AISTATS 2015 论文列表

Regularization has played a key role in deriving sensible estimators in high dimensional statistical inference. A substantial amount of recent works has argued for nonconvex regularizers in favor of their superior theoretical properties and excellent practical performances. In a different but analogous vein, nonconvex loss functions are promoted because of their robustness against "outliers". However, these nonconvex formulations are computationally more challenging, especially in the presence of nonsmoothness and non-separability. To address this issue, we propose a new proximal gradient meta-algorithm by rigorously extending the proximal average to the nonconvex setting. We formally prove its nice convergence properties, and illustrate its effectiveness on two applications: multi-task graph-guided fused lasso and robust support vector machines. Experiments demonstrate that our method compares favorably against other alternatives.

We analyze directed, unweighted graphs obtained from x_i∈\RR^d by connecting vertex i to j iff |x_i - x_j| < ε(x_i). Examples of such graphs include k-nearest neighbor graphs, where ε(x_i) varies from point to point, and, arguably, many real world graphs such as co-purchasing graphs. We ask whether we can recover the underlying Euclidean metric ε(x_i) and the associated density p(x_i) given only the directed graph and d. We show that consistent recovery is possible up to isometric scaling when the vertex degree is at least ω(n^2/(2+d)\log(n)^d/(d+2)). Our estimator is based on a careful characterization of a random walk over the directed graph and the associated continuum limit. As an algorithm, it resembles the PageRank centrality metric. We demonstrate empirically that the estimator performs well on simulated examples as well as on real-world co-purchasing graphs even with a small number of points and degree scaling as low as \log(n).

We consider a set of probabilistic functions of some input variables as a representation of the inputs. We present bounds on how informative a representation is about input data. We extend these bounds to hierarchical representations so that we can quantify the contribution of each layer towards capturing the information in the original data. The special form of these bounds leads to a simple, bottom-up optimization procedure to construct hierarchical representations that are also maximally informative about the data. This optimization has linear computational complexity and constant sample complexity in the number of variables. These results establish a new approach to unsupervised learning of deep representations that is both principled and practical. We demonstrate the usefulness of the approach on both synthetic and real-world data.

Due to the dramatic expanse of data categories and the lack of labeled instances, zero-shot learning, which transfers knowledge from observed classes to recognize unseen classes, has started drawing a lot of attention from the research community. In this paper, we propose a semi-supervised max-margin learning framework that integrates the semi-supervised classification problem over observed classes and the unsupervised clustering problem over unseen classes together to tackle zero-shot multi-class classification. By further integrating label embedding into this framework, we produce a dual formulation that permits convenient incorporation of auxiliary label semantic knowledge to improve zero-shot learning. We conduct extensive experiments on three standard image data sets to evaluate the proposed approach by comparing to two state-of-the-art methods. Our results demonstrate the efficacy of the proposed framework.

Nonlinear dimensionality reduction by manifold embedding has become a popular and powerful approach both for visualization and as preprocessing for predictive tasks, but more efficient optimization algorithms are still crucially needed. Majorization-Minimization (MM) is a promising approach that monotonically decreases the cost function, but it remains unknown how to tightly majorize the manifold embedding objective functions such that the resulting MM algorithms are efficient and robust. We propose a new MM procedure that yields fast MM algorithms for a wide variety of manifold embedding problems. In our majorization step, two parts of the cost function are respectively upper bounded by quadratic and Lipschitz surrogates, and the resulting upper bound can be minimized in closed form. For cost functions amenable to such QL-majorization, the MM yields monotonic improvement and is efficient: in experiments the newly developed MM algorithms outperform five state-of-the-art optimization approaches in manifold embedding tasks.

Kulesza et al. recently observed that low-rank spectral learning algorithms, which discard the smallest singular values of a moment matrix during training, can behave in unexpected ways, producing large errors even when the discarded singular values are arbitrarily small. In this paper we prove that when learning predictive state representations those problematic cases disappear if we introduce a particular weighted loss function and learn using sufficiently large sets of statistics; our main result is a bound on the loss of the learned low-rank model in terms of the singular values that are discarded. Practically speaking, this suggests that regardless of the model rank we should use the largest possible sets of statistics, and we show empirically that this is true on both synthetic and real-world domains.

Learning complex control policies from high-dimensional sensory input is a challenge for reinforcement learning algorithms. Kernel methods that approximate values functions or transition models can address this problem. Yet, many current approaches rely on instable greedy maximization. In this paper, we develop a policy search algorithm that integrates robust policy updates and kernel embeddings. Our method can learn non-parametric control policies for infinite horizon continuous MDPs with high-dimensional sensory representations. We show that our method outperforms related approaches, and that our algorithm can learn an underpowered swing-up task task directly from high-dimensional image data.

We consider learning from data of variable quality that may be obtained from different heterogeneous sources. Addressing learning from heterogeneous data in its full generality is a challenging problem. In this paper, we adopt instead a model in which data is observed through heterogeneous noise, where the noise level reflects the quality of the data source. We study how to use stochastic gradient algorithms to learn in this model. Our study is motivated by two concrete examples where this problem arises naturally: learning with local differential privacy based on data from multiple sources with different privacy requirements, and learning from data with labels of variable quality. The main contribution of this paper is to identify how heterogeneous noise impacts performance. We show that given two datasets with heterogeneous noise, the order in which to use them in standard SGD depends on the learning rate. We propose a method for changing the learning rate as a function of the heterogeneity, and prove new regret bounds for our method in two cases of interest. Finally, we evaluate the performance of our algorithm on real data.

In structured prediction, most inference algorithms allocate a homogeneous amount of computation to all parts of the output, which can be wasteful when different parts vary widely in terms of difficulty. In this paper, we propose a heterogeneous approach that dynamically allocates computation to the different parts. Given a pre-trained model, we tune its inference algorithm (a sampler) to increase test-time throughput. The inference algorithm is parametrized by a meta-model and trained via reinforcement learning, where actions correspond to sampling candidate parts of the output, and rewards are log-likelihood improvements. The meta-model is based on a set of domain-general meta-features capturing the progress of the sampler. We test our approach on five datasets and show that it attains the same accuracy as Gibbs sampling but is 2 to 5 times faster.

We propose a non-parametric anomaly detection algorithm for high dimensional data. We score each datapoint by its average K-NN distance, and rank them accordingly. We then train limited complexity models to imitate these scores based on the max-margin learning-to-rank framework. A test-point is declared as an anomaly at α-false alarm level if the predicted score is in the α-percentile. The resulting anomaly detector is shown to be asymptotically optimal in that for any false alarm rate α, its decision region converges to the α-percentile minimum volume level set of the unknown underlying density. In addition, we test both the statistical performance and computational efficiency of our algorithm on a number of synthetic and real-data experiments. Our results demonstrate the superiority of our algorithm over existing K-NN based anomaly detection algorithms, with significant computational savings.

Deep directed generative models are developed. The multi-layered model is designed by stacking sigmoid belief networks, with sparsity-encouraging priors placed on the model parameters. Learning and inference of layer-wise model parameters are implemented in a Bayesian setting. By exploring the idea of data augmentation and introducing auxiliary Polya-Gamma variables, simple and efficient Gibbs sampling and mean-field variational Bayes (VB) inference are implemented. To address large-scale datasets, an online version of VB is also developed. Experimental results are presented for three publicly available datasets: MNIST, Caltech 101 Silhouettes and OCR letters.

We consider the problem of regression on multivariate count data and present a Gibbs sampler for a latent feature regression model suitable for both under- and overdispersed response variables. The model learns count-valued latent features conditional on arbitrary covariates, modeling them as negative binomial variables, and maps them into the dependent count-valued observations using a Dirichlet-multinomial distribution. From another viewpoint, the model can be seen as a generalization of a specific topic model for scenarios where we are interested in generating the actual counts of observations and not just their relative frequencies and co-occurrences. The model is demonstrated on a smart traffic application where the task is to predict public transportation volume for unknown locations based on a characterization of the close-by services and venues.

A hierarchical gamma process infinite edge partition model is proposed to factorize the binary adjacency matrix of an unweighted undirected relational network under a Bernoulli-Poisson link. The model describes both homophily and stochastic equivalence, and is scalable to big sparse networks by focusing its computation on pairs of linked nodes. It can not only discover overlapping communities and inter-community interactions, but also predict missing edges. A simplified version omitting inter-community interactions is also provided and we reveal its interesting connections to existing models. The number of communities is automatically inferred in a nonparametric Bayesian manner, and efficient inference via Gibbs sampling is derived using novel data augmentation techniques. Experimental results on four real networks demonstrate the models’ scalability and state-of-the-art performance.

Learning the structure of a graphical model is a fundamental problem and it is used extensively to infer the relationship between random variables. In many real world applications, we usually have some prior knowledge about the underlying graph structure, such as degree distribution and block structure. In this paper, we propose a novel generative model for describing the block structure in general exponential families, and optimize it by an Expectation-Maximization(EM) algorithm with variational Bayes. Experimental results show that our method performs well on both synthetic and real data. Further, our method can predict overlapped block structure of a graphical model in general exponential families.

We address the problem of causal discovery in the two-variable case given a sample from their joint distribution. The proposed method is based on a known assumption that, if X -> Y (X causes Y), the marginal distribution of the cause, P(X), contains no information about the conditional distribution P(Y|X). Consequently, estimating P(Y|X) from P(X) should not be possible. However, estimating P(X|Y) based on P(Y) may be possible. This paper employs this asymmetry to propose CURE, a causal discovery method which decides upon the causal direction by comparing the accuracy of the estimations of P(Y|X) and P(X|Y). To this end, we propose a method for estimating a conditional from samples of the corresponding marginal, which we call unsupervised inverse GP regression. We evaluate CURE on synthetic and real data. On the latter, our method outperforms existing causal inference methods.

We consider the setting of linear regression in high dimension. We focus on the problem of constructing adaptive and honest confidence sets for the sparse parameter θ, i.e. we want to construct a confidence set for theta that contains theta with high probability, and that is as small as possible. The l_2 diameter of a such confidence set should depend on the sparsity S of θ- the larger S, the wider the confidence set. However, in practice, S is unknown. This paper focuses on constructing a confidence set for θwhich contains θwith high probability, whose diameter is adaptive to the unknown sparsity S, and which is implementable in practice.

We consider the problem of learning from a similarity matrix (such as spectral clustering and low-dimensional embedding), when computing pairwise similarities are costly, and only a limited number of entries can be observed. We provide a theoretical analysis using standard notions of graph approximation, significantly generalizing previous results, which focused on spectral clustering with two clusters. We also propose a new algorithmic approach based on adaptive sampling, which experimentally matches or improves on previous methods, while being considerably more general and computationally cheaper.

Standard Multi-Armed Bandit (MAB) problems assume that the arms are independent. However, in many application scenarios, the information obtained by playing an arm provides information about the remainder of the arms. Hence, in such applications, this informativeness can and should be exploited to enable faster convergence to the optimal solution. In this paper, formalize a new class of multi-armed bandit methods, Global Multi-armed Bandit (GMAB), in which arms are globally informative through a global parameter, i.e., choosing an arm reveals information about all the arms. We propose a greedy policy for the GMAB which always selects the arm with the highest estimated expected reward, and prove that it achieves bounded parameter-dependent regret. Hence, this policy selects suboptimal arms only finitely many times, and after a finite number of initial time steps, the optimal arm is selected in all of the remaining time steps with probability one. In addition, we also study how the informativeness of the arms about each other’s rewards affects the speed of learning. Specifically, we prove that the parameter-free (worst-case) regret is sublinear in time, and decreases with the informativeness of the arms. We also prove a sublinear in time Bayesian risk bound for the GMAB which reduces to the well-known Bayesian risk bound for linearly parameterized bandits when the arms are fully informative. GMABs have applications ranging from drug dosage control to dynamic pricing.

Databases in domains such as healthcare are routinely released to the public in aggregated form. Unfortunately, naive modeling with aggregated data may significantly diminish the accuracy of inferences at the individual level. This paper addresses the scenario where features are provided at the individual level, but the target variables are only available as histogram aggregates or order statistics. We consider a limiting case of generalized linear modeling when the target variables are only known up to permutation, and explore how this relates to permutation testing; a standard technique for assessing statistical dependency. Based on this relationship, we propose a simple algorithm to estimate the model parameters and individual level inferences via alternating imputation and standard generalized linear model fitting. Our results suggest the effectiveness of the proposed approach when, in the original data, permutation testing accurately ascertains the veracity of the linear relationship. The framework is extended to general histogram data with larger bins - with order statistics such as the median as a limiting case. Our experimental results on simulated data and aggregated healthcare data suggest a diminishing returns property with respect to the granularity of the histogram - when a linear relationship holds in the original data, the targets can be predicted accurately given relatively coarse histograms.