that it penalises functions with high-frequency components in the Fourier domain; particularly in layers closer to a neural network's output. We show analytically and empirically that such regularisation produces calibrated classifiers with large classification margins.

However, there are only a few datasets that include concept-level meta-labels and most of these meta-labels are relevant for natural images that do not require domain expertise. Previous densely annotated datasets in medicine focused on meta-labels that are relevant to a single disease such as osteoarthritis or melanoma. In dermatology, skin disease is described using an established clinical lexicon that allows clinicians to describe physical exam findings to one another. To provide a medical dataset densely annotated by domain experts with annotations useful across multiple disease processes, we developed SkinCon: a skin disease dataset densely annotated by dermatologists. SkinCon includes 3230 images from the Fitzpatrick 17k skin disease dataset densely annotated with 48 clinical concepts, 22 of which have at least 50 images representing the concept. The concepts used were chosen by two dermatologists considering the clinical descriptor terms used to describe skin lesions.

Many tasks in deep learning involve optimizing over the inputs to a network to minimize or maximize some objective; examples include optimization over latent spaces in a generative model to match a target image, or adversarially perturbing an input to worsen classifier performance. Performing such optimization, however, is traditionally quite costly, as it involves a complete forward and backward pass through the network for each gradient step. In a separate line of work, a recent thread of research has developed the deep equilibrium (DEQ) model, a class of models that foregoes traditional network depth and instead computes the output of a network by finding the fixed point of a single nonlinear layer. In this paper, we show that there is a natural synergy between these two settings. Although, naively using DEQs for these optimization problems is expensive (owing to the time needed to compute a fixed point for each gradient step), we can leverage the fact that gradientbased optimization can itself be cast as a fixed point iteration to substantially improve the overall speed. That is, we simultaneously both solve for the DEQ fixed point and optimize over network inputs, all within a single "augmented" DEQ model that jointly encodes both the original network and the optimization process. Indeed, the procedure is fast enough that it allows us to efficiently train DEQ models for tasks traditionally relying on an "inner" optimization loop. We demonstrate this strategy on various tasks such as training generative models while optimizing over latent codes, training models for inverse problems like denoising and inpainting, adversarial training and gradient based meta-learning.