{"title":"Hoeffding's inequality for general Markov chains with its applications to statistical learning.","authors":"Jianqing Fan, Bai Jiang, Qiang Sun","doi":"","DOIUrl":"","url":null,"abstract":"<p><p>This paper establishes Hoeffding's lemma and inequality for bounded functions of general-state-space and not necessarily reversible Markov chains. The sharpness of these results is characterized by the optimality of the ratio between variance proxies in the Markov-dependent and independent settings. The boundedness of functions is shown necessary for such results to hold in general. To showcase the usefulness of the new results, we apply them for non-asymptotic analyses of MCMC estimation, respondent-driven sampling and high-dimensional covariance matrix estimation on time series data with a Markovian nature. In addition to statistical problems, we also apply them to study the time-discounted rewards in econometric models and the multi-armed bandit problem with Markovian rewards arising from the field of machine learning.</p>","PeriodicalId":314696,"journal":{"name":"Journal of machine learning research : JMLR","volume":" ","pages":""},"PeriodicalIF":6.0,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8457514/pdf/nihms-1639585.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"39450202","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Bayesian time-aligned factor analysis of paired multivariate time series.","authors":"Arkaprava Roy, Jana Schaich Borg, David B Dunson","doi":"","DOIUrl":"","url":null,"abstract":"<p><p>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.</p>","PeriodicalId":314696,"journal":{"name":"Journal of machine learning research : JMLR","volume":" ","pages":""},"PeriodicalIF":6.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9221555/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"40398444","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Integrative Generalized Convex Clustering Optimization and Feature Selection for Mixed Multi-View Data.","authors":"Minjie Wang, Genevera I Allen","doi":"","DOIUrl":"","url":null,"abstract":"<p><p>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.</p>","PeriodicalId":314696,"journal":{"name":"Journal of machine learning research : JMLR","volume":" ","pages":""},"PeriodicalIF":6.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8570363/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"39596948","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Learning and Planning for Time-Varying MDPs Using Maximum Likelihood Estimation.","authors":"Melkior Ornik, Ufuk Topcu","doi":"","DOIUrl":"","url":null,"abstract":"<p><p>This paper proposes a formal approach to online learning and planning for agents operating in a priori unknown, time-varying environments. The proposed method computes the maximally likely model of the environment, given the observations about the environment made by an agent earlier in the system run and assuming knowledge of a bound on the maximal rate of change of system dynamics. Such an approach generalizes the estimation method commonly used in learning algorithms for unknown Markov decision processes with time-invariant transition probabilities, but is also able to quickly and correctly identify the system dynamics following a change. Based on the proposed method, we generalize the exploration bonuses used in learning for time-invariant Markov decision processes by introducing a notion of uncertainty in a learned time-varying model, and develop a control policy for time-varying Markov decision processes based on the exploitation and exploration trade-off. We demonstrate the proposed methods on four numerical examples: a patrolling task with a change in system dynamics, a two-state MDP with periodically changing outcomes of actions, a wind flow estimation task, and a multi-armed bandit problem with periodically changing probabilities of different rewards.</p>","PeriodicalId":314696,"journal":{"name":"Journal of machine learning research : JMLR","volume":" ","pages":"1-40"},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8739185/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"39913174","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Estimation and Inference for High Dimensional Generalized Linear Models: A Splitting and Smoothing Approach.","authors":"Zhe Fei, Yi Li","doi":"","DOIUrl":"","url":null,"abstract":"<p><p>The focus of modern biomedical studies has gradually shifted to explanation and estimation of joint effects of high dimensional predictors on disease risks. Quantifying uncertainty in these estimates may provide valuable insight into prevention strategies or treatment decisions for both patients and physicians. High dimensional inference, including confidence intervals and hypothesis testing, has sparked much interest. While much work has been done in the linear regression setting, there is lack of literature on inference for high dimensional generalized linear models. We propose a novel and computationally feasible method, which accommodates a variety of outcome types, including normal, binomial, and Poisson data. We use a \"splitting and smoothing\" approach, which splits samples into two parts, performs variable selection using one part and conducts partial regression with the other part. Averaging the estimates over multiple random splits, we obtain the smoothed estimates, which are numerically stable. We show that the estimates are consistent, asymptotically normal, and construct confidence intervals with proper coverage probabilities for all predictors. We examine the finite sample performance of our method by comparing it with the existing methods and applying it to analyze a lung cancer cohort study.</p>","PeriodicalId":314696,"journal":{"name":"Journal of machine learning research : JMLR","volume":" ","pages":""},"PeriodicalIF":6.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8442657/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"39443931","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The flare package for high dimensional linear regression and precision matrix estimation in R","authors":"Xingguo Li, T. Zhao, Xiaoming Yuan, Han Liu","doi":"10.5555/2789272.2789290","DOIUrl":"https://doi.org/10.5555/2789272.2789290","url":null,"abstract":"This paper describes an R package named flare, which implements a family of new high dimensional regression methods (LAD Lasso, SQRT Lasso, ℓ q Lasso, and Dantzig selector) and their extensions to sparse precision matrix estimation (TIGER and CLIME). These methods exploit different nonsmooth loss functions to gain modeling exibility, estimation robustness, and tuning insensitiveness. The developed solver is based on the alternating direction method of multipliers (ADMM), which is further accelerated by the multistage screening approach. The package flare is coded in double precision C, and called from R by a user-friendly interface. The memory usage is optimized by using the sparse matrix output. The experiments show that flare is efficient and can scale up to large problems.","PeriodicalId":314696,"journal":{"name":"Journal of machine learning research : JMLR","volume":"98 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122594319","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Generalized Score Matching for Non-Negative Data.","authors":"Shiqing Yu, Mathias Drton, Ali Shojaie","doi":"","DOIUrl":"","url":null,"abstract":"<p><p>A common challenge in estimating parameters of probability density functions is the intractability of the normalizing constant. While in such cases maximum likelihood estimation may be implemented using numerical integration, the approach becomes computationally intensive. The score matching method of Hyvärinen (2005) avoids direct calculation of the normalizing constant and yields closed-form estimates for exponential families of continuous distributions over <math> <mrow><msup><mi>R</mi> <mi>m</mi></msup> </mrow> </math> . Hyvärinen (2007) extended the approach to distributions supported on the non-negative orthant, <math> <mrow><msubsup><mi>R</mi> <mo>+</mo> <mi>m</mi></msubsup> </mrow> </math> . In this paper, we give a generalized form of score matching for non-negative data that improves estimation efficiency. As an example, we consider a general class of pairwise interaction models. Addressing an overlooked inexistence problem, we generalize the regularized score matching method of Lin et al. (2016) and improve its theoretical guarantees for non-negative Gaussian graphical models.</p>","PeriodicalId":314696,"journal":{"name":"Journal of machine learning research : JMLR","volume":" ","pages":""},"PeriodicalIF":6.0,"publicationDate":"2019-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8291733/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"39208339","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"All Models are Wrong, but <i>Many</i> are Useful: Learning a Variable's Importance by Studying an Entire Class of Prediction Models Simultaneously.","authors":"Aaron Fisher, Cynthia Rudin, Francesca Dominici","doi":"","DOIUrl":"","url":null,"abstract":"<p><p>Variable importance (VI) tools describe how much covariates contribute to a prediction model's accuracy. However, important variables for one well-performing model (for example, a linear model <i>f</i> (x) = x <sup><i>T</i></sup> <i>β</i> with a fixed coefficient vector <i>β</i>) may be unimportant for another model. In this paper, we propose model class reliance (MCR) as the range of VI values across <i>all</i> well-performing model in a prespecified class. Thus, MCR gives a more comprehensive description of importance by accounting for the fact that many prediction models, possibly of different parametric forms, may fit the data well. In the process of deriving MCR, we show several informative results for permutation-based VI estimates, based on the VI measures used in Random Forests. Specifically, we derive connections between permutation importance estimates for a <i>single</i> prediction model, U-statistics, conditional variable importance, conditional causal effects, and linear model coefficients. We then give probabilistic bounds for MCR, using a novel, generalizable technique. We apply MCR to a public data set of Broward County criminal records to study the reliance of recidivism prediction models on sex and race. In this application, MCR can be used to help inform VI for unknown, proprietary models.</p>","PeriodicalId":314696,"journal":{"name":"Journal of machine learning research : JMLR","volume":" ","pages":""},"PeriodicalIF":6.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8323609/pdf/nihms-1670270.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"39264727","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Determining the Number of Latent Factors in Statistical Multi-Relational Learning.","authors":"Chengchun Shi, Wenbin Lu, Rui Song","doi":"","DOIUrl":"","url":null,"abstract":"<p><p>Statistical relational learning is primarily concerned with learning and inferring relationships between entities in large-scale knowledge graphs. Nickel et al. (2011) proposed a RESCAL tensor factorization model for statistical relational learning, which achieves better or at least comparable results on common benchmark data sets when compared to other state-of-the-art methods. Given a positive integer <i>s</i>, RESCAL computes an <i>s</i>-dimensional latent vector for each entity. The latent factors can be further used for solving relational learning tasks, such as collective classification, collective entity resolution and link-based clustering. The focus of this paper is to determine the number of latent factors in the RESCAL model. Due to the structure of the RESCAL model, its log-likelihood function is not concave. As a result, the corresponding maximum likelihood estimators (MLEs) may not be consistent. Nonetheless, we design a specific pseudometric, prove the consistency of the MLEs under this pseudometric and establish its rate of convergence. Based on these results, we propose a general class of information criteria and prove their model selection consistencies when the number of relations is either bounded or diverges at a proper rate of the number of entities. Simulations and real data examples show that our proposed information criteria have good finite sample properties.</p>","PeriodicalId":314696,"journal":{"name":"Journal of machine learning research : JMLR","volume":" ","pages":""},"PeriodicalIF":6.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6980192/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"37581845","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Nonuniformity of P-values Can Occur Early in Diverging Dimensions.","authors":"Yingying Fan, Emre Demirkaya, Jinchi Lv","doi":"","DOIUrl":"","url":null,"abstract":"<p><p>Evaluating the joint significance of covariates is of fundamental importance in a wide range of applications. To this end, p-values are frequently employed and produced by algorithms that are powered by classical large-sample asymptotic theory. It is well known that the conventional p-values in Gaussian linear model are valid even when the dimensionality is a non-vanishing fraction of the sample size, but can break down when the design matrix becomes singular in higher dimensions or when the error distribution deviates from Gaussianity. A natural question is when the conventional p-values in generalized linear models become invalid in diverging dimensions. We establish that such a breakdown can occur early in nonlinear models. Our theoretical characterizations are confirmed by simulation studies.</p>","PeriodicalId":314696,"journal":{"name":"Journal of machine learning research : JMLR","volume":" ","pages":""},"PeriodicalIF":6.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7079742/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"37753218","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}