Journal of Machine Learning Research最新文献

The development of models and methodology for the analysis of data from multiple heterogeneous networks is of importance both in statistical network theory and across a wide spectrum of application domains. Although single-graph analysis is well-studied, multiple graph inference is largely unexplored, in part because of the challenges inherent in appropriately modeling graph differences and yet retaining sufficient model simplicity to render estimation feasible. This paper addresses exactly this gap, by introducing a new model, the common subspace independent-edge multiple random graph model, which describes a heterogeneous collection of networks with a shared latent structure on the vertices but potentially different connectivity patterns for each graph. The model encompasses many popular network representations, including the stochastic blockmodel. The model is both flexible enough to meaningfully account for important graph differences, and tractable enough to allow for accurate inference in multiple networks. In particular, a joint spectral embedding of adjacency matrices-the multiple adjacency spectral embedding-leads to simultaneous consistent estimation of underlying parameters for each graph. Under mild additional assumptions, the estimates satisfy asymptotic normality and yield improvements for graph eigenvalue estimation. In both simulated and real data, the model and the embedding can be deployed for a number of subsequent network inference tasks, including dimensionality reduction, classification, hypothesis testing, and community detection. Specifically, when the embedding is applied to a data set of connectomes constructed through diffusion magnetic resonance imaging, the result is an accurate classification of brain scans by human subject and a meaningful determination of heterogeneity across scans of different individuals.

Many modern data sets require inference methods that can estimate the shared and individual-specific components of variability in collections of matrices that change over time. Promising methods have been developed to analyze these types of data in static cases, but only a few approaches are available for dynamic settings. To address this gap, we consider novel models and inference methods for pairs of matrices in which the columns correspond to multivariate observations at different time points. In order to characterize common and individual features, we propose a Bayesian dynamic factor modeling framework called Time Aligned Common and Individual Factor Analysis (TACIFA) that includes uncertainty in time alignment through an unknown warping function. We provide theoretical support for the proposed model, showing identifiability and posterior concentration. The structure enables efficient computation through a Hamiltonian Monte Carlo (HMC) algorithm. We show excellent performance in simulations, and illustrate the method through application to a social mimicry experiment.

Statistical methods relating tensor predictors to scalar outcomes in a regression model generally vectorize the tensor predictor and estimate the coefficients of its entries employing some form of regularization, use summaries of the tensor covariate, or use a low dimensional approximation of the coefficient tensor. However, low rank approximations of the coefficient tensor can suffer if the true rank is not small. We propose a tensor regression framework which assumes a soft version of the parallel factors (PARAFAC) approximation. In contrast to classic PARAFAC where each entry of the coefficient tensor is the sum of products of row-specific contributions across the tensor modes, the soft tensor regression (Softer) framework allows the row-specific contributions to vary around an overall mean. We follow a Bayesian approach to inference, and show that softening the PARAFAC increases model flexibility, leads to improved estimation of coefficient tensors, more accurate identification of important predictor entries, and more precise predictions, even for a low approximation rank. From a theoretical perspective, we show that employing Softer leads to a weakly consistent posterior distribution of the coefficient tensor, irrespective of the true or approximation tensor rank, a result that is not true when employing the classic PARAFAC for tensor regression. In the context of our motivating application, we adapt Softer to symmetric and semi-symmetric tensor predictors and analyze the relationship between brain network characteristics and human traits.

In mixed multi-view data, multiple sets of diverse features are measured on the same set of samples. By integrating all available data sources, we seek to discover common group structure among the samples that may be hidden in individualistic cluster analyses of a single data view. While several techniques for such integrative clustering have been explored, we propose and develop a convex formalization that enjoys strong empirical performance and inherits the mathematical properties of increasingly popular convex clustering methods. Specifically, our Integrative Generalized Convex Clustering Optimization (iGecco) method employs different convex distances, losses, or divergences for each of the different data views with a joint convex fusion penalty that leads to common groups. Additionally, integrating mixed multi-view data is often challenging when each data source is high-dimensional. To perform feature selection in such scenarios, we develop an adaptive shifted group-lasso penalty that selects features by shrinking them towards their loss-specific centers. Our so-called iGecco+ approach selects features from each data view that are best for determining the groups, often leading to improved integrative clustering. To solve our problem, we develop a new type of generalized multi-block ADMM algorithm using sub-problem approximations that more efficiently fits our model for big data sets. Through a series of numerical experiments and real data examples on text mining and genomics, we show that iGecco+ achieves superior empirical performance for high-dimensional mixed multi-view data.

Effective decision making requires understanding the uncertainty inherent in a prediction. In regression, this uncertainty can be estimated by a variety of methods; however, many of these methods are laborious to tune, generate overconfident uncertainty intervals, or lack sharpness (give imprecise intervals). We address these challenges by proposing a novel method to capture predictive distributions in regression by defining two neural networks with two distinct loss functions. Specifically, one network approximates the cumulative distribution function, and the second network approximates its inverse. We refer to this method as Collaborating Networks (CN). Theoretical analysis demonstrates that a fixed point of the optimization is at the idealized solution, and that the method is asymptotically consistent to the ground truth distribution. Empirically, learning is straightforward and robust. We benchmark CN against several common approaches on two synthetic and six real-world datasets, including forecasting A1c values in diabetic patients from electronic health records, where uncertainty is critical. In the synthetic data, the proposed approach essentially matches ground truth. In the real-world datasets, CN improves results on many performance metrics, including log-likelihood estimates, mean absolute errors, coverage estimates, and prediction interval widths.

Model-based clustering is widely used in a variety of application areas. However, fundamental concerns remain about robustness. In particular, results can be sensitive to the choice of kernel representing the within-cluster data density. Leveraging on properties of pairwise differences between data points, we propose a class of Bayesian distance clustering methods, which rely on modeling the likelihood of the pairwise distances in place of the original data. Although some information in the data is discarded, we gain substantial robustness to modeling assumptions. The proposed approach represents an appealing middle ground between distance- and model-based clustering, drawing advantages from each of these canonical approaches. We illustrate dramatic gains in the ability to infer clusters that are not well represented by the usual choices of kernel. A simulation study is included to assess performance relative to competitors, and we apply the approach to clustering of brain genome expression data.

Labeling patients in electronic health records with respect to their statuses of having a disease or condition, i.e. case or control statuses, has increasingly relied on prediction models using high-dimensional variables derived from structured and unstructured electronic health record data. A major hurdle currently is a lack of valid statistical inference methods for the case probability. In this paper, considering high-dimensional sparse logistic regression models for prediction, we propose a novel bias-corrected estimator for the case probability through the development of linearization and variance enhancement techniques. We establish asymptotic normality of the proposed estimator for any loading vector in high dimensions. We construct a confidence interval for the case probability and propose a hypothesis testing procedure for patient case-control labelling. We demonstrate the proposed method via extensive simulation studies and application to real-world electronic health record data.

Matrix factorization methods, which include Factor analysis (FA) and Principal Components Analysis (PCA), are widely used for inferring and summarizing structure in multivariate data. Many such methods use a penalty or prior distribution to achieve sparse representations ("Sparse FA/PCA"), and a key question is how much sparsity to induce. Here we introduce a general Empirical Bayes approach to matrix factorization (EBMF), whose key feature is that it estimates the appropriate amount of sparsity by estimating prior distributions from the observed data. The approach is very flexible: it allows for a wide range of different prior families and allows that each component of the matrix factorization may exhibit a different amount of sparsity. The key to this flexibility is the use of a variational approximation, which we show effectively reduces fitting the EBMF model to solving a simpler problem, the so-called "normal means" problem. We demonstrate the benefits of EBMF with sparse priors through both numerical comparisons with competing methods and through analysis of data from the GTEx (Genotype Tissue Expression) project on genetic associations across 44 human tissues. In numerical comparisons EBMF often provides more accurate inferences than other methods. In the GTEx data, EBMF identifies interpretable structure that agrees with known relationships among human tissues. Software implementing our approach is available at https://github.com/stephenslab/flashr.

We frame the meta-learning of prediction procedures as a search for an optimal strategy in a two-player game. In this game, Nature selects a prior over distributions that generate labeled data consisting of features and an associated outcome, and the Predictor observes data sampled from a distribution drawn from this prior. The Predictor's objective is to learn a function that maps from a new feature to an estimate of the associated outcome. We establish that, under reasonable conditions, the Predictor has an optimal strategy that is equivariant to shifts and rescalings of the outcome and is invariant to permutations of the observations and to shifts, rescalings, and permutations of the features. We introduce a neural network architecture that satisfies these properties. The proposed strategy performs favorably compared to standard practice in both parametric and nonparametric experiments.

There is tremendous interest in precision medicine as a means to improve patient outcomes by tailoring treatment to individual characteristics. An individualized treatment rule formalizes precision medicine as a map from patient information to a recommended treatment. A treatment rule is defined to be optimal if it maximizes the mean of a scalar outcome in a population of interest, e.g., symptom reduction. However, clinical and intervention scientists often seek to balance multiple and possibly competing outcomes, e.g., symptom reduction and the risk of an adverse event. One approach to precision medicine in this setting is to elicit a composite outcome which balances all competing outcomes; unfortunately, eliciting a composite outcome directly from patients is difficult without a high-quality instrument, and an expert-derived composite outcome may not account for heterogeneity in patient preferences. We propose a new paradigm for the study of precision medicine using observational data that relies solely on the assumption that clinicians are approximately (i.e., imperfectly) making decisions to maximize individual patient utility. Estimated composite outcomes are subsequently used to construct an estimator of an individualized treatment rule which maximizes the mean of patient-specific composite outcomes. The estimated composite outcomes and estimated optimal individualized treatment rule provide new insights into patient preference heterogeneity, clinician behavior, and the value of precision medicine in a given domain. We derive inference procedures for the proposed estimators under mild conditions and demonstrate their finite sample performance through a suite of simulation experiments and an illustrative application to data from a study of bipolar depression.