UAI 2021 论文列表

Neural architecture search (NAS) has seen a steep rise in interest over the last few years. Many algorithms for NAS consist of searching through a space of architectures by iteratively choosing an architecture, evaluating its performance by training it, and using all prior evaluations to come up with the next choice. The evaluation step is noisy - the final accuracy varies based on the random initialization of the weights. Prior work has focused on devising new search algorithms to handle this noise, rather than quantifying or understanding the level of noise in architecture evaluations. In this work, we show that (1) the simplest hill-climbing algorithm is a powerful baseline for NAS, and (2), when the noise in popular NAS benchmark datasets is reduced to a minimum, the loss landscape becomes near-convex, causing hill-climbing to outperform many popular state-of-the-art algorithms. We further back up this observation by showing that the number of local minima is substantially reduced as the noise decreases and by giving a theoretical characterization of the performance of local search in NAS. Based on our findings, for NAS research we suggest (1) using local search as a baseline, and (2) denoising the training pipeline when possible.

Node features and structural information of a graph are both crucial for semi-supervised node classification problems. A variety of graph neural network (GNN) based approaches have been proposed to tackle these problems, which typically determine output labels through feature aggregation. This can be problematic, as it implies conditional independence of output nodes given hidden representations, despite their direct connections in the graph. To learn the direct influence among output nodes in a graph, we propose the Explicit Pairwise Factorized Graph Neural Network (EPFGNN), which models the whole graph as a partially observed Markov Random Field. It contains explicit pairwise factors to model output-output relations and uses a GNN backbone to model input-output relations. To balance model complexity and expressivity, the pairwise factors have a shared component and a separate scaling coefficient for each edge. We apply the EM algorithm to train our model, and utilize a star-shaped piecewise likelihood for the tractable surrogate objective. We conduct experiments on various datasets, which shows that our model can effectively improve the performance for semi-supervised node classification on graphs.

Online imitation learning (IL) is an algorithmic framework that leverages interactions with expert policies for efficient policy optimization. Here policies are optimized by performing online learning on a sequence of loss functions that encourage the learner to mimic expert actions, and if the online learning has no regret, the agent can provably learn an expert-like policy. Online IL has demonstrated empirical successes in many applications and interestingly, its policy improvement speed observed in practice is usually much faster than existing theory suggests. In this work, we provide an explanation of this phenomenon. Let $\xi$ denote the policy class bias and assume the online IL loss functions are convex, smooth, and non-negative. We prove that, after $N$ rounds of online IL with stochastic feedback, the policy improves in $\tilde{O}(1/N + \sqrt{\xi/N})$ in both expectation and high probability. In other words, we show that adopting a sufficiently expressive policy class in online IL has two benefits: both the policy improvement speed increases and the performance bias decreases.

Hierarchical clustering is a critical task in numerous domains. Many approaches are based on heuristics and the properties of the resulting clusterings are studied post hoc. However, in several applications, there is a natural cost function that can be used to characterize the quality of the clustering. In those cases, hierarchical clustering can be seen as a combinatorial optimization problem. To that end, we introduce a new approach based on A* search. We overcome the prohibitively large search space by combining A* with a novel

Given a causal graph, the do-calculus can express treatment effects as functionals of the observational joint distribution that can be estimated empirically. Sometimes the do-calculus identifies multiple valid formulae, prompting us to compare the statistical properties of the corresponding estimators. For example, the backdoor formula applies when all confounders are observed and the frontdoor formula applies when an observed mediator transmits the causal effect. In this paper, we investigate the over-identified scenario where both confounders and mediators are observed, rendering both estimators valid. Addressing the linear Gaussian causal model, we demonstrate that either estimator can dominate the other by an unbounded constant factor. Next, we derive an optimal estimator, which leverages all observed variables, and bound its finite-sample variance. We show that it strictly outperforms the backdoor and frontdoor estimators and that this improvement can be unbounded. We also present a procedure for combining two datasets, one with observed confounders and another with observed mediators. Finally, we evaluate our methods on both simulated data and the IHDP and JTPA datasets.

Action-constrained reinforcement learning (RL) is a widely-used approach in various real-world applications, such as scheduling in networked systems with resource constraints and control of a robot with kinematic constraints. While the existing projection-based approaches ensure zero constraint violation, they could suffer from the zero-gradient problem due to the tight coupling of the policy gradient and the projection, which results in sample-inefficient training and slow convergence. To tackle this issue, we propose a learning algorithm that decouples the action constraints from the policy parameter update by leveraging state-wise Frank-Wolfe and a regression-based policy update scheme. Moreover, we show that the proposed algorithm enjoys convergence and policy improvement properties in the tabular case as well as generalizes the popular DDPG algorithm for action-constrained RL in the general case. Through experiments, we demonstrate that the proposed algorithm significantly outperforms the benchmark methods on a variety of control tasks.

Directed acyclic graphs (DAGs) with hidde variables are often used to characterize causal relations between variables in a system. When some variables are unobserved, DAGs imply a notoriously complicated set of constraints on the distribution of observed variables. In this work, we present entropic inequality constraints that are implied by e-separation relations in hidden variable DAGs with discrete observed variables. The constraints can intuitively be understood to follow from the fact that the capacity of variables along a causal pathway to convey information is restricted by their entropy; e.g. at the extreme case, a variable with entropy 0 can convey no information. We show how these constraints can be used to learn about the true causal model from an observed data distribution. In addition, we propose a measure of causal influence called the minimal mediary entropy, and demonstrate that it can concisely augment traditional measures such as the average treatment effect.

We consider the problem of minimizing multi-modal loss functions with a large number of local optima. Since the local gradient points to the direction of the steepest slope in an infinitesimal neighborhood, an optimizer guided by the local gradient is often trapped in a local minimum. To address this issue, we develop a novel nonlocal gradient to skip small local minima by capturing major structures of the loss’s landscape in black-box optimization. The nonlocal gradient is defined by a directional Gaussian smoothing (DGS) approach. The key idea of DGS is to conducts 1D long-range exploration with a large smoothing radius along $d$ orthogonal directions in $R^d$, each of which defines a nonlocal directional derivative as a 1D integral. Such long-range exploration enables the nonlocal gradient to skip small local minima. The $d$ directional derivatives are then assembled to form the nonlocal gradient. We use the Gauss-Hermite quadrature rule to approximate the $d$ 1D integrals to obtain an accurate estimator. The superior performance of our method is demonstrated in three sets of examples, including benchmark functions for global optimization, and two real-world scientific problems.

Natural data are often well-described as belonging to latent clusters. When the number of clusters is unknown, Bayesian nonparametric (BNP) models can provide a flexible and powerful technique to model the data. However, algorithms for inference in nonparametric mixture models fail to meet two critical requirements for practical use: (1) that inference can be performed online, and (2) that inference is efficient in the large time/sample limit. In this work, we propose a novel Bayesian recursion to efficiently infer a posterior distribution over discrete latent variables from a sequence of observations in an online manner, assuming a Chinese Restaurant Process prior on the sequence of latent variables. Our recursive filter, which we call the Recursive Chinese Restaurant Process (R-CRP), has quasilinear average time complexity and logarithmic average space complexity in the total number of observations. We experimentally compare our filtering method against both online and offline inference algorithms including Markov chain Monte Carlo, variational approximations and DP-Means, and demonstrate that our inference algorithm achieves comparable or better performance for a fraction of the runtime.

Greedy coordinate descent (GCD) is an efficient optimization algorithm for a wide range of machine learning and data mining applications. GCD could be significantly faster than randomized coordinate descent (RCD) if they have similar per iteration cost. Nevertheless, in some cases, the greedy rule used in GCD cannot be efficiently implemented, leading to huge per iteration cost and making GCD slower than RCD. To alleviate the cost per iteration, the existing solutions rely on maximum inner product search (MIPS) as an approximate greedy rule. But it has been empirically shown that GCD with approximate greedy rule could suffer from slow convergence even with the state-of-the-art MIPS algorithms. We propose a hybrid coordinate descent algorithm with a simple variable partition strategy to tackle the cases when greedy rule cannot be implemented efficiently. The convergence rate and theoretical properties of the new algorithm are presented. The proposed method is shown to be especially useful when the data matrix has a group structure. Numerical experiments with both synthetic and real-world data demonstrate that our new algorithm is competitive against RCD, GCD, approximate GCD with MIPS and their accelerated variants.

In this paper, we propose a new stochastic optimization algorithm for Bayesian inference based on multilevel Monte Carlo (MLMC) methods. In Bayesian statistics, biased estimators of the model evidence have been often used as stochastic objectives because the existing debiasing techniques are computationally costly to apply. To overcome this issue, we apply an MLMC sampling technique to construct low-variance unbiased estimators both for the model evidence and its gradient. In the theoretical analysis, we show that the computational cost required for our proposed MLMC estimator to estimate the model evidence or its gradient with a given accuracy is an order of magnitude smaller than those of the previously known estimators. Our numerical experiments confirm considerable computational savings compared to the conventional estimators. Combining our MLMC estimator with gradient-based stochastic optimization results in a new scalable, efficient, debiased inference algorithm for Bayesian statistical models.

Convex clustering has drawn recent attention because of its competitive performance and nice property to guarantee global optimality. However, convex clustering is infeasible due to its high computational cost for large-scale data sets. We propose a novel method to solve the L1 fusion convex clustering problem by dynamic programming. We develop the Convex clustering Path Algorithm In Near-linear Time (C-PAINT) algorithm to construct the solution path efficiently. The proposed C-PAINT yields the exact solution while other general solvers for convex problems applied in the convex clustering depend on tuning parameters such as step size and threshold, and it usually takes many iterations to converge. Including a sorting process that almost takes no time in practice, the main part of the algorithm takes only linear time. Thus, C-PAINT has superior scalability comparing to other state-of-art algorithms. Moreover, C-PAINT enables the path visualization of clustering solutions for large data. In particular, experiments show our proposed method can solve the convex clustering with 10^7 data points in two minutes. We demonstrate the proposed method using both synthetic data and real data. Our algorithms are implemented in the dpcc R package.

We present a new non-negative matrix factorization model for $(0,1)$ bounded-support data based on the doubly non-central beta (DNCB) distribution, a generalization of the beta distribution. The expressiveness of the DNCB distribution is particularly useful for modeling DNA methylation datasets, which are typically highly dispersed and multi-modal; however, the model structure is sufficiently general that it can be adapted to many other domains where latent representations of $(0,1)$ bounded-support data are of interest. Although the DNCB distribution lacks a closed-form conjugate prior, several augmentations let us derive an efficient posterior inference algorithm composed entirely of analytic updates. Our model improves out-of-sample predictive performance on both real and synthetic DNA methylation datasets over state-of-the-art methods in bioinformatics. In addition, our model yields meaningful latent representations that accord with existing biological knowledge.

Trustworthy deployment of ML models requires a proper measure of uncertainty, especially in safety-critical applications. We focus on uncertainty quantification (UQ) for classification problems via two avenues — prediction sets using conformal prediction and calibration of probabilistic predictors by post-hoc binning — since these possess distribution-free guarantees for i.i.d. data. Two common ways of generalizing beyond the i.i.d. setting include handling

In many real-world scenarios, such as gene knockout experiments, targeted interventions are often accompanied by unknown interventions at off-target sites. Moreover, different units can get randomly exposed to different unknown interventions, thereby creating a mixture of interventions. Identifying different components of this mixture can be very valuable in some applications. Motivated by such situations, in this work, we study the problem of identifying all components present in a mixture of interventions on a given causal Bayesian Network. We construct examples to show that, in general, the components are not identifiable from the mixture distribution. Next, assuming that the given network satisfies a positivity condition, we show that, if the set of mixture components satisfy a mild exclusion assumption, then they can be uniquely identified. Our proof gives an efficient algorithm to recover these targets from the exponentially large search space of possible targets. In the more realistic scenario, where distributions are given via finitely many samples, we conduct a simulation study to analyze the performance of an algorithm derived from our identifiability proof.

Dimension reduction plays a pivotal role in analysing high-dimensional data. However, observations with missing values present serious difficulties in directly applying standard dimension reduction techniques. As a large number of dimension reduction approaches are based on the Gram matrix, we first investigate the effects of missingness on dimension reduction by studying the statistical properties of the Gram matrix with or without missingness, and then we present a bias-corrected Gram matrix with nice statistical properties under heterogeneous missingness. Extensive empirical results, on both simulated and publicly available real datasets, show that the proposed unbiased Gram matrix can significantly improve a broad spectrum of representative dimension reduction approaches.

There has been growing interest in the AI community for precise uncertainty quantification. Conditional density models f(y|x), where x represents potentially high-dimensional features, are an integral part of uncertainty quantification in prediction and Bayesian inference. However, it is challenging to assess conditional density estimates and gain insight into modes of failure. While existing diagnostic tools can determine whether an approximated conditional density is compatible overall with a data sample, they lack a principled framework for identifying, locating, and interpreting the nature of statistically significant discrepancies over the entire feature space. In this paper, we present rigorous and easy-to-interpret diagnostics such as (i) the “Local Coverage Test” (LCT), which distinguishes an arbitrarily misspecified model from the true conditional density of the sample, and (ii) “Amortized Local P-P plots” (ALP) which can quickly provide interpretable graphical summaries of distributional differences at any location x in the feature space. Our validation procedures scale to high dimensions and can potentially adapt to any type of data at hand. We demonstrate the effectiveness of LCT and ALP through a simulated experiment and applications to prediction and parameter inference for image data.

Directed acyclic graph models with hidden variables have been much studied, particularly in view of their computational efficiency and connection with causal methods. In this paper we provide the circumstances under which it is possible for two variables to be identically equal, while all other observed variables stay jointly independent of them and mutually of each other. We find that this is possible if and only if the two variables are ‘densely connected’; in other words, if applications of identifiable causal interventions on the graph cannot (non-trivially) separate them. As a consequence of this, we can also allow such pairs of random variables have any bivariate joint distribution that we choose. This has implications for model search, since it suggests that we can reduce to only consider graphs in which densely connected vertices are always joined by an edge.

Adversarial machine learning has attracted a great amount of attention in recent years. Due to the great importance of support vector machines (SVM) in machine learning, we consider defending SVM against poisoning attacks in this paper. We study two commonly used strategies for defending: designing robust SVM algorithms and data sanitization. Though several robust SVM algorithms have been proposed before, most of them either are in lack of adversarial-resilience, or rely on strong assumptions about the data distribution or the attacker’s behavior. Moreover, the research on the hardness of designing a quality-guaranteed adversarially-resilient SVM algorithm is still quite limited. We are the first, to the best of our knowledge, to prove that even the simplest hard-margin one-class SVM with adversarial outliers problem is NP-complete, and has no fully PTAS unless P=NP. For data sanitization, we explain the effectiveness of DBSCAN (as a density-based outlier removal method) for defending against poisoning attacks. In particular, we link it to the intrinsic dimensionality by proving a sampling theorem in doubling metrics. In our empirical experiments, we systematically compare several defenses including the DBSCAN and robust SVM methods, and investigate the influences from the intrinsic dimensionality and poisoned fraction to their performances.