GenAI4ELab/papercli-papers huggingface dataset:
All You Need is a Good Functional Prior for Bayesian Deep Learning
Authors: Ba-Hien Tran; Simone Rossi; Dimitrios Milios; Maurizio Filippone
Venue: JMLR 2022 (main)

Abstract: The Bayesian treatment of neural networks dictates that a prior distribution is specified over their weight and bias parameters. This poses a challenge because modern neural networks are characterized by a large number of parameters, and the choice of these priors has an uncontrolled effect on the induced functional prior, which is the distribution of the functions obtained by sampling the parameters from their prior distribution. We argue that this is a hugely limiting aspect of Bayesian deep learning, and this work tackles this limitation in a practical and effective way. Our proposal is to reason in terms of functional priors, which are easier to elicit, and to âtuneâ the priors of neural network parameters in a way that they reflect such functional priors. Gaussian processes offer a rigorous framework to define prior distributions over functions, and we propose a novel and robust framework to match their prior with the functional prior of neural networks based on the minimization of their Wasserstein distance. We provide vast experimental evidence that coupling these priors with scalable Markov chain Monte Carlo sampling offers systematically large performance improvements over alternative choices of priors and state-of-the-art approximate Bayesian deep learning approaches. We consider this work a considerable step in the direction of making the long-standing challenge of carrying out a fully Bayesian treatment of neural networks, including convolutional neural networks, a concrete possibility.
Mutual Information Constraints for Monte-Carlo Objectives to Prevent Posterior Collapse Especially in Language Modelling
Authors: GÃ¡bor Melis; AndrÃ¡s GyÃ¶rgy; Phil Blunsom
Venue: JMLR 2022 (main)

Abstract: Posterior collapse is a common failure mode of density models trained as variational autoencoders, wherein they model the data without relying on their latent variables, rendering these variables useless. We focus on two factors contributing to posterior collapse, that have been studied separately in the literature. First, the underspecification of the model, which in an extreme but common case allows posterior collapse to be the theoretical optimium. Second, the looseness of the variational lower bound and the related underestimation of the utility of the latents. We weave these two strands of research together, specifically the tighter bounds of multi-sample Monte-Carlo objectives and constraints on the mutual information between the observable and the latent variables. The main obstacle is that the usual method of estimating the mutual information as the average Kullback-Leibler divergence between the easily available variational posterior q(z|x) and the prior does not work with Monte-Carlo objectives because their q(z|x) is not a direct approximation to the model's true posterior p(z|x). Hence, we construct estimators of the Kullback-Leibler divergence of the true posterior from the prior by recycling samples used in the objective, with which we train models of continuous and discrete latents at much improved rate-distortion and no posterior collapse. While alleviated, the tradeoff between modelling the data and using the latents still remains, and we urge for evaluating inference methods across a range of mutual information values.
Joint Inference of Multiple Graphs from Matrix Polynomials
Authors: Madeline Navarro; Yuhao Wang; Antonio G. Marques; Caroline Uhler; Santiago Segarra
Venue: JMLR 2022 (main)

Abstract: Inferring graph structure from observations on the nodes is an important and popular network science task. Departing from the more common inference of a single graph, we study the problem of jointly inferring multiple graphs from the observation of signals at their nodes (graph signals), which are assumed to be stationary in the sought graphs. Graph stationarity implies that the mapping between the covariance of the signals and the sparse matrix representing the underlying graph is given by a matrix polynomial. A prominent example is that of Markov random fields, where the inverse of the covariance yields the sparse matrix of interest. From a modeling perspective, stationary graph signals can be used to model linear network processes evolving on a set of (not necessarily known) networks. Leveraging that matrix polynomials commute, a convex optimization method along with sufficient conditions that guarantee the recovery of the true graphs are provided when perfect covariance information is available. Particularly important from an empirical viewpoint, we provide high-probability bounds on the recovery error as a function of the number of signals observed and other key problem parameters. Numerical experiments demonstrate the effectiveness of the proposed method with perfect covariance information as well as its robustness in the noisy regime.
Efficient Change-Point Detection for Tackling Piecewise-Stationary Bandits
Authors: Lilian Besson; Emilie Kaufmann; Odalric-Ambrym Maillard; Julien Seznec
Venue: JMLR 2022 (main)

Abstract: We introduce GLRklUCB, a novel algorithm for the piecewise iid non-stationary bandit problem with bounded rewards. This algorithm combines an efficient bandit algorithm, klUCB, with an efficient, parameter-free, change-point detector, the Bernoulli Generalized Likelihood Ratio Test, for which we provide new theoretical guarantees of independent interest. Unlike previous non-stationary bandit algorithms using a change-point detector, GLRklUCB does not need to be calibrated based on prior knowledge on the arms' means. We prove that this algorithm can attain a $O(\sqrt{TA\Upsilon_T\log(T)})$ regret in $T$ rounds on some âeasyâ instances in which there is sufficient delay between two change-points, where $A$ is the number of arms and $\Upsilon_T$ the number of change-points, without prior knowledge of $\Upsilon_T$. In contrast with recently proposed algorithms that are agnostic to $\Upsilon_T$, we perform a numerical study showing that GLRklUCB is also very efficient in practice, beyond easy instances.
Multi-Agent Online Optimization with Delays: Asynchronicity, Adaptivity, and Optimism
Authors: Yu-Guan Hsieh; Franck Iutzeler; JÃ©rÃ´me Malick; Panayotis Mertikopoulos
Venue: JMLR 2022 (main)

Abstract: In this paper, we provide a general framework for studying multi-agent online learning problems in the presence of delays and asynchronicities. Specifically, we propose and analyze a class of adaptive dual averaging schemes in which agents only need to accumulate gradient feedback received from the whole system, without requiring any between-agent coordination. In the single-agent case, the adaptivity of the proposed method allows us to extend a range of existing results to problems with potentially unbounded delays between playing an action and receiving the corresponding feedback. In the multi-agent case, the situation is significantly more complicated because agents may not have access to a global clock to use as a reference point; to overcome this, we focus on the information that is available for producing each prediction rather than the actual delay associated with each feedback. This allows us to derive adaptive learning strategies with optimal regret bounds, even in a fully decentralized, asynchronous environment. Finally, we also analyze an âoptimisticâ variant of the proposed algorithm which is capable of exploiting the predictability of problems with a slower variation and leads to improved regret bounds.
Stacking for Non-mixing Bayesian Computations: The Curse and Blessing of Multimodal Posteriors
Authors: Yuling Yao; Aki Vehtari; Andrew Gelman
Venue: JMLR 2022 (main)

Abstract: When working with multimodal Bayesian posterior distributions, Markov chain Monte Carlo (MCMC) algorithms have difficulty moving between modes, and default variational or mode-based approximate inferences will understate posterior uncertainty. And, even if the most important modes can be found, it is difficult to evaluate their relative weights in the posterior. Here we propose an approach using parallel runs of MCMC, variational, or mode-based inference to hit as many modes or separated regions as possible and then combine these using Bayesian stacking, a scalable method for constructing a weighted average of distributions. The result from stacking efficiently samples from multimodal posterior distribution, minimizes cross validation prediction error, and represents the posterior uncertainty better than variational inference, but it is not necessarily equivalent, even asymptotically, to fully Bayesian inference. We present theoretical consistency with an example where the stacked inference approximates the true data generating process from the misspecified model and a non-mixing sampler, from which the predictive performance is better than full Bayesian inference, hence the multimodality can be considered a blessing rather than a curse under model misspecification. We demonstrate practical implementation in several model families: latent Dirichlet allocation, Gaussian process regression, hierarchical regression, horseshoe variable selection, and neural networks.
Posterior Asymptotics for Boosted Hierarchical Dirichlet Process Mixtures
Authors: Marta Catalano; Pierpaolo De Blasi; Antonio Lijoi; Igor Pruenster
Venue: JMLR 2022 (main)

Abstract: Bayesian hierarchical models are powerful tools for learning common latent features across multiple data sources. The Hierarchical Dirichlet Process (HDP) is invoked when the number of latent components is a priori unknown. While there is a rich literature on finite sample properties and performance of hierarchical processes, the analysis of their frequentist posterior asymptotic properties is still at an early stage. Here we establish theoretical guarantees for recovering the true data generating process when the data are modeled as mixtures over the HDP or a generalization of the HDP, which we term boosted because of the faster growth in the number of discovered latent features. By extending Schwartz's theory to partially exchangeable sequences we show that posterior contraction rates are crucially affected by the relationship between the sample sizes corresponding to the different groups. The effect varies according to the smoothness level of the true data distributions. In the supersmooth case,  when the generating densities are Gaussian mixtures, we recover the parametric rate up to a logarithmic factor, provided that the sample sizes are related in a polynomial fashion. Under ordinary smoothness assumptions more caution is needed as a polynomial deviation in the sample sizes could drastically deteriorate the convergence to the truth.
Dependent randomized rounding for clustering and partition systems with knapsack constraints
Authors: David G. Harris; Thomas Pensyl; Aravind Srinivasan; Khoa Trinh
Venue: JMLR 2022 (main)

Abstract: Clustering problems are fundamental to unsupervised learning. There is an increased emphasis on fairness in machine learning and AI; one representative notion of fairness is that no single group should be over-represented among the cluster-centers. This, and much more general clustering problems, can be formulated with âknapsack" and âpartition" constraints. We develop new randomized algorithms targeting such problems, and study two in particular: multi-knapsack median and multi-knapsack center. Our rounding algorithms give new approximation and pseudo-approximation algorithms for these problems. One key technical tool, which may be of independent interest, is a new tail bound analogous to Feige (2006) for sums of random variables with unbounded variances. Such bounds can be useful in inferring properties of large networks using few samples.
FuDGE: A Method to Estimate a Functional Differential Graph in a High-Dimensional Setting
Authors: Boxin Zhao; Y. Samuel Wang; Mladen Kolar
Venue: JMLR 2022 (main)

Abstract: We consider the problem of estimating the difference between two undirected functional graphical models with shared structures. In many applications, data are naturally regarded as a vector of random functions rather than as a vector of scalars. For example, electroencephalography (EEG) data are treated more appropriately as functions of time. In such a problem, not only can the number of functions measured per sample be large, but each function is itself an infinite dimensional object, making estimation of model parameters challenging. This is further complicated by the fact that curves are usually observed only at discrete time points. We first define a functional differential graph that captures the differences between two functional graphical models and formally characterize when the functional differential graph is well defined. We then propose a method, FuDGE, that directly estimates the functional differential graph without first estimating each individual graph. This is particularly beneficial in settings where the individual graphs are dense but the differential graph is sparse. We show that FuDGE consistently estimates the functional differential graph even in a high-dimensional setting for both fully observed and discretely observed function paths. We illustrate the finite sample properties of our method through simulation studies. We also propose a competing method, the Joint Functional Graphical Lasso, which generalizes the Joint Graphical Lasso to the functional setting. Finally, we apply our method to EEG data to uncover differences in functional brain connectivity between a group of individuals with alcohol use disorder and a control group.
Prior Adaptive Semi-supervised Learning with Application to EHR Phenotyping
Authors: Yichi Zhang; Molei Liu; Matey Neykov; Tianxi Cai
Venue: JMLR 2022 (main)

Abstract: Electronic Health Record (EHR) data, a rich source for biomedical research, have been successfully used to gain novel insight into a wide range of diseases. Despite its potential, EHR is currently underutilized for discovery research due to its major limitation in the lack of precise phenotype information. To overcome such difficulties, recent efforts have been devoted to developing supervised algorithms to accurately predict phenotypes based on relatively small training datasets with gold-standard labels extracted via chart review. However, supervised methods typically require a sizable training set to yield generalizable algorithms, especially when the number of candidate features is large. In this paper, we propose a semi-supervised (SS) EHR phenotyping method that borrows information from both a small, labeled dataset (where both the label Y and the feature set X are observed) and a much larger, weakly-labeled dataset in which the feature set X is accompanied only by a surrogate label S that is available to all patients. Under a working prior assumption that S is related to X only through Y and allowing it to hold approximately, we propose a prior adaptive semi-supervised (PASS) estimator that incorporates the prior knowledge by shrinking the estimator towards a direction derived under the prior. We derive asymptotic theory for the proposed estimator and justify its efficiency and robustness to prior information of poor quality. We also demonstrate its superiority over existing estimators under various scenarios via simulation studies and on three real-world EHR phenotyping studies at a large tertiary hospital.
Distributed Bayesian Varying Coefficient Modeling Using a Gaussian Process Prior
Authors: Rajarshi Guhaniyogi; Cheng Li; Terrance D. Savitsky; Sanvesh Srivastava
Venue: JMLR 2022 (main)

Abstract: Varying coefficient models (VCMs) are widely used for estimating nonlinear regression functions for functional data. Their Bayesian variants using Gaussian process priors on the functional coefficients, however, have received limited attention in massive data applications, mainly due to the prohibitively slow posterior computations using Markov chain Monte Carlo (MCMC) algorithms. We address this problem using a divide-and-conquer Bayesian approach. We first create a large number of data subsamples with much smaller sizes. Then, we formulate the VCM as a linear mixed-effects model and develop a data augmentation algorithm for obtaining MCMC draws on all the subsets in parallel. Finally, we aggregate the MCMC-based estimates of subset posteriors into a single Aggregated Monte Carlo (AMC) posterior, which is used as a computationally efficient alternative to the true posterior distribution. Theoretically, we derive minimax optimal posterior convergence rates for the AMC posteriors of both the varying coefficients and the mean regression function. We provide quantification on the orders of subset sample sizes and the number of subsets. The empirical results show that the combination schemes that satisfy our theoretical assumptions, including the AMC posterior, have better estimation performance than their main competitors across diverse simulations and in a real data analysis.
A Distribution Free Conditional Independence Test with Applications to Causal Discovery
Authors: Zhanrui Cai; Runze Li; Yaowu Zhang
Venue: JMLR 2022 (main)

Abstract: This paper is concerned with test of the conditional independence. We first establish an equivalence between the conditional independence and the mutual independence. Based on the equivalence, we propose an index to measure the conditional dependence by quantifying the mutual dependence among the transformed variables. The proposed index has several appealing properties. (a) It is distribution free since the limiting null distribution of the proposed index does not depend on the population distributions of the data. Hence the critical values can be tabulated by simulations. (b) The proposed index ranges from zero to one, and equals zero if and only if the conditional independence holds. Thus, it has nontrivial power under the alternative hypothesis. (c) It is robust to outliers and heavy-tailed data since it is invariant to conditional strictly monotone transformations. (d) It has low computational cost since it incorporates a simple closed-form expression and can be implemented in quadratic time. (e) It is insensitive to tuning parameters involved in the calculation of the proposed index. (f) The new index is applicable for multivariate random vectors as well as for discrete data. All these properties enable us to use the new index as statistical inference tools for various data. The effectiveness of the method is illustrated through extensive simulations and a real application on causal discovery.
Robust and scalable manifold learning via landmark diffusion for long-term medical signal processing
Authors: Chao Shen; Yu-Ting Lin; Hau-Tieng Wu
Venue: JMLR 2022 (main)

Abstract: Motivated by analyzing long-term physiological time series, we design a robust and scalable spectral embedding algorithm that we refer to as RObust and Scalable Embedding via LANdmark Diffusion (Roseland).  The key is designing a diffusion process on the dataset where the diffusion is done via a small subset called the landmark set. Roseland is theoretically justified under the manifold model, and its computational complexity is comparable with commonly applied subsampling scheme such as the NystrÃ¶m extension. Specifically, when there are $n$ data points in $\mathbb{R}^q$ and $n^\beta$ points in the landmark set, where $\beta\in (0,1)$, the computational complexity of Roseland is $O(n^{1+2\beta}+qn^{1+\beta})$, while that of Nystrom is $O(n^{2.81\beta}+qn^{1+2\beta})$. To demonstrate the potential of Roseland, we apply it to { three} datasets and compare it with several other existing algorithms. First, we apply Roseland to the task of spectral clustering using the MNIST dataset (70,000 images), achieving 85\% accuracy when the dataset is clean and 78\% accuracy when the dataset is noisy. Compared with other subsampling schemes, overall Roseland achieves a better performance. Second, we apply Roseland to the task of image segmentation using images from COCO. Finally, we demonstrate how to apply Roseland to explore long-term arterial blood pressure waveform dynamics during a liver transplant operation lasting for 12 hours. In conclusion, Roseland is scalable and robust, and it has a potential for analyzing large datasets.
CD-split and HPD-split: Efficient Conformal Regions in High Dimensions
Authors: Rafael Izbicki; Gilson Shimizu; Rafael B. Stern
Venue: JMLR 2022 (main)

Abstract: Conformal methods create prediction bands that control average coverage assuming solely i.i.d. data. Although the literature has mostly focused on  prediction intervals, more general regions can often better represent uncertainty. For instance, a bimodal target is better represented by the union of two intervals. Such prediction regions are obtained by CD-split, which combines the split method and a data-driven partition of the feature space which scales to high dimensions. CD-split however contains many tuning parameters, and their role is not clear. In this paper, we provide new insights on CD-split by exploring its theoretical properties. In particular, we show that CD-split converges asymptotically to the oracle highest predictive density set and satisfies local and asymptotic conditional validity. We also present simulations that show how to tune CD-split. Finally, we introduce HPD-split, a variation of CD-split that requires less tuning, and show that it shares the same theoretical guarantees as CD-split. In a wide variety of our simulations, CD-split and HPD-split have better conditional coverage and yield smaller prediction regions than other methods.
Generalized Ambiguity Decomposition for Ranking Ensemble Learning
Authors: Hongzhi Liu; Yingpeng Du; Zhonghai Wu
Venue: JMLR 2022 (main)

Abstract: Error decomposition analysis is a key problem for ensemble learning, which indicates that proper combination of multiple models can achieve better performance than any individual one. Existing theoretical research of ensemble learning focuses on regression or classification tasks. There is limited theoretical research for ranking ensemble. In this paper, we first generalize the ambiguity decomposition theory from regression ensemble to ranking ensemble, which proves the effectiveness of ranking ensemble with consideration of list-wise ranking information. According to the generalized theory, we propose an explicit diversity measure for ranking ensemble, which can be used to enhance the diversity of ensemble and improve the performance of ensemble model. Furthermore, we adopt an adaptive learning scheme to learn query-dependent ensemble weights, which can fit into the generalized theory and help to further improve the performance of ensemble model. Extensive experiments on recommendation and information retrieval tasks demonstrate the effectiveness and theoretical advantages of the proposed method compared with several state-of-the-art methods.