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In this work we introduce the notion of the excess risk in the setup of estimation of the Gaussian mean when the observations are corrupted by outliers. It is known that the sample mean loses its good properties in the presence of outliers [5-6]. In addition, even the sample median is not minimax-rate-optimal in the multivariate setting. The optimal rate of the minimax risk in this setting was established by [1]. However, even these minimax-rate-optimality results do not quantify how fast the risk in the contaminated model approaches the risk in the uncontaminated model when the rate of contamination goes to zero. The present paper does a first step in filling this gap by showing that the group hard thresholding estimator has an excess risk that goes to zero when the corruption rate approaches zero. [ABSTRACT FROM AUTHOR]

Recently there has been a surge of interest in understanding implicit regularization properties of iterative gradient-based optimization algorithms. In this paper, we study the statistical guarantees on the excess risk achieved by early-stopped unconstrained mirror descent algorithms applied to the unregularized empirical risk. We consider the set-up of learning linear models and kernel methods for strongly convex and Lipschitz loss functions while imposing only boundedness conditions on the unknown data-generating mechanism. By completing an inequality that characterizes convexity for the squared loss, we identify an intrinsic link between offset Rademacher complexities and potential-based convergence analysis of mirror descent methods. Our observation immediately yields excess risk guarantees for the path traced by the iterates of mirror descent in terms of offset complexities of certain function classes depending only on the choice of the mirror map, initialization point, step size and the number of iterations. We apply our theory to recover, in a clean and elegant manner via rather short proofs, some of the recent results in the implicit regularization literature while also showing how to improve upon them in some settings. [ABSTRACT FROM AUTHOR]

We critically examined existing approaches for the estimation of the excess familial risk of cancer that can be attributed to identified common genetic risk variants and propose an alternative, more straightforward approach for calculating this proportion using well‐established epidemiological methodology. We applied the underlying equations of the traditional approaches and the new epidemiological approach for colorectal cancer (CRC) in a large population‐based case–control study in Germany with 4,447 cases and 3,480 controls, who were recruited from 2003 to 2016 and for whom interview, medical and genomic data were available. Having a family history of CRC (FH) was associated with a 1.77‐fold risk increase in our study population (95% CI 1.52–2.07). Traditional approaches yielded estimates of the FH‐associated risk explained by 97 common genetics variants from 9.6% to 23.1%, depending on various assumptions. Our alternative approach resulted in smaller and more consistent estimates of this proportion, ranging from 5.4% to 14.3%. Commonly employed methods may lead to strongly divergent and possibly exaggerated estimates of excess familial risk of cancer explained by associated known common genetic variants. Our results suggest that familial risk and risk associated with known common genetic variants might reflect two complementary major sources of risk. What's new? Today's methods to evaluate excess familial risk of cancer explained by associated known common genetic variants may lead to strongly divergent and possibly exaggerated estimates. This paper presents an alternative, more straightforward approach using well‐established epidemiological methodology. Application in a large population‐based case–control study in colorectal cancer supports suggestions that this proportion may be substantially smaller than previously assumed and highly dependent on SNP pruning methods, the assumed risk for having a family history of CRC, and the number of identified SNPs. Rather than reflecting a major subcomponent of familial risk, common genetic variants appear to reflect substantial complementary risk. [ABSTRACT FROM AUTHOR]

In this paper, we perform deep neural networks for learning stationary ψ -weakly dependent processes. Such weak-dependence property includes a class of weak dependence conditions such as mixing, association ⋯ and the setting considered here covers many commonly used situations such as: regression estimation, time series prediction, time series classification ⋯ The consistency of the empirical risk minimization algorithm in the class of deep neural networks predictors is established. We achieve the generalization bound and obtain an asymptotic learning rate, which is less than O (n − 1 / α) , for all α > 2. A bound of the excess risk, for a wide class of target functions, is also derived. Applications to binary time series classification and prediction in affine causal models with exogenous covariates are carried out. Some simulation results are provided, as well as an application to the US recession data. [ABSTRACT FROM AUTHOR]

Distance metric learning (DML) aims to find a suitable measure to compute a distance between instances. Facilitated by side information, the learned metric can often improve the performance of similarity or distance based methods such as kNN. Theoretical analyses of DML focus on the learning effectiveness for squared Mahalanobis distance. Specifically, whether the Mahalanobis metric learned from the empirically sampled pairwise constraints is in accordance with the optimal metric optimized over the paired samples generated from the true distribution, and the sample complexity of this process. The excess risk could measure the quality of the generalization, i.e., the gap between the expected objective of empirical metric learned from a regularized objective with convex loss function and the one with the optimal metric. Given N training examples, existing analyses over this non-i.i.d. learning problem have proved the excess risk of DML converges to zero at a rate of O1N. In this paper, we obtain a faster convergence rate of DML, O1N, when learning the distance metric with a smooth loss function and a strongly convex objective. In addition, when the problem is relatively easy, and the number of training samples is large enough, this rate can be further improved to O1N2. Synthetic experiments validate that DML can achieve the specified faster generalization rate, and results under various settings help explore the theoretical properties of DML a lot. [ABSTRACT FROM AUTHOR]

The problem of ranking/ordering instances, instead of simply classifying them, has recently gained much attention in machine learning. Ranking from binary comparisons is a ubiquitous problem in modern machine learning applications. In this paper, we consider ℓ1-norm SVM for ranking. As well known, learning with ℓ1-norm restrictions usually leads to sparsity. Moreover, instead of independently draw sample sequence, we are given sample of exponentially strongly mixing sequence. Under some mild conditions, a learning rate is established. [ABSTRACT FROM AUTHOR]

Introduction: The treatment with tyrosine kinase inhibitors (TKIs) has drastically improved the outcome of chronic myeloid leukemia (CML) patients. This study was conducted to examine the risk of secondary cancers (SCs) in the CML patients who were diagnosed and treated in the TKI era in the United States. Methods: The surveillance epidemiology and end results (SEER) database was used to identify CML patients who were diagnosed and received treatment during January 2002-December 2014. Standardized incidence ratios (SIRs) and absolute excess risks (AER) were calculated. Results: Overall, 511 SCs (excluding acute leukemia) developed in 9,200 CML patients followed for 38,433 person-years. The risk of developing SCs in the CML patients was 30% higher than the age, sex and race matched standard population (SIR 1.30, 95% CI: 1.2-1.40; p < 0.001). The SIRs for CLL (SIR 3.4, 95% CI: 2-5.5; p < 0.001), thyroid (SIR 2.2, 95% CI: 1.2-3.5; p < 0.001), small intestine (SIR 3.1, 95% CI: 1.1-7; p = 0.004), gingiva (SIR 3.7, 95% CI: 1.2-8.7; p = 0.002), stomach (SIR 2.1, 95% CI: 1.1-3.5; p = 0.005), lung (SIR 1.4, 95% CI: 1.1-1.7; p = 0.006) and prostate (SIR 1.3, 95% CI: 1.02-1.6; p = 0.026) cancer among CML patients were significantly higher than the general population. The risk of SCs was higher irrespective of age and it was highest in the period 2-12 months after the diagnosis of CML. The risk of SCs in women was similar to that of the general population. Conclusion: CML patients diagnosed and treated in the TKI era in the United States are at an increased risk of developing a second malignancy. The increased risk of SCs in the early period after CML diagnosis suggests that the risk of SCs may be increased due to the factors other than TKIs treatment. [ABSTRACT FROM AUTHOR]

We analyze the best achievable performance of Bayesian learning under generative models by defining and upper-bounding the minimum excess risk (MER): the gap between the minimum expected loss attainable by learning from data and the minimum expected loss that could be achieved if the model realization were known. The definition of MER provides a principled way to define different notions of uncertainties in Bayesian learning, including the aleatoric uncertainty and the minimum epistemic uncertainty. Two methods for deriving upper bounds for the MER are presented. The first method, generally suitable for Bayesian learning with a parametric generative model, upper-bounds the MER by the conditional mutual information between the model parameters and the quantity being predicted given the observed data. It allows us to quantify the rate at which the MER decays to zero as more data becomes available. Under realizable models, this method also relates the MER to the richness of the generative function class, notably the VC dimension in binary classification. The second method, particularly suitable for Bayesian learning with a parametric predictive model, relates the MER to the minimum estimation error of the model parameters from data via various continuity arguments. We also extend the definition and analysis of MER to the setting with multiple model families and the setting with nonparametric models. Along the discussions we draw some comparisons between the MER in Bayesian learning and the excess risk in frequentist learning. [ABSTRACT FROM AUTHOR]

Indoor air quality (IAQ) is impacted by polluted outdoor air in naturally ventilated schools, especially in places where both anthropogenic and natural sources of ambient air pollution exist. CO2, PM2.5, PM10, temperature, relative humidity (RH), and noise were measured in five naturally ventilated primary schools in City of Sanliurfa, in a dusty region of Turkey, Southeast Anatolia. Excess risk levels were estimated for particulate matter. Investigation was conducted through an educational year including two seasons in terms of anthropogenic effect, that is, heating/non‐heating, and natural effect, that is, desert dust transport/non‐dust transport. The median CO2 concentration was measured to be >1000 ppm in all seasons/schools. Temperature and RH fell out of the comfort zone in October–December, during which pollutant concentrations were considerably increased, specifically in November, that heating and dust transport periods coincide. The overall mean indoor PM10 and PM2.5 levels were 58 and 31.8 μg/m3, respectively. Risk assessment indicate that both short (incidence of asthma symptoms in asthmatic children) and long‐term (prevalence of bronchitis) effects are considerable with 10.9 (2.4–19.6)% and 19.5 (2.2–38.8)%, respectively. The findings suggest that mechanical ventilation retrofitting with particle filtration is needed to mitigate potential negative health consequences on children. [ABSTRACT FROM AUTHOR]

The ranking problem has received increasing attention in both the statistical and machine learning literature. This paper considers support vector machines for ranking. Under some mild conditions, a learning rate is established. [ABSTRACT FROM AUTHOR]

The problem of ranking is to predict or to guess the ordering between objects on the basis of their observed features. In this paper we consider ranking estimators that minimize the empirical convex risk. We prove generalization bounds for the excess risk of such estimators with rates that are faster than 1/√n. We apply our results to commonly used ranking algorithms, for instance boosting or support vector machines. Moreover, we study the performance of considered estimators on real data sets. [ABSTRACT FROM AUTHOR]

A framework previously introduced in Wilson et al. (2018) for solving a sequence of stochastic optimization problems with bounded changes in the minimizers is extended and applied to machine learning problems such as regression and classification. The stochastic optimization problems arising in these machine learning problems are solved using algorithms such as stochastic gradient descent (SGD). A method based on estimates of the change in the minimizers and properties of the optimization algorithm is introduced for adaptively selecting the number of samples at each time step to ensure that the excess risk—that is, the expected gap between the loss achieved by the approximate minimizer produced by the optimization algorithm and the exact minimizer—does not exceed a target level. A bound is developed to show that the estimate of the change in the minimizers is non trivial provided that the excess risk is small enough. Extensions relevant to the machine learning setting are considered, including a cost-based approach to select the number of samples with a cost budget over a fixed horizon, and an approach to applying cross-validation for model selection. Finally, experiments with synthetic and real data are used to validate the algorithms. [ABSTRACT FROM AUTHOR]

Parametric models of discrete data with exchangeable dependence structure present substantial computational challenges for maximum likelihood estimation. Coordinate descent algorithms such as the Newton's method are usually unstable, becoming a hit or miss adventure on initialization with a good starting value. We propose a method for computing maximum likelihood estimates of parametric models for finitely exchangeable binary data, formalized as an iterative weighted least squares algorithm. [ABSTRACT FROM AUTHOR]

The use of imaging markers to predict clinical outcomes can have a great impact in public health. The aim of this article is to develop a class of generalized scalar-on-image regression models via total variation (GSIRM-TV), in the sense of generalized linear models, for scalar response and imaging predictor with the presence of scalar covariates. A key novelty of GSIRM-TV is that it is assumed that the slope function (or image) of GSIRM-TV belongs to the space of bounded total variation to explicitly account for the piecewise smooth nature of most imaging data. We develop an efficient penalized total variation optimization to estimate the unknown slope function and other parameters. We also establish nonasymptotic error bounds on the excess risk. These bounds are explicitly specified in terms of sample size, image size, and image smoothness. Our simulations demonstrate a superior performance of GSIRM-TV against many existing approaches. We apply GSIRM-TV to the analysis of hippocampus data obtained from the Alzheimers Disease Neuroimaging Initiative (ADNI) dataset. Supplementary materials for this article are available online. [ABSTRACT FROM AUTHOR]

Background: Due to recent emergence, dengue is becoming one of the major public health problems in Nepal. The numbers of reported dengue cases in general and the area with reported dengue cases are both continuously increasing in recent years. However, spatiotemporal patterns and clusters of dengue have not been investigated yet. This study aims to fill this gap by analyzing spatiotemporal patterns based on monthly surveillance data aggregated at district.Methods: Dengue cases from 2010 to 2014 at district level were collected from the Nepal government's health and mapping agencies respectively. GeoDa software was used to map crude incidence, excess hazard and spatially smoothed incidence. Cluster analysis was performed in SaTScan software to explore spatiotemporal clusters of dengue during the above-mentioned time period.Results: Spatiotemporal distribution of dengue fever in Nepal from 2010 to 2014 was mapped at district level in terms of crude incidence, excess risk and spatially smoothed incidence. Results show that the distribution of dengue fever was not random but clustered in space and time. Chitwan district was identified as the most likely cluster and Jhapa district was the first secondary cluster in both spatial and spatiotemporal scan. July to September of 2010 was identified as a significant temporal cluster.Conclusion: This study assessed and mapped for the first time the spatiotemporal pattern of dengue fever in Nepal. Two districts namely Chitwan and Jhapa were found highly affected by dengue fever. The current study also demonstrated the importance of geospatial approach in epidemiological research. The initial result on dengue patterns and risk of this study may assist institutions and policy makers to develop better preventive strategies. [ABSTRACT FROM AUTHOR]

We define mechanistic interaction between the effects of two variables on an outcome in terms of departure of these effects from a generalized noisy-OR model in a stratum of the population. We develop a fully probabilistic framework for the observational identification of this type of interaction via excess risk or superadditivity, one novel feature of which is its applicability when the interacting variables have been generated by arbitrarily dichotomizing continuous exposures. The method allows for stochastic mediators of the interacting effects. The required assumptions are provided in the form of conditional independencies between the problem variables, which may relate to a causal-graph representation of the problem. We also develop a theory of mechanistic interaction between effects associated with specific paths of the causal graph. [ABSTRACT FROM AUTHOR]

Consider a standard binary classification problem, in which $$(X,Y)$$ is a random couple in $$\mathcal{X}\times \{0,1\}$$ , and the training data consist of $$n$$ i.i.d. copies of $$(X,Y).$$ Given a binary classifier $$f:\mathcal{X}\mapsto \{0,1\},$$ the generalization error of $$f$$ is defined by $$R(f)={\mathbb P}\{Y\ne f(X)\}$$ . Its minimum $$R^*$$ over all binary classifiers $$f$$ is called the Bayes risk and is attained at a Bayes classifier. The performance of any binary classifier $$\hat{f}_n$$ based on the training data is characterized by the excess risk $$R(\hat{f}_n)-R^*$$ . We study Bahadur's type exponential bounds on the following minimax accuracy confidence function based on the excess risk: [Equation not available: see fulltext.]where the supremum is taken over all distributions $$P$$ of $$(X,Y)$$ from a given class of distributions $$\mathcal{M}$$ and the infimum is over all binary classifiers $$\hat{f}_n$$ based on the training data. We study how this quantity depends on the complexity of the class of distributions $$\mathcal{M}$$ characterized by exponents of entropies of the class of regression functions or of the class of Bayes classifiers corresponding to the distributions from $$\mathcal{M}.$$ We also study its dependence on margin parameters of the classification problem. In particular, we show that, in the case when $$\mathcal{X}=[0,1]^d$$ and $$\mathcal{M}$$ is the class of all distributions satisfying the margin condition with exponent $$\alpha >0$$ and such that the regression function $$\eta $$ belongs to a given Hölder class of smoothness $$\beta >0,$$ [Equation not available: see fulltext.]for some constants $$D,\lambda _0>0$$ . [ABSTRACT FROM AUTHOR]

Given two variables that causally influence a binary response, we formalize the idea that their effects operate through a common mechanism, in which case we say that the two variables interact mechanistically. We introduce a mechanistic interaction relationship of “interference” that is asymmetric in the two causal factors. Conditions and assumptions under which such mechanistic interaction can be tested under a given regime of data collection, be it interventional or observational, are expressed in terms of conditional independence relationships between the problem variables, which can be manipulated with the aid of causal diagrams. The proposed method is able, under appropriate conditions, to test for interaction between direct effects, and to deal with the situation where one of the two factors is a dichotomized version of a continuous variable. The method is illustrated with the aid of a study on heart disease. [ABSTRACT FROM AUTHOR]

We study the popular benchmark dose (BMD) approach for estimation of low exposure levels in toxicological risk assessment, focusing on dose-response experiments with quantal data. In such settings, representations of the risk are traditionally based on a specified, parametric, dose-response model. It is a well-known concern, however, that uncertainty can exist in specification and selection of the model. If the chosen parametric form is in fact misspecified, this can lead to inaccurate, and possibly unsafe, low-dose inferences. We study the effects of model selection and possible misspecification on the BMD, on its corresponding lower confidence limit (BMDL), and on the associated extra risks achieved at these values, via large-scale Monte Carlo simulation. It is seen that an uncomfortably high percentage of instances can occur where the true extra risk at the BMDL under a misspecified or incorrectly selected model can surpass the target benchmark response, exposing potential dangers of traditional strategies for model selection when calculating BMDs and BMDLs. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Borgan and Langholz (1997) describe a method for estimating the parameter functions in Aalen's linear hazard regression model from sampled risk set data. Using a counting process formulation and the martingale central limit theorem, we provide a study of the asymptotic distributional properties of the estimator. The results are applied to study the efficiencies of the nested case-control and counter-matched designs relative to a full cohort analysis. [ABSTRACT FROM AUTHOR]

The additive risk model assumes that the hazard function associated with a set of covariates is the sum of the baseline hazard function and the regression function of covariates. We propose two different test procedures for checking the adequacy of two-sample additive risk models for randomly censored observations. One is based on the martingale residuals and the other on the difference between weighted estimators of the excess risk. The test statistics are shown to be asymptotically normal under appropriate regularity conditions and consistent under any model misspecifications. Finally, two real examples are provided, along with results of a simulation study. [ABSTRACT FROM AUTHOR]