AISTATS 2019 论文列表

Predicting properties of nodes in a graph is an important problem with applications in a variety of domains. Graph-based Semi Supervised Learning (SSL) methods aim to address this problem by labeling a small subset of the nodes as seeds, and then utilizing the graph structure to predict label scores for the rest of the nodes in the graph. Recently, Graph Convolutional Networks (GCNs) have achieved impressive performance on the graph-based SSL task. In addition to label scores, it is also desirable to have confidence scores associated with them. Unfortunately, confidence estimation in the context of GCN has not been previously explored. We fill this important gap in this paper and propose ConfGCN, which estimates labels scores along with their confidences jointly in GCN-based setting. ConfGCN uses these estimated confidences to determine the influence of one node on another during neighborhood aggregation, thereby acquiring anisotropic capabilities. Through extensive analysis and experiments on standard benchmarks, we find that ConfGCN is able to outperform state-of-the-art baselines. We have made ConfGCN’s source code available to encourage reproducible research.

We propose a novel confidence scoring mechanism for deep neural networks based on a two-model paradigm involving a base model and a meta-model. The confidence score is learned by the meta-model observing the base model succeeding/failing at its task. As features to the meta-model, we investigate linear classifier probes inserted between the various layers of the base model. Our experiments demonstrate that this approach outperforms multiple baselines in a filtering task, i.e., task of rejecting samples with low confidence. Experimental results are presented using CIFAR-10 and CIFAR-100 dataset with and without added noise. We discuss the importance of confidence scoring to bridge the gap between experimental and real-world applications.

The multiresolution Gaussian process (GP) has gained increasing attention as a viable approach towards improving the quality of approximations in GPs that scale well to large-scale data. Most of the current constructions assume full independence across resolutions. This assumption simplifies the inference, but it underestimates the uncertainties in transitioning from one resolution to another. This in turn results in models which are prone to overfitting in the sense of excessive sensitivity to the chosen resolution, and predictions which are non-smooth at the boundaries. Our contribution is a new construction which instead assumes conditional independence among GPs across resolutions. We show that relaxing the full independence assumption enables robustness against overfitting, and that it delivers predictions that are smooth at the boundaries. Our new model is compared against current state of the art on 2 synthetic and 9 real-world datasets. In most cases, our new conditionally independent construction performed favorably when compared against models based on the full independence assumption. In particular, it exhibits little to no signs of overfitting.

We consider the following conditional linear regression problem: the task is to identify both (i) a $k$-DNF condition $c$ and (ii) a linear rule $f$ such that the probability of $c$ is (approximately) at least some given bound $\mu$, and minimizing the $l_p$ loss of $f$ at predicting the target $z$ in the distribution conditioned on $c$. Thus, the task is to identify a portion of the distribution on which a linear rule can provide a good fit. Algorithms for this task are useful in cases where portions of the distribution are not modeled well by simple, learnable rules, but on other portions such rules perform well. The prior state-of-the-art for such algorithms could only guarantee finding a condition of probability $O(\mu/n^k )$ when a condition of probability $\mu$ exists, and achieved a $O(n^k)$-approximation to the target loss. Here, we give efficient algorithms for solving this task with a condition $c$ that nearly matches the probability of the ideal condition, while also improving the approximation to the target loss to a $O  (n^{k/2})$ factor. We also give an algorithm for finding a k-DNF reference class for prediction at a given query point, that obtains a sparse regression fit that has loss within $O(n^k)$ of optimal among all sparse regression parameters and sufficiently large $k$-DNF reference classes containing the query point.

In large-scale distributed linear transform problems, coded computation plays an important role to reduce the delay caused by slow machines. However, existing coded schemes could end up destroying the significant sparsity that exists in large-scale machine learning problems, and in turn increase the computational delay. In this paper, we propose a coded computation strategy, referred to as diagonal code, that achieves the optimum recovery threshold and the optimum computation load. Furthermore, by leveraging the ideas from random proposal graph theory, we design a random code that achieves a constant computation load, which significantly outperforms the existing best known result. We apply our schemes to the distributed gradient descent problem and demonstrate the advantage of the approach over current fastest coded schemes.

For constrained nonconvex minimization problems, we propose a meta stochastic projection-free optimization algorithm, named Normalized Frank Wolfe Updating, that can take any Gradient Estimator (GE) as input. For this algorithm, we prove its convergence rate, regardless of the choice of GE. Using a sophisticated GE, this algorithm can significantly improve the Stochastic First order Oracle (SFO) complexity. Further, a new second order GE strategy is proposed to incorporate curvature information, which enjoys theoretical advantage over the first order ones. Besides, this paper also provides a lower bound of Linear-optimization Oracle (LO) queried to achieve an approximate stationary point. Simulation studies validate our analysis under various parameter settings.

We propose a general statistical framework for clustering multiple time series that exhibit nonlinear dynamics into an a-priori-unknown number of sub-groups. Our motivation comes from neuroscience, where an important problem is to identify, within a large assembly of neurons, subsets that respond similarly to a stimulus or contingency. Upon modeling the multiple time series as the output of a Dirichlet process mixture of nonlinear state-space models, we derive a Metropolis-within-Gibbs algorithm for full Bayesian inference that alternates between sampling cluster assignments and sampling parameter values that form the basis of the clustering. The Metropolis step employs recent innovations in particle-based methods. We apply the framework to clustering time series acquired from the prefrontal cortex of mice in an experiment designed to characterize the neural underpinnings of fear.

We present a novel and hierarchical approach for supervised classification of signals spanning over a fixed graph, reflecting shared properties of the dataset. To this end, we introduce a Convolutional Cluster Pooling layer exploiting a multi-scale clustering in order to highlight, at different resolutions, locally connected regions on the input graph. Our proposal generalises well-established neural models such as Convolutional Neural Networks (CNNs) on irregular and complex domains, by means of the exploitation of the weight sharing property in a graph-oriented architecture. In this work, such property is based on the centrality of each vertex within its soft-assigned cluster. Extensive experiments on NTU RGB+D, CIFAR-10 and 20NEWS demonstrate the effectiveness of the proposed technique in capturing both local and global patterns in graph-structured data out of different domains.

In this work, we study a new approach to optimizing the margin distribution realized by binary classifiers, in which the learner searches the hypothesis space in such a way that a pre-set margin level ends up being a distribution-robust estimator of the margin location. This procedure is easily implemented using gradient descent, and admits finite-sample bounds on the excess risk under unbounded inputs, yielding competitive rates under mild assumptions. Empirical tests on real-world benchmark data reinforce the basic principles highlighted by the theory.

Missing data are ubiquitous in many domains such as healthcare. When these data entries are not missing completely at random, the (conditional) independence relations in the observed data may be different from those in the complete data generated by the underlying causal process. Consequently, simply applying existing causal discovery methods to the observed data may lead to wrong conclusions. In this paper, we aim at developing a causal discovery method to recover the underlying causal structure from observed data that are missing under different mechanisms, including missing completely at random (MCAR), missing at random (MAR), and missing not at random (MNAR). With missingness mechanisms represented by missingness graphs (m-graphs), we analyze conditions under which additional correction is needed to derive conditional independence/dependence relations in the complete data. Based on our analysis, we propose Missing Value PC (MVPC), which extends the PC algorithm to incorporate additional corrections. Our proposed MVPC is shown in theory to give asymptotically correct results even on data that are MAR or MNAR. Experimental results on both synthetic data and real healthcare applications illustrate that the proposed algorithm is able to find correct causal relations even in the general case of MNAR.

To use machine learning in high stakes applications (e.g. medicine), we need tools for building confidence in the system and evaluating whether it is reliable. Methods to improve model reliability often require new learning algorithms (e.g. using Bayesian inference to obtain uncertainty estimates). An alternative is to audit a model after it is trained. In this paper, we describe resampling uncertainty estimation (RUE), an algorithm to audit the pointwise reliability of predictions. Intuitively, RUE estimates the amount that a prediction would change if the model had been fit on different training data. The algorithm uses the gradient and Hessian of the model’s loss function to create an ensemble of predictions. Experimentally, we show that RUE more effectively detects inaccurate predictions than existing tools for auditing reliability subsequent to training. We also show that RUE can create predictive distributions that are competitive with state-of-the-art methods like Monte Carlo dropout, probabilistic backpropagation, and deep ensembles, but does not depend on specific algorithms at train-time like these methods do.

The wide adoption of Convolutional Neural Networks CNNs in applications where decision-making under uncertainty is fundamental, has brought a great deal of attention to the ability of these models to accurately quantify the uncertainty in their predictions. Previous work on combining CNNs with Gaussian processes GPs has been developed under the assumption that the predictive probabilities of these models are well-calibrated. In this paper we show that, in fact, current combinations of CNNs and GPs are miscalibrated. We proposes a novel combination that considerably outperforms previous approaches on this aspect, while achieving state-of-the-art performance on image classification tasks.

State of the art online learning procedures focus either on selecting the best alternative (“best arm identification”) or on minimizing the cost (the “regret”). We merge these two objectives by providing the theoretical analysis of cost minimizing algorithms that are also $\delta$-PAC (with a proven guaranteed bound on the decision time), hence fulfilling at the same time regret minimization and best arm identification. This analysis sheds light on the common observation that ill-callibrated UCB-algorithms minimize regret while still identifying quickly the best arm. We also extend these results to the non-iid case faced by many practitioners. This provides a technique to make cost versus decision time compromise when doing adaptive tests with applications ranging from website A/B testing to clinical trials.

Games with continuous strategy sets arise in several machine learning problems (e.g. adversarial learning). For such games, simple no-regret learning algorithms exist in several cases and ensure convergence to coarse correlated equilibria (CCE). The efficiency of such equilibria with respect to a social function, however, is not well understood. In this paper, we define the class of valid utility games with continuous strategies and provide efficiency bounds for their CCEs. Our bounds rely on the social function being a monotone DR-submodular function. We further refine our bounds based on the curvature of the social function. Furthermore, we extend our efficiency bounds to a class of non-submodular functions that satisfy approximate submodularity properties. Finally, we show that valid utility games with continuous strategies can be designed to maximize monotone DR-submodular functions subject to disjoint constraints with approximation guarantees. The approximation guarantees we derive are based on the efficiency of the equilibria of such games and can improve the existing ones in the literature. We illustrate and validate our results on a budget allocation game and a sensor coverage problem.

Survival models derived from health care data are an important support to inform critical screening and therapeutic decisions. Most models however, do not generalize to populations outside the marginal and conditional distribution assumptions for which they were derived. This presents a significant barrier to the deployment of machine learning techniques into wider clinical practice as most medical studies are data scarce, especially for the analysis of time-to-event outcomes. In this work we propose a survival prediction model that is able to improve predictions on a small data domain of interest - such as a local hospital - by leveraging related data from other domains - such as data from other hospitals. We construct an ensemble of weak survival predictors which iteratively adapt the marginal distributions of the source and target data such that similar source patients contribute to the fit and ultimately improve predictions on target patients of interest. This represents the first boosting-based transfer learning algorithm in the survival analysis literature. We demonstrate the performance and utility of our algorithm on synthetic and real healthcare data collected at various locations.

Recent work (Lang et al., 2018) has shown that some popular approximate MAP inference algorithms perform very well when the input instance is stable. The simplest stability condition assumes that the MAP solution does not change at all when some of the pairwise potentials are adversarially perturbed. Unfortunately, this strong condition does not seem to hold in practice. We introduce a significantly more relaxed condition that only requires portions of an input instance to be stable. Under this block stability condition, we prove that the pairwise LP relaxation is persistent on the stable blocks. We complement our theoretical results with an evaluation of real-world examples from computer vision, and we find that these instances have large stable regions.

This paper concerns the problem of demixing a series of source signals from the sum of bilinear measurements. This problem spans diverse areas such as communication, imaging processing, machine learning, etc. However, semidefinite programming for blind demixing is prohibitive to large-scale problems due to high computational complexity and storage cost. Although several efficient algorithms have been developed recently that enjoy the benefits of fast convergence rates and even regularization free, they still call for spectral initialization. To find simple initialization approach that works equally well as spectral initialization, we propose to solve blind demixing problem via Wirtinger flow with random initialization, which yields a natural implementation. To reveal the efficiency of this algorithm, we provide the global convergence guarantee concerning randomly initialized Wirtinger flow for blind demixing. Specifically, it shows that with sufficient samples, the iterates of randomly initialized Wirtinger flow can enter a local region that enjoys strong convexity and strong smoothness within a few iterations at the first stage. At the second stage, iterates of randomly initialized Wirtinger flow further converge linearly to the ground truth.

Kernel methods have been successfully used in various domains to model nonlinear patterns. However, the structure of the kernels is typically handcrafted for each dataset based on the experience of the data analyst. In this paper, we present a novel technique to learn kernels that best fit the data. We exploit the measure-theoretic view of a shift-invariant kernel given by the Bochner’s theorem, and automatically learn the measure in terms of a parameterized quantile function. This flexible black box quantile function, evaluated on Quasi-Monte Carlo samples, builds up quasi-random Fourier feature maps that can approximate arbitrary kernels. The proposed method is not only general enough to be used in any kernel machine, but can also be combined with other kernel design techniques. We learn expressive kernels on a variety of datasets, verifying the methods ability to automatically discover complex patterns without being guided by human expert knowledge.

The Binary Space Partitioning (BSP)-Tree process is proposed to produce flexible 2-D partition structures which are originally used as a Bayesian nonparametric prior for relational modelling. It can hardly be applied to other learning tasks such as regression trees because extending the BSP-Tree process to a higher dimensional space is nontrivial. This paper is the first attempt to extend the BSP-Tree process to a d-dimensional ($d>2$) space. We propose to generate a cutting hyperplane, which is assumed to be parallel to $d-2$ dimensions, to cut each node in the d-dimensional BSP-tree. By designing a subtle strategy to sample two free dimensions from d dimensions, the extended BSP-Tree process can inherit the essential self-consistency property from the original version. Based on the extended BSP-Tree process, an ensemble model, which is named the BSP-Forest, is further developed for regression tasks. Thanks to the retained self-consistency property, we can thus significantly reduce the geometric calculations in the inference stage. Compared to its counterpart, the Mondrian Forest, the BSP-Forest can achieve similar performance with fewer cuts due to its flexibility. The BSP-Forest also outperforms other (Bayesian) regression forests on a number of real-world data sets.