Journal of Machine Learning Research最新文献

We consider conducting inference on the output of the Classification and Regression Tree (CART) (Breiman et al., 1984) algorithm. A naive approach to inference that does not account for the fact that the tree was estimated from the data will not achieve standard guarantees, such as Type 1 error rate control and nominal coverage. Thus, we propose a selective inference framework for conducting inference on a fitted CART tree. In a nutshell, we condition on the fact that the tree was estimated from the data. We propose a test for the difference in the mean response between a pair of terminal nodes that controls the selective Type 1 error rate, and a confidence interval for the mean response within a single terminal node that attains the nominal selective coverage. Efficient algorithms for computing the necessary conditioning sets are provided. We apply these methods in simulation and to a dataset involving the association between portion control interventions and caloric intake.

The neighborhood selection method directly explores the conditional dependence structure and has been widely used to construct undirected graphical models. However, except for some special cases with discrete data, there is little research on nonparametric methods for neighborhood selection with mixed data. This paper develops a fully nonparametric neighborhood selection method under a consolidated smoothing spline ANOVA (SS ANOVA) decomposition framework. The proposed model is flexible and contains many existing models as special cases. The proposed method provides a unified framework for mixed data without any restrictions on the type of each random variable. We detect edges by applying an $L_1$ regularization to interactions in the SS ANOVA decomposition. We propose an iterative procedure to compute the estimates and establish the convergence rates for conditional density and interactions. Simulations indicate that the proposed methods perform well under Gaussian and non-Gaussian settings. We illustrate the proposed methods using two real data examples.

The current paper studies the problem of minimizing a loss f(x) subject to constraints of the form Dx ∈ S, where S is a closed set, convex or not, and D is a matrix that fuses parameters. Fusion constraints can capture smoothness, sparsity, or more general constraint patterns. To tackle this generic class of problems, we combine the Beltrami-Courant penalty method of optimization with the proximal distance principle. The latter is driven by minimization of penalized objectives $f\left(x\right)+\frac{\rho }{2}\text{dist}{(Dx,S)}^2$ involving large tuning constants ρ and the squared Euclidean distance of Dx from S. The next iterate x_n+1 of the corresponding proximal distance algorithm is constructed from the current iterate x_n by minimizing the majorizing surrogate function $f\left(x\right)+\frac{\rho }{2}{\Vert Dx-{𝒫}_S\left(D{x}_n\right)\Vert }^2$. For fixed ρ and a subanalytic loss f(x) and a subanalytic constraint set S, we prove convergence to a stationary point. Under stronger assumptions, we provide convergence rates and demonstrate linear local convergence. We also construct a steepest descent (SD) variant to avoid costly linear system solves. To benchmark our algorithms, we compare their results to those delivered by the alternating direction method of multipliers (ADMM). Our extensive numerical tests include problems on metric projection, convex regression, convex clustering, total variation image denoising, and projection of a matrix to a good condition number. These experiments demonstrate the superior speed and acceptable accuracy of our steepest variant on high-dimensional problems. Julia code to replicate all of our experiments can be found at https://github.com/alanderos91/ProximalDistanceAlgorithms.jl.

Spectral inference on multiple networks is a rapidly-developing subfield of graph statistics. Recent work has demonstrated that joint, or simultaneous, spectral embedding of multiple independent networks can deliver more accurate estimation than individual spectral decompositions of those same networks. Such inference procedures typically rely heavily on independence assumptions across the multiple network realizations, and even in this case, little attention has been paid to the induced network correlation that can be a consequence of such joint embeddings. In this paper, we present a generalized omnibus embedding methodology and we provide a detailed analysis of this embedding across both independent and correlated networks, the latter of which significantly extends the reach of such procedures, and we describe how this omnibus embedding can itself induce correlation. This leads us to distinguish between inherent correlation-that is, the correlation that arises naturally in multisample network data-and induced correlation, which is an artifice of the joint embedding methodology. We show that the generalized omnibus embedding procedure is flexible and robust, and we prove both consistency and a central limit theorem for the embedded points. We examine how induced and inherent correlation can impact inference for network time series data, and we provide network analogues of classical questions such as the effective sample size for more generally correlated data. Further, we show how an appropriately calibrated generalized omnibus embedding can detect changes in real biological networks that previous embedding procedures could not discern, confirming that the effect of inherent and induced correlation can be subtle and transformative. By allowing for and deconstructing both forms of correlation, our methodology widens the scope of spectral techniques for network inference, with import in theory and practice.

We present a unified framework for estimation and analysis of generalized additive models in high dimensions. The framework defines a large class of penalized regression estimators, encompassing many existing methods. An efficient computational algorithm for this class is presented that easily scales to thousands of observations and features. We prove minimax optimal convergence bounds for this class under a weak compatibility condition. In addition, we characterize the rate of convergence when this compatibility condition is not met. Finally, we also show that the optimal penalty parameters for structure and sparsity penalties in our framework are linked, allowing cross-validation to be conducted over only a single tuning parameter. We complement our theoretical results with empirical studies comparing some existing methods within this framework.

With the increasing adoption of electronic health records, there is an increasing interest in developing individualized treatment rules, which recommend treatments according to patients' characteristics, from large observational data. However, there is a lack of valid inference procedures for such rules developed from this type of data in the presence of high-dimensional covariates. In this work, we develop a penalized doubly robust method to estimate the optimal individualized treatment rule from high-dimensional data. We propose a split-and-pooled de-correlated score to construct hypothesis tests and confidence intervals. Our proposal adopts the data splitting to conquer the slow convergence rate of nuisance parameter estimations, such as non-parametric methods for outcome regression or propensity models. We establish the limiting distributions of the split-and-pooled de-correlated score test and the corresponding one-step estimator in high-dimensional setting. Simulation and real data analysis are conducted to demonstrate the superiority of the proposed method.

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, $p$, 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.

Instrumental variables (IV) are widely used in the social and health sciences in situations where a researcher would like to measure a causal effect but cannot perform an experiment. For valid causal inference in an IV model, there must be external (exogenous) variation that (i) has a sufficiently large impact on the variable of interest (called the relevance assumption) and where (ii) the only pathway through which the external variation impacts the outcome is via the variable of interest (called the exclusion restriction). For statistical inference, researchers must also make assumptions about the functional form of the relationship between the three variables. Current practice assumes (i) and (ii) are met, then postulates a functional form with limited input from the data. In this paper, we describe a framework that leverages machine learning to validate these typically unchecked but consequential assumptions in the IV framework, providing the researcher empirical evidence about the quality of the instrument given the data at hand. Central to the proposed approach is the idea of prediction validity. Prediction validity checks that error terms - which should be independent from the instrument - cannot be modeled with machine learning any better than a model that is identically zero. We use prediction validity to develop both one-stage and two-stage approaches for IV, and demonstrate their performance on an example relevant to climate change policy.