Norbert Hirschauer, Sven Grüner, Oliver Mußhoff, Claudia Becker, Antje Jantsch.

Source: Statistics Surveys, Volume 14, 71--91.

Abstract:
Besides the inferential errors that abound in the interpretation of $p$-values, the probabilistic pre-conditions (i.e. random sampling or equivalent) for using them at all are not often met by observational studies in the social sciences. This paper systematizes different sampling designs and discusses the restrictive requirements of data collection that are the indispensable prerequisite for using $p$-values.

Stanislav Nagy, Carsten Schütt, Elisabeth M. Werner.

Source: Statistics Surveys, Volume 13, 52--118.

Abstract:
Little known relations of the renown concept of the halfspace depth for multivariate data with notions from convex and affine geometry are discussed. Maximum halfspace depth may be regarded as a measure of symmetry for random vectors. As such, the maximum depth stands as a generalization of a measure of symmetry for convex sets, well studied in geometry. Under a mild assumption, the upper level sets of the halfspace depth coincide with the convex floating bodies of measures used in the definition of the affine surface area for convex bodies in Euclidean spaces. These connections enable us to partially resolve some persistent open problems regarding theoretical properties of the depth.

Solveig Engebretsen, Ingrid K. Glad.

Source: Statistics Surveys, Volume 13, 1--51.

Abstract:
In numerous problems where the aim is to estimate the effect of a predictor variable on a response, one can assume a monotone relationship. For example, dose-effect models in medicine are of this type. In a multiple regression setting, additive monotone regression models assume that each predictor has a monotone effect on the response. In this paper, we present an overview and comparison of very recent frequentist methods for fitting additive monotone regression models. Three of the methods we present can be used both in the high dimensional setting, where the number of parameters $p$ exceeds the number of observations $n$, and in the classical multiple setting where $1<pleq n$. However, many of the most recent methods only apply to the classical setting. The methods are compared through simulation experiments in terms of efficiency, prediction error and variable selection properties in both settings, and they are applied to the Boston housing data. We conclude with some recommendations on when the various methods perform best.

Norbert Hirschauer, Sven Grüner, Oliver Mußhoff, Claudia Becker.

Source: Statistics Surveys, Volume 12, 136--172.

Abstract:
Data on how many scientific findings are reproducible are generally bleak and a wealth of papers have warned against misuses of the $p$-value and resulting false findings in recent years. This paper discusses the question of what we can(not) learn from the $p$-value, which is still widely considered as the gold standard of statistical validity. We aim to provide a non-technical and easily accessible resource for statistical practitioners who wish to spot and avoid misinterpretations and misuses of statistical significance tests. For this purpose, we first classify and describe the most widely discussed (“classical”) pitfalls of significance testing, and review published work on these misuses with a focus on regression-based “confirmatory” study. This includes a description of the single-study bias and a simulation-based illustration of how proper meta-analysis compares to misleading significance counts (“vote counting”). Going beyond the classical pitfalls, we also use simulation to provide intuition that relying on the statistical estimate “$p$-value” as a measure of evidence without considering its sample-to-sample variability falls short of the mark even within an otherwise appropriate interpretation. We conclude with a discussion of the exigencies of informed approaches to statistical inference and corresponding institutional reforms.

Miklós Z. Rácz, Sébastien Bubeck.

Source: Statistics Surveys, Volume 11, 1--47.

Abstract:
Extracting information from large graphs has become an important statistical problem since network data is now common in various fields. In this minicourse we will investigate the most natural statistical questions for three canonical probabilistic models of networks: (i) community detection in the stochastic block model, (ii) finding the embedding of a random geometric graph, and (iii) finding the original vertex in a preferential attachment tree. Along the way we will cover many interesting topics in probability theory such as Pólya urns, large deviation theory, concentration of measure in high dimension, entropic central limit theorems, and more.

Julie Josse, Susan Holmes.

Source: Statistics Surveys, Volume 10, 132--167.

Abstract:
Simple correlation coefficients between two variables have been generalized to measure association between two matrices in many ways. Coefficients such as the RV coefficient, the distance covariance (dCov) coefficient and kernel based coefficients are being used by different research communities. Scientists use these coefficients to test whether two random vectors are linked. Once it has been ascertained that there is such association through testing, then a next step, often ignored, is to explore and uncover the association’s underlying patterns. This article provides a survey of various measures of dependence between random vectors and tests of independence and emphasizes the connections and differences between the various approaches. After providing definitions of the coefficients and associated tests, we present the recent improvements that enhance their statistical properties and ease of interpretation. We summarize multi-table approaches and provide scenarii where the indices can provide useful summaries of heterogeneous multi-block data. We illustrate these different strategies on several examples of real data and suggest directions for future research.

Clément Marteau, Theofanis Sapatinas.

Source: Statistics Surveys, Volume 9, 253--297.

Abstract:
We are concerned with minimax signal detection. In this setting, we discuss non-asymptotic and asymptotic approaches through a unified treatment. In particular, we consider a Gaussian sequence model that contains classical models as special cases, such as, direct, well-posed inverse and ill-posed inverse problems. Working with certain ellipsoids in the space of squared-summable sequences of real numbers, with a ball of positive radius removed, we compare the construction of lower and upper bounds for the minimax separation radius (non-asymptotic approach) and the minimax separation rate (asymptotic approach) that have been proposed in the literature. Some additional contributions, bringing to light links between non-asymptotic and asymptotic approaches to minimax signal, are also presented. An example of a mildly ill-posed inverse problem is used for illustrative purposes. In particular, it is shown that tools used to derive ‘asymptotic’ results can be exploited to draw ‘non-asymptotic’ conclusions, and vice-versa. In order to enhance our understanding of these two minimax signal detection paradigms, we bring into light hitherto unknown similarities and links between non-asymptotic and asymptotic approaches.

José A. Ferreira.

Source: Statistics Surveys, Volume 9, 106--208.

Abstract:
This article provides a concise and essentially self-contained exposition of some of the most important models and non-parametric methods for the analysis of observational data, and a substantial number of illustrations of their application. Although for the most part our presentation follows P. Rosenbaum’s book, “Observational Studies”, and naturally draws on related literature, it contains original elements and simplifies and generalizes some basic results. The illustrations, based on simulated data, show the methods at work in some detail, highlighting pitfalls and emphasizing certain subjective aspects of the statistical analyses.

Adrien Saumard, Jon A. Wellner.

Source: Statistics Surveys, Volume 8, 45--114.

Abstract:
We review and formulate results concerning log-concavity and strong-log-concavity in both discrete and continuous settings. We show how preservation of log-concavity and strong log-concavity on $mathbb{R}$ under convolution follows from a fundamental monotonicity result of Efron (1965). We provide a new proof of Efron’s theorem using the recent asymmetric Brascamp-Lieb inequality due to Otto and Menz (2013). Along the way we review connections between log-concavity and other areas of mathematics and statistics, including concentration of measure, log-Sobolev inequalities, convex geometry, MCMC algorithms, Laplace approximations, and machine learning.

Aki Vehtari, Janne Ojanen.

Source: Statistics Surveys, Volume 8, , 1--1.

Abstract:
Errata for “A survey of Bayesian predictive methods for model assessment, selection and comparison” by A. Vehtari and J. Ojanen, Statistics Surveys , 6 (2012), 142–228. doi:10.1214/12-SS102.

Sean L. Simpson, F. DuBois Bowman, Paul J. Laurienti

Source: Statist. Surv., Volume 7, 1--36.

Abstract:
Complex functional brain network analyses have exploded over the last decade, gaining traction due to their profound clinical implications. The application of network science (an interdisciplinary offshoot of graph theory) has facilitated these analyses and enabled examining the brain as an integrated system that produces complex behaviors. While the field of statistics has been integral in advancing activation analyses and some connectivity analyses in functional neuroimaging research, it has yet to play a commensurate role in complex network analyses. Fusing novel statistical methods with network-based functional neuroimage analysis will engender powerful analytical tools that will aid in our understanding of normal brain function as well as alterations due to various brain disorders. Here we survey widely used statistical and network science tools for analyzing fMRI network data and discuss the challenges faced in filling some of the remaining methodological gaps. When applied and interpreted correctly, the fusion of network scientific and statistical methods has a chance to revolutionize the understanding of brain function.

Aki Vehtari, Janne Ojanen

Source: Statist. Surv., Volume 6, 142--228.

Abstract:
To date, several methods exist in the statistical literature for model assessment, which purport themselves specifically as Bayesian predictive methods. The decision theoretic assumptions on which these methods are based are not always clearly stated in the original articles, however. The aim of this survey is to provide a unified review of Bayesian predictive model assessment and selection methods, and of methods closely related to them. We review the various assumptions that are made in this context and discuss the connections between different approaches, with an emphasis on how each method approximates the expected utility of using a Bayesian model for the purpose of predicting future data.

Nancy Heckman

Source: Statist. Surv., Volume 6, 113--141.

Abstract:
The popular cubic smoothing spline estimate of a regression function arises as the minimizer of the penalized sum of squares $sum_{j}(Y_{j}-mu(t_{j}))^{2}+lambda int_{a}^{b}[mu''(t)]^{2},dt$, where the data are $t_{j},Y_{j}$, $j=1,ldots,n$. The minimization is taken over an infinite-dimensional function space, the space of all functions with square integrable second derivatives. But the calculations can be carried out in a finite-dimensional space. The reduction from minimizing over an infinite dimensional space to minimizing over a finite dimensional space occurs for more general objective functions: the data may be related to the function $mu$ in another way, the sum of squares may be replaced by a more suitable expression, or the penalty, $int_{a}^{b}[mu''(t)]^{2},dt$, might take a different form. This paper reviews the Reproducing Kernel Hilbert Space structure that provides a finite-dimensional solution for a general minimization problem. Particular attention is paid to the construction and study of the Reproducing Kernel Hilbert Space corresponding to a penalty based on a linear differential operator. In this case, one can often calculate the minimizer explicitly, using Green’s functions.

Gery Geenens

Source: Statist. Surv., Volume 5, 30--43.

Abstract:
Recently, some nonparametric regression ideas have been extended to the case of functional regression. Within that framework, the main concern arises from the infinite dimensional nature of the explanatory objects. Specifically, in the classical multivariate regression context, it is well-known that any nonparametric method is affected by the so-called “curse of dimensionality”, caused by the sparsity of data in high-dimensional spaces, resulting in a decrease in fastest achievable rates of convergence of regression function estimators toward their target curve as the dimension of the regressor vector increases. Therefore, it is not surprising to find dramatically bad theoretical properties for the nonparametric functional regression estimators, leading many authors to condemn the methodology. Nevertheless, a closer look at the meaning of the functional data under study and on the conclusions that the statistician would like to draw from it allows to consider the problem from another point-of-view, and to justify the use of slightly modified estimators. In most cases, it can be entirely legitimate to measure the proximity between two elements of the infinite dimensional functional space via a semi-metric, which could prevent those estimators suffering from what we will call the “curse of infinite dimensionality”.

References:
[1] Ait-Saïdi, A., Ferraty, F., Kassa, K. and Vieu, P. (2008). Cross-validated estimations in the single-functional index model, Statistics, 42, 475–494.

[2] Aneiros-Perez, G. and Vieu, P. (2008). Nonparametric time series prediction: A semi-functional partial linear modeling, J. Multivariate Anal., 99, 834–857.

[3] Baillo, A. and Grané, A. (2009). Local linear regression for functional predictor and scalar response, J. Multivariate Anal., 100, 102–111.

[4] Burba, F., Ferraty, F. and Vieu, P. (2009). k-Nearest Neighbour method in functional nonparametric regression, J. Nonparam. Stat., 21, 453–469.

[5] Cardot, H., Ferraty, F. and Sarda, P. (1999). Functional linear model, Stat. Probabil. Lett., 45, 11–22.

[6] Crambes, C., Kneip, A. and Sarda, P. (2009). Smoothing splines estimators for functional linear regression, Ann. Statist., 37, 35–72.

[7] Delsol, L. (2009). Advances on asymptotic normality in nonparametric functional time series analysis, Statistics, 43, 13–33.

[8] Fan, J. and Gijbels, I. (1996). Local Polynomial Modelling and Its Applications, Chapman and Hall, London.

[9] Fan, J. and Zhang, J.-T. (2000). Two-step estimation of functional linear models with application to longitudinal data, J. Roy. Stat. Soc. B, 62, 303–322.

[10] Ferraty, F. and Vieu, P. (2006). Nonparametric Functional Data Analysis, Springer-Verlag, New York.

[11] Ferraty, F., Laksaci, A. and Vieu, P. (2006). Estimating Some Characteristics of the Conditional Distribution in Nonparametric Functional Models, Statist. Inf. Stoch. Proc., 9, 47–76.

[12] Ferraty, F., Mas, A. and Vieu, P. (2007). Nonparametric regression on functional data: inference and practical aspects, Aust. NZ. J. Stat., 49, 267–286.

[13] Ferraty, F., Van Keilegom, I. and Vieu, P. (2010). On the validity of the bootstrap in nonparametric functional regression, Scand. J. Stat., 37, 286–306.

[14] Ferraty, F., Laksaci, A., Tadj, A. and Vieu, P. (2010). Rate of uniform consistency for nonparametric estimates with functional variables, J. Stat. Plan. Inf., 140, 335–352.

[15] Ferraty, F. and Romain, Y. (2011). Oxford handbook on functional data analysis (Eds), Oxford University Press.

[16] Gasser, T., Hall, P. and Presnell, B. (1998). Nonparametric estimation of the mode of a distribution of random curves, J. Roy. Stat. Soc. B, 60, 681–691.

[17] Geenens, G. (2011). A nonparametric functional method for signature recognition, Manuscript.

[18] Härdle, W., Müller, M., Sperlich, S. and Werwatz, A. (2004). Nonparametric and semiparametric models, Springer-Verlag, Berlin.

[19] James, G.M. (2002). Generalized linear models with functional predictors, J. Roy. Stat. Soc. B, 64, 411–432.

[20] Masry, E. (2005). Nonparametric regression estimation for dependent functional data: asymptotic normality, Stochastic Process. Appl., 115, 155–177.

[21] Nadaraya, E.A. (1964). On estimating regression, Theory Probab. Applic., 9, 141–142.

[22] Quintela-Del-Rio, A. (2008). Hazard function given a functional variable: nonparametric estimation under strong mixing conditions, J. Nonparam. Stat., 20, 413–430.

[23] Rachdi, M. and Vieu, P. (2007). Nonparametric regression for functional data: automatic smoothing parameter selection, J. Stat. Plan. Inf., 137, 2784–2801.

[24] Ramsay, J. and Silverman, B.W. (1997). Functional Data Analysis, Springer-Verlag, New York.

[25] Ramsay, J. and Silverman, B.W. (2002). Applied functional data analysis; methods and case study, Springer-Verlag, New York.

[26] Ramsay, J. and Silverman, B.W. (2005). Functional Data Analysis, 2nd Edition, Springer-Verlag, New York.

[27] Stone, C.J. (1982). Optimal global rates of convergence for nonparametric regression, Ann. Stat., 10, 1040–1053.

[28] Watson, G.S. (1964). Smooth regression analysis, Sankhya A, 26, 359–372.

[29] Yeung, D.T., Chang, H., Xiong, Y., George, S., Kashi, R., Matsumoto, T. and Rigoll, G. (2004). SVC2004: First International Signature Verification Competition, Proceedings of the International Conference on Biometric Authentication (ICBA), Hong Kong, July 2004.

Gregory J. Matthews, Ofer Harel

Source: Statist. Surv., Volume 5, 1--29.

Abstract:
There is an ever increasing demand from researchers for access to useful microdata files. However, there are also growing concerns regarding the privacy of the individuals contained in the microdata. Ideally, microdata could be released in such a way that a balance between usefulness of the data and privacy is struck. This paper presents a review of proposed methods of statistical disclosure control and techniques for assessing the privacy of such methods under different definitions of disclosure.

References:
Abowd, J., Woodcock, S., 2001. Disclosure limitation in longitudinal linked data. Confidentiality, Disclosure, and Data Access: Theory and Practical Applications for Statistical Agencies, 215–277.

Adam, N.R., Worthmann, J.C., 1989. Security-control methods for statistical databases: a comparative study. ACM Comput. Surv. 21 (4), 515–556.

Armstrong, M., Rushton, G., Zimmerman, D.L., 1999. Geographically masking health data to preserve confidentiality. Statistics in Medicine 18 (5), 497–525.

Bethlehem, J.G., Keller, W., Pannekoek, J., 1990. Disclosure control of microdata. Jorunal of the American Statistical Association 85, 38–45.

Blum, A., Dwork, C., McSherry, F., Nissam, K., 2005. Practical privacy: The sulq framework. In: Proceedings of the 24th ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems. pp. 128–138.

Bowden, R.J., Sim, A.B., 1992. The privacy bootstrap. Journal of Business and Economic Statistics 10 (3), 337–345.

Carlson, M., Salabasis, M., 2002. A data-swapping technique for generating synthetic samples; a method for disclosure control. Res. Official Statist. (5), 35–64.

Cox, L.H., 1980. Suppression methodology and statistical disclosure control. Journal of the American Statistical Association 75, 377–385.

Cox, L.H., 1984. Disclosure control methods for frequency count data. Tech. rep., U.S. Bureau of the Census.

Cox, L.H., 1987. A constructive procedure for unbiased controlled rounding. Journal of the American Statistical Association 82, 520–524.

Cox, L.H., 1994. Matrix masking methods for disclosure limitation in microdata. Survey Methodology 6, 165–169.

Cox, L.H., Fagan, J.T., Greenberg, B., Hemmig, R., 1987. Disclosure avoidance techniques for tabular data. Tech. rep., U.S. Bureau of the Census.

Dalenius, T., 1977. Towards a methodology for statistical disclosure control. Statistik Tidskrift 15, 429–444.

Dalenius, T., 1986. Finding a needle in a haystack - or identifying anonymous census record. Journal of Official Statistics 2 (3), 329–336.

Dalenius, T., Denning, D., 1982. A hybrid scheme for release of statistics. Statistisk Tidskrift.

Dalenius, T., Reiss, S.P., 1982. Data-swapping: A technique for disclosure control. Journal of Statistical Planning and Inference 6, 73–85.

De Waal, A., Hundepool, A., Willenborg, L., 1995. Argus: Software for statistical disclosure control of microdata. U.S. Census Bureau.

DeGroot, M.H., 1962. Uncertainty, information, and sequential experiments. Annals of Mathematical Statistics 33, 404–419.

DeGroot, M.H., 1970. Optimal Statistical Decisions. Mansell, London.

Dinur, I., Nissam, K., 2003. Revealing information while preserving privacy. In: Proceedings of the 22nd ACM SIGMOD-SIGACT-SIGART Symposium on Principlesof Database Systems. pp. 202–210.

Domingo-Ferrer, J., Torra, V., 2001a. A Quantitative Comparison of Disclosure Control Methods for Microdata. In: Doyle, P., Lane, J., Theeuwes, J., Zayatz, L. (Eds.), Confidentiality, Disclosure and Data Access - Theory and Practical Applications for Statistical Agencies. North-Holland, Amsterdam, Ch. 6, pp. 113–135.

Domingo-Ferrer, J., Torra, V., 2001b. Disclosure control methods and information loss for microdata. In: Doyle, P., Lane, J., Theeuwes, J., Zayatz, L. (Eds.), Confidentiality, Disclosure and Data Access - Theory and Practical Applications for Statistical Agencies. North-Holland, Amsterdam, Ch. 5, pp. 93–112.

Duncan, G., Lambert, D., 1986. Disclosure-limited data dissemination. Journal of the American Statistical Association 81, 10–28.

Duncan, G., Lambert, D., 1989. The risk of disclosure for microdata. Journal of Business & Economic Statistics 7, 207–217.

Duncan, G., Pearson, R., 1991. Enhancing access to microdata while protecting confidentiality: prospects for the future (with discussion). Statistical Science 6, 219–232.

Dwork, C., 2006. Differential privacy. In: ICALP. Springer, pp. 1–12.

Dwork, C., 2008. An ad omnia approach to defining and achieving private data analysis. In: Lecture Notes in Computer Science. Springer, p. 10.

Dwork, C., Lei, J., 2009. Differential privacy and robust statistics. In: Proceedings of the 41th Annual ACM Symposium on Theory of Computing (STOC). pp. 371–380.

Dwork, C., Mcsherry, F., Nissim, K., Smith, A., 2006. Calibrating noise to sensitivity in private data analysis. In: Proceedings of the 3rd Theory of Cryptography Conference. Springer, pp. 265–284.

Dwork, C., Nissam, K., 2004. Privacy-preserving datamining on vertically partitioned databases. In: Advances in Cryptology: Proceedings of Crypto. pp. 528–544.

Elliot, M., 2000. DIS: a new approach to the measurement of statistical disclosure risk. International Journal of Risk Assessment and Management 2, 39–48.

Federal Committee on Statistical Methodology (FCSM), 2005. Statistical policy working group 22 - report on statistical disclosure limitation methodology. U.S. Census Bureau.

Fellegi, I.P., 1972. On the question of statistical confidentiality. Journal of the American Statistical Association 67 (337), 7–18.

Fienberg, S.E., McIntyre, J., 2004. Data swapping: Variations on a theme by Dalenius and Reiss. In: Domingo-Ferrer, J., Torra, V. (Eds.), Privacy in Statistical Databases. Vol. 3050 of Lecture Notes in Computer Science. Springer Berlin/Heidelberg, pp. 519, http://dx.doi.org/10.1007/ 978-3-540-25955-8_2

Fuller, W., 1993. Masking procedurse for microdata disclosure limitation. Journal of Official Statistics 9, 383–406.

General Assembly of the United Nations, 1948. Universal declaration of human rights.

Gouweleeuw, J., P. Kooiman, L.W., de Wolf, P.-P., 1998. Post randomisation for statistical disclosure control: Theory and implementation. Journal of Official Statistics 14 (4), 463–478.

Greenberg, B., 1987. Rank swapping for masking ordinal microdata. Tech. rep., U.S. Bureau of the Census (unpublished manuscript), Suitland, Maryland, USA.

Greenberg, B.G., Abul-Ela, A.-L.A., Simmons, W.R., Horvitz, D.G., 1969. The unrelated question randomized response model: Theoretical framework. Journal of the American Statistical Association 64 (326), 520–539.

Harel, O., Zhou, X.-H., 2007. Multiple imputation: Review and theory, implementation and software. Statistics in Medicine 26, 3057–3077.

Hundepool, A., Domingo-ferrer, J., Franconi, L., Giessing, S., Lenz, R., Longhurst, J., Nordholt, E.S., Seri, G., paul De Wolf, P., 2006. A CENtre of EXcellence for Statistical Disclosure Control Handbook on Statistical Disclosure Control Version 1.01.

Hundepool, A., Wetering, A. v.d., Ramaswamy, R., Wolf, P.d., Giessing, S., Fischetti, M., Salazar, J., Castro, J., Lowthian, P., Feb. 2005. τ-argus 3.1 user manual. Statistics Netherlands, Voorburg NL.

Hundepool, A., Willenborg, L., 1996. μ- and τ-argus: Software for statistical disclosure control. Third International Seminar on Statistical Confidentiality, Bled.

Karr, A., Kohnen, C.N., Oganian, A., Reiter, J.P., Sanil, A.P., 2006. A framework for evaluating the utility of data altered to protect confidentiality. American Statistician 60 (3), 224–232.

Kaufman, S., Seastrom, M., Roey, S., 2005. Do disclosure controls to protect confidentiality degrade the quality of the data? In: American Statistical Association, Proceedings of the Section on Survey Research.

Kennickell, A.B., 1997. Multiple imputation and disclosure protection: the case of the 1995 survey of consumer finances. Record Linkage Techniques, 248–267.

Kim, J., 1986. Limiting disclosure in microdata based on random noise and transformation. Bureau of the Census.

Krumm, J., 2007. Inference attacks on location tracks. Proceedings of Fifth International Conference on Pervasive Computingy, 127–143.

Li, N., Li, T., Venkatasubramanian, S., 2007. t-closeness: Privacy beyond k-anonymity and l-diversity. In: Data Engineering, 2007. ICDE 2007. IEEE 23rd International Conference on. pp. 106–115.

Liew, C.K., Choi, U.J., Liew, C.J., 1985. A data distortion by probability distribution. ACM Trans. Database Syst. 10 (3), 395–411.

Little, R.J.A., 1993. Statistical analysis of masked data. Journal of Official Statistics 9, 407–426.

Little, R.J.A., Rubin, D.B., 1987. Statistical Analysis with Missing Data. John Wiley & Sons.

Liu, F., Little, R.J.A., 2002. Selective multiple mputation of keys for statistical disclosure control in microdata. In: Proceedings Joint Statistical Meet. pp. 2133–2138.

Machanavajjhala, A., Kifer, D., Abowd, J., Gehrke, J., Vilhuber, L., April 2008. Privacy: Theory meets practice on the map. In: International Conference on Data Engineering. Cornell University Comuputer Science Department, Cornell, USA, p. 10.

Machanavajjhala, A., Kifer, D., Gehrke, J., Venkitasubramaniam, M., 2007. L-diversity: Privacy beyond k-anonymity. ACM Trans. Knowl. Discov. Data 1 (1), 3.

Manning, A.M., Haglin, D.J., Keane, J.A., 2008. A recursive search algorithm for statistical disclosure assessment. Data Min. Knowl. Discov. 16 (2), 165–196.

Marsh, C., Skinner, C., Arber, S., Penhale, B., Openshaw, S., Hobcraft, J., Lievesley, D., Walford, N., 1991. The case for samples of anonymized records from the 1991 census. Journal of the Royal Statistical Society 154 (2), 305–340.

Matthews, G.J., Harel, O., Aseltine, R.H., 2010a. Assessing database privacy using the area under the receiver-operator characteristic curve. Health Services and Outcomes Research Methodology 10 (1), 1–15.

Matthews, G.J., Harel, O., Aseltine, R.H., 2010b. Examining the robustness of fully synthetic data techniques for data with binary variables. Journal of Statistical Computation and Simulation 80 (6), 609–624.

Moore, Jr., R., 1996. Controlled data-swapping techniques for masking public use microdata. Census Tech Report.

Mugge, R., 1983. Issues in protecting confidentiality in national health statistics. Proceedings of the Section on Survey Research Methods.

Nissim, K., Raskhodnikova, S., Smith, A., 2007. Smooth sensitivity and sampling in private data analysis. In: STOC ’07: Proceedings of the thirty-ninth annual ACM symposium on Theory of computing. pp. 75–84.

Paass, G., 1988. Disclosure risk and disclosure avoidance for microdata. Journal of Business and Economic Statistics 6 (4), 487–500.

Palley, M., Simonoff, J., 1987. The use of regression methodology for the compromise of confidential information in statistical databases. ACM Trans. Database Systems 12 (4), 593–608.

Raghunathan, T.E., Reiter, J.P., Rubin, D.B., 2003. Multiple imputation for statistical disclosure limitation. Journal of Official Statistics 19 (1), 1–16.

Rajasekaran, S., Harel, O., Zuba, M., Matthews, G.J., Aseltine, Jr., R., 2009. Responsible data releases. In: Proceedings 9th Industrial Conference on Data Mining (ICDM). Springer LNCS, pp. 388–400.

Reiss, S.P., 1984. Practical data-swapping: The first steps. CM Transactions on Database Systems 9, 20–37.

Reiter, J.P., 2002. Satisfying disclosure restriction with synthetic data sets. Journal of Official Statistics 18 (4), 531–543.

Reiter, J.P., 2003. Inference for partially synthetic, public use microdata sets. Survey Methodology 29 (2), 181–188.

Reiter, J.P., 2004a. New approaches to data dissemination: A glimpse into the future (?). Chance 17 (3), 11–15.

Reiter, J.P., 2004b. Simultaneous use of multiple imputation for missing data and disclosure limitation. Survey Methodology 30 (2), 235–242.

Reiter, J.P., 2005a. Estimating risks of identification disclosure in microdata. Journal of the American Statistical Association 100, 1103–1112.

Reiter, J.P., 2005b. Releasing multiply imputed, synthetic public use microdata: An illustration and empirical study. Journal of the Royal Statistical Society, Series A: Statistics in Society 168 (1), 185–205.

Reiter, J.P., 2005c. Using CART to generate partially synthetic public use microdata. Journal of Official Statistics 21 (3), 441–462.

Rubin, D.B., 1987. Multiple Imputation for Nonresponse in Surveys. John Wiley & Sons.

Rubin, D.B., 1993. Comment on “Statistical disclosure limitation”. Journal of Official Statistics 9, 461–468.

Rubner, Y., Tomasi, C., Guibas, L.J., 1998. A metric for distributions with applications to image databases. Computer Vision, IEEE International Conference on 0, 59.

Sarathy, R., Muralidhar, K., 2002a. The security of confidential numerical data in databases. Information Systems Research 13 (4), 389–403.

Sarathy, R., Muralidhar, K., 2002b. The security of confidential numerical data in databases. Info. Sys. Research 13 (4), 389–403.

Schafer, J.L., Graham, J.W., 2002. Missing data: Our view of state of the art. Psychological Methods 7 (2), 147–177.

Singh, A., Yu, F., Dunteman, G., 2003. MASSC: A new data mask for limiting statistical information loss and disclosure. In: Proceedings of the Joint UNECE/EUROSTAT Work Session on Statistical Data Confidentiality. pp. 373–394.

Skinner, C., 2009. Statistical disclosure control for survey data. In: Pfeffermann, D and Rao, C.R. eds. Handbook of Statistics Vol. 29A: Sample Surveys: Design, Methods and Applications. pp. 381–396.

Skinner, C., Marsh, C., Openshaw, S., Wymer, C., 1994. Disclosure control for census microdata. Journal of Official Statistics 10, 31–51.

Skinner, C., Shlomo, N., 2008. Assessing identification risk in survey microdata using log-linear models. Journal of the American Statistical Association 103, 989–1001.

Skinner, C.J., Elliot, M.J., 2002. A measure of disclosure risk for microdata. Journal of the Royal Statistical Society. Series B (Statistical Methodology) 64 (4), 855–867.

Smith, A., 2008. Efficient, dfferentially private point estimators. arXiv:0809.4794v1 [cs.CR].

Spruill, N.L., 1982. Measures of confidentiality. Statistics of Income and Related Administrative Record Research, 131–136.

Spruill, N.L., 1983. The confidentiality and analytic usefulness of masked business microdata. In: Proceedings of the Section on Survey Reserach Microdata. American Statistical Association, pp. 602–607.

Sweeney, L., 1996. Replacing personally-identifying information in medical records, the scrub system. In: American Medical Informatics Association. Hanley and Belfus, Inc., pp. 333–337.

Sweeney, L., 1997. Guaranteeing anonymity when sharing medical data, the datafly system. Journal of the American Medical Informatics Association 4, 51–55.

Sweeney, L., 2002a. Achieving k-anonymity privacy protection using generalization and suppression. International Journal of Uncertainty, Fuzziness and Knowledge Based Systems 10 (5), 571–588.

Sweeney, L., 2002b. k-anonymity: A model for protecting privacy. International Journal of Uncertainty, Fuzziness and Knowledge Based Systems 10 (5), 557–570.

Tendick, P., 1991. Optimal noise addition for preserving confidentiality in multivariate data. Journal of Statistical Planning and Inference 27 (2), 341–353.

United Nations Economic Comission for Europe (UNECE), 2007. Manging statistical cinfidentiality and microdata access: Principles and guidlinesof good practice.

Warner, S.L., 1965. Randomized response: A survey technique for eliminating evasive answer bias. Journal of the American Statistical Association 60 (309), 63–69.

Wasserman, L., Zhou, S., 2010. A statistical framework for differential privacy. Journal of the American Statistical Association 105 (489), 375–389.

Willenborg, L., de Waal, T., 2001. Elements of Statistical Disclosure Control. Springer-Verlag.

Woodward, B., 1995. The computer-based patient record and confidentiality. The New England Journal of Medicine, 1419–1422.

Johan A.K. Suykens, Carlos Alzate, Kristiaan Pelckmans

Source: Statist. Surv., Volume 4, 148--183.

Abstract:
This paper discusses the role of primal and (Lagrange) dual model representations in problems of supervised and unsupervised learning. The specification of the estimation problem is conceived at the primal level as a constrained optimization problem. The constraints relate to the model which is expressed in terms of the feature map. From the conditions for optimality one jointly finds the optimal model representation and the model estimate. At the dual level the model is expressed in terms of a positive definite kernel function, which is characteristic for a support vector machine methodology. It is discussed how least squares support vector machines are playing a central role as core models across problems of regression, classification, principal component analysis, spectral clustering, canonical correlation analysis, dimensionality reduction and data visualization.

Sophie Achard, Jean-François Coeurjolly

Source: Statist. Surv., Volume 4, 117--147.

Abstract:
This paper gives an overview of the problem of estimating the Hurst parameter of a fractional Brownian motion when the data are observed with outliers and/or with an additive noise by using methods based on discrete variations. We show that the classical estimation procedure based on the log-linearity of the variogram of dilated series is made more robust to outliers and/or an additive noise by considering sample quantiles and trimmed means of the squared series or differences of empirical variances. These different procedures are compared and discussed through a large simulation study and are implemented in the R package dvfBm.

Volodymyr Melnykov, Ranjan Maitra

Source: Statist. Surv., Volume 4, 80--116.

Abstract:
Finite mixture models have a long history in statistics, having been used to model population heterogeneity, generalize distributional assumptions, and lately, for providing a convenient yet formal framework for clustering and classification. This paper provides a detailed review into mixture models and model-based clustering. Recent trends as well as open problems in the area are also discussed.

Michael P. Fay, Michael A. Proschan

Source: Statist. Surv., Volume 4, 1--39.

Abstract:
In a mathematical approach to hypothesis tests, we start with a clearly defined set of hypotheses and choose the test with the best properties for those hypotheses. In practice, we often start with less precise hypotheses. For example, often a researcher wants to know which of two groups generally has the larger responses, and either a t-test or a Wilcoxon-Mann-Whitney (WMW) test could be acceptable. Although both t-tests and WMW tests are usually associated with quite different hypotheses, the decision rule and p-value from either test could be associated with many different sets of assumptions, which we call perspectives. It is useful to have many of the different perspectives to which a decision rule may be applied collected in one place, since each perspective allows a different interpretation of the associated p-value. Here we collect many such perspectives for the two-sample t-test, the WMW test and other related tests. We discuss validity and consistency under each perspective and discuss recommendations between the tests in light of these many different perspectives. Finally, we briefly discuss a decision rule for testing genetic neutrality where knowledge of the many perspectives is vital to the proper interpretation of the decision rule.

Monte Carlo simulation is useful to compute or estimate expected functionals of random elements if those random samples are possible to be generated from the true distribution. However, when the distribution has some unknown parameters, the samples must be generated from an estimated distribution with the parameters replaced by some estimators, which causes a statistical error in Monte Carlo estimation. This paper considers such a statistical error and investigates the asymptotic distributions of Monte Carlo-based estimators when the random elements are not only the real valued, but also functional valued random variables. We also investigate expected functionals for semimartingales in details. The consideration indicates that the Monte Carlo estimation can get worse when a semimartingale has a jump part with unremovable unknown parameters.

Methods for generating synthetic data have become of increasing importance to build large datasets required for Convolution Neural Networks (CNN) based deep learning techniques for a wide range of computer vision applications. In this work, we extend existing methodologies to show how 2D thermal facial data can be mapped to provide 3D facial models. For the proposed research work we have used tufts datasets for generating 3D varying face poses by using a single frontal face pose. The system works by refining the existing image quality by performing fusion based image preprocessing operations. The refined outputs have better contrast adjustments, decreased noise level and higher exposedness of the dark regions. It makes the facial landmarks and temperature patterns on the human face more discernible and visible when compared to original raw data. Different image quality metrics are used to compare the refined version of images with original images. In the next phase of the proposed study, the refined version of images is used to create 3D facial geometry structures by using Convolution Neural Networks (CNN). The generated outputs are then imported in blender software to finally extract the 3D thermal facial outputs of both males and females. The same technique is also used on our thermal face data acquired using prototype thermal camera (developed under Heliaus EU project) in an indoor lab environment which is then used for generating synthetic 3D face data along with varying yaw face angles and lastly facial depth map is generated.

Building a scalable machine learning system for unsupervised anomaly detection via representation learning is highly desirable. One of the prevalent methods is using a reconstruction error from variational autoencoder (VAE) via maximizing the evidence lower bound. We revisit VAE from the perspective of information theory to provide some theoretical foundations on using the reconstruction error, and finally arrive at a simpler and more effective model for anomaly detection. In addition, to enhance the effectiveness of detecting anomalies, we incorporate a practical model uncertainty measure into the metric. We show empirically the competitive performance of our approach on benchmark datasets.

In this paper we propose a bimodal gamma distribution using a quadratic transformation based on the alpha-skew-normal model. We discuss several properties of this distribution such as mean, variance, moments, hazard rate and entropy measures. Further, we propose a new regression model with censored data based on the bimodal gamma distribution. This regression model can be very useful to the analysis of real data and could give more realistic fits than other special regression models. Monte Carlo simulations were performed to check the bias in the maximum likelihood estimation. The proposed models are applied to two real data sets found in literature.

Official counts of COVID-19 deaths have been criticized for potentially including people who did not die of COVID-19 but merely died with COVID-19. I address that critique by fitting a generalized additive model to weekly counts of all registered deaths in England and Wales during the 2010s. The model produces baseline rates of death registrations expected in the absence of the COVID-19 pandemic, and comparing those baselines to recent counts of registered deaths exposes the emergence of excess deaths late in March 2020. Among adults aged 45+, about 38,700 excess deaths were registered in the 5 weeks comprising 21 March through 24 April (612 $pm$ 416 from 21$-$27 March, 5675 $pm$ 439 from 28 March through 3 April, then 9183 $pm$ 468, 12,712 $pm$ 589, and 10,511 $pm$ 567 in April's next 3 weeks). Both the Office for National Statistics's respective count of 26,891 death certificates which mention COVID-19, and the Department of Health and Social Care's hospital-focused count of 21,222 deaths, are appreciably less, implying that their counting methods have underestimated rather than overestimated the pandemic's true death toll. If underreporting rates have held steady, about 45,900 direct and indirect COVID-19 deaths might have been registered by April's end but not yet publicly reported in full.

Spatial trajectories are ubiquitous and complex signals. Their analysis is crucial in many research fields, from urban planning to neuroscience. Several approaches have been proposed to cluster trajectories. They rely on hand-crafted features, which struggle to capture the spatio-temporal complexity of the signal, or on Artificial Neural Networks (ANNs) which can be more efficient but less interpretable. In this paper we present a novel ANN architecture designed to capture the spatio-temporal patterns characteristic of a set of trajectories, while taking into account the demographics of the navigators. Hence, our model extracts markers linked to both behaviour and demographics. We propose a composite signal analyser (CompSNN) combining three simple ANN modules. Each of these modules uses different signal representations of the trajectory while remaining interpretable. Our CompSNN performs significantly better than its modules taken in isolation and allows to visualise which parts of the signal were most useful to discriminate the trajectories.

Beginning from a basic neural-network architecture, we test the potential benefits offered by a range of advanced techniques for machine learning, in particular deep learning, in the context of a typical classification problem encountered in the domain of high-energy physics, using a well-studied dataset: the 2014 Higgs ML Kaggle dataset. The advantages are evaluated in terms of both performance metrics and the time required to train and apply the resulting models. Techniques examined include domain-specific data-augmentation, learning rate and momentum scheduling, (advanced) ensembling in both model-space and weight-space, and alternative architectures and connection methods.

Following the investigation, we arrive at a model which achieves equal performance to the winning solution of the original Kaggle challenge, whilst being significantly quicker to train and apply, and being suitable for use with both GPU and CPU hardware setups. These reductions in timing and hardware requirements potentially allow the use of more powerful algorithms in HEP analyses, where models must be retrained frequently, sometimes at short notice, by small groups of researchers with limited hardware resources. Additionally, a new wrapper library for PyTorch called LUMINis presented, which incorporates all of the techniques studied.

This paper develops a general framework for analyzing asymptotics of $V$-statistics. Previous literature on limiting distribution mainly focuses on the cases when $n o infty$ with fixed kernel size $k$. Under some regularity conditions, we demonstrate asymptotic normality when $k$ grows with $n$ by utilizing existing results for $U$-statistics. The key in our approach lies in a mathematical reduction to $U$-statistics by designing an equivalent kernel for $V$-statistics. We also provide a unified treatment on variance estimation for both $U$- and $V$-statistics by observing connections to existing methods and proposing an empirically more accurate estimator. Ensemble methods such as random forests, where multiple base learners are trained and aggregated for prediction purposes, serve as a running example throughout the paper because they are a natural and flexible application of $V$-statistics.

A graph homomorphism is a map between two graphs that preserves adjacency relations. We consider the problem of sampling a random graph homomorphism from a graph $F$ into a large network $mathcal{G}$. We propose two complementary MCMC algorithms for sampling a random graph homomorphisms and establish bounds on their mixing times and concentration of their time averages. Based on our sampling algorithms, we propose a novel framework for network data analysis that circumvents some of the drawbacks in methods based on independent and neigborhood sampling. Various time averages of the MCMC trajectory give us various computable observables, including well-known ones such as homomorphism density and average clustering coefficient and their generalizations. Furthermore, we show that these network observables are stable with respect to a suitably renormalized cut distance between networks. We provide various examples and simulations demonstrating our framework through synthetic networks. We also apply our framework for network clustering and classification problems using the Facebook100 dataset and Word Adjacency Networks of a set of classic novels.

A major difficulty of solving continuous POMDPs is to infer the multi-modal distribution of the unobserved true states and to make the planning algorithm dependent on the perceived uncertainty. We cast POMDP filtering and planning problems as two closely related Sequential Monte Carlo (SMC) processes, one over the real states and the other over the future optimal trajectories, and combine the merits of these two parts in a new model named the DualSMC network. In particular, we first introduce an adversarial particle filter that leverages the adversarial relationship between its internal components. Based on the filtering results, we then propose a planning algorithm that extends the previous SMC planning approach [Piche et al., 2018] to continuous POMDPs with an uncertainty-dependent policy. Crucially, not only can DualSMC handle complex observations such as image input but also it remains highly interpretable. It is shown to be effective in three continuous POMDP domains: the floor positioning domain, the 3D light-dark navigation domain, and a modified Reacher domain.

We study the interplay of two important issues on Bayesian model selection (BMS): censoring and model misspecification. We consider additive accelerated failure time (AAFT), Cox proportional hazards and probit models, and a more general concave log-likelihood structure. A fundamental question is what solution can one hope BMS to provide, when (inevitably) models are misspecified. We show that asymptotically BMS keeps any covariate with predictive power for either the outcome or censoring times, and discards other covariates. Misspecification refers to assuming the wrong model or functional effect on the response, including using a finite basis for a truly non-parametric effect, or omitting truly relevant covariates. We argue for using simple models that are computationally practical yet attain good power to detect potentially complex effects, despite misspecification. Misspecification and censoring both have an asymptotically negligible effect on (suitably-defined) false positives, but their impact on power is exponential. We portray these issues via simple descriptions of early/late censoring and the drop in predictive accuracy due to misspecification. From a methods point of view, we consider local priors and a novel structure that combines local and non-local priors to enforce sparsity. We develop algorithms to capitalize on the AAFT tractability, approximations to AAFT and probit likelihoods giving significant computational gains, a simple augmented Gibbs sampler to hierarchically explore linear and non-linear effects, and an implementation in the R package mombf. We illustrate the proposed methods and others based on likelihood penalties via extensive simulations under misspecification and censoring. We present two applications concerning the effect of gene expression on colon and breast cancer.

Given a multivariate data set, sparse principal component analysis (SPCA) aims to extract several linear combinations of the variables that together explain the variance in the data as much as possible, while controlling the number of nonzero loadings in these combinations. In this paper we consider 8 different optimization formulations for computing a single sparse loading vector; these are obtained by combining the following factors: we employ two norms for measuring variance (L2, L1) and two sparsity-inducing norms (L0, L1), which are used in two different ways (constraint, penalty). Three of our formulations, notably the one with L0 constraint and L1 variance, have not been considered in the literature. We give a unifying reformulation which we propose to solve via a natural alternating maximization (AM) method. We show the the AM method is nontrivially equivalent to GPower (Journ'{e}e et al; JMLR 11:517--553, 2010) for all our formulations. Besides this, we provide 24 efficient parallel SPCA implementations: 3 codes (multi-core, GPU and cluster) for each of the 8 problems. Parallelism in the methods is aimed at i) speeding up computations (our GPU code can be 100 times faster than an efficient serial code written in C++), ii) obtaining solutions explaining more variance and iii) dealing with big data problems (our cluster code is able to solve a 357 GB problem in about a minute).

Increasing number of sectors which affect human lives, are using Machine Learning (ML) tools. Hence the need for understanding their working mechanism and evaluating their fairness in decision-making, are becoming paramount, ushering in the era of Explainable AI (XAI). In this contribution we introduced a few intrinsically interpretable models which are also capable of dealing with missing values, in addition to extracting knowledge from the dataset and about the problem. These models are also capable of visualisation of the classifier and decision boundaries: they are the angle based variants of Learning Vector Quantization. We have demonstrated the algorithms on a synthetic dataset and a real-world one (heart disease dataset from the UCI repository). The newly developed classifiers helped in investigating the complexities of the UCI dataset as a multiclass problem. The performance of the developed classifiers were comparable to those reported in literature for this dataset, with additional value of interpretability, when the dataset was treated as a binary class problem.

This paper considers the problem of estimation of the Fisher information for location from a random sample of size $n$. First, an estimator proposed by Bhattacharya is revisited and improved convergence rates are derived. Second, a new estimator, termed a clipped estimator, is proposed. Superior upper bounds on the rates of convergence can be shown for the new estimator compared to the Bhattacharya estimator, albeit with different regularity conditions. Third, both of the estimators are evaluated for the practically relevant case of a random variable contaminated by Gaussian noise. Moreover, using Brown's identity, which relates the Fisher information and the minimum mean squared error (MMSE) in Gaussian noise, two corresponding consistent estimators for the MMSE are proposed. Simulation examples for the Bhattacharya estimator and the clipped estimator as well as the MMSE estimators are presented. The examples demonstrate that the clipped estimator can significantly reduce the required sample size to guarantee a specific confidence interval compared to the Bhattacharya estimator.

In many Machine Learning domains, datasets are characterized by highly imbalanced and overlapping classes. Particularly in the medical domain, a specific list of symptoms can be labeled as one of various different conditions. Some of these conditions may be more prevalent than others by several orders of magnitude. Here we present a novel unsupervised Domain Adaptation scheme for such datasets. The scheme, based on a specific type of Quantification, is designed to work under both label and conditional shifts. It is demonstrated on datasets generated from Electronic Health Records and provides high quality results for both Quantification and Domain Adaptation in very challenging scenarios. Potential benefits of using this scheme in the current COVID-19 outbreak, for estimation of prevalence and probability of infection, are discussed.

Early detection of patients vulnerable to infections acquired in the hospital environment is a challenge in current health systems given the impact that such infections have on patient mortality and healthcare costs. This work is focused on both the identification of risk factors and the prediction of healthcare-associated infections in intensive-care units by means of machine-learning methods. The aim is to support decision making addressed at reducing the incidence rate of infections. In this field, it is necessary to deal with the problem of building reliable classifiers from imbalanced datasets. We propose a clustering-based undersampling strategy to be used in combination with ensemble classifiers. A comparative study with data from 4616 patients was conducted in order to validate our proposal. We applied several single and ensemble classifiers both to the original dataset and to data preprocessed by means of different resampling methods. The results were analyzed by means of classic and recent metrics specifically designed for imbalanced data classification. They revealed that the proposal is more efficient in comparison with other approaches.

We propose a new semiparametric approach for modelling nonlinear univariate diffusions, where the observed process is a nonparametric transformation of an underlying parametric diffusion (UPD). This modelling strategy yields a general class of semiparametric Markov diffusion models with parametric dynamic copulas and nonparametric marginal distributions. We provide primitive conditions for the identification of the UPD parameters together with the unknown transformations from discrete samples. Likelihood-based estimators of both parametric and nonparametric components are developed and we analyze the asymptotic properties of these. Kernel-based drift and diffusion estimators are also proposed and shown to be normally distributed in large samples. A simulation study investigates the finite sample performance of our estimators in the context of modelling US short-term interest rates. We also present a simple application of the proposed method for modelling the CBOE volatility index data.

This paper deals with robust marginal estimation under a general regression model when missing data occur in the response and also in some of covariates. The target is a marginal location parameter which is given through an $M-$functional. To obtain robust Fisher--consistent estimators, properly defined marginal distribution function estimators are considered. These estimators avoid the bias due to missing values by assuming a missing at random condition. Three methods are considered to estimate the marginal distribution function which allows to obtain the $M-$location of interest: the well-known inverse probability weighting, a convolution--based method that makes use of the regression model and an augmented inverse probability weighting procedure that prevents against misspecification. The robust proposed estimators and the classical ones are compared through a numerical study under different missing models including clean and contaminated samples. We illustrate the estimators behaviour under a nonlinear model. A real data set is also analysed.

Text summarization refers to the process that generates a shorter form of text from the source document preserving salient information. Recently, many models for text summarization have been proposed. Most of those models were evaluated using recall-oriented understudy for gisting evaluation (ROUGE) scores. However, as ROUGE scores are computed based on n-gram overlap, they do not reflect semantic meaning correspondences between generated and reference summaries. Because Korean is an agglutinative language that combines various morphemes into a word that express several meanings, ROUGE is not suitable for Korean summarization. In this paper, we propose evaluation metrics that reflect semantic meanings of a reference summary and the original document, Reference and Document Aware Semantic Score (RDASS). We then propose a method for improving the correlation of the metrics with human judgment. Evaluation results show that the correlation with human judgment is significantly higher for our evaluation metrics than for ROUGE scores.

Introducing common shocks is a popular dependence modelling approach, with some recent applications in loss reserving. The main advantage of this approach is the ability to capture structural dependence coming from known relationships. In addition, it helps with the parsimonious construction of correlation matrices of large dimensions. However, complications arise in the presence of "unbalanced data", that is, when (expected) magnitude of observations over a single triangle, or between triangles, can vary substantially. Specifically, if a single common shock is applied to all of these cells, it can contribute insignificantly to the larger values and/or swamp the smaller ones, unless careful adjustments are made. This problem is further complicated in applications involving negative claim amounts. In this paper, we address this problem in the loss reserving context using a common shock Tweedie approach for unbalanced data. We show that the solution not only provides a much better balance of the common shock proportions relative to the unbalanced data, but it is also parsimonious. Finally, the common shock Tweedie model also provides distributional tractability.

Recent advancements in diagnostic learning and development of gesture-based human machine interfaces have driven surface electromyography (sEMG) towards significant importance. Analysis of hand gestures requires an accurate assessment of sEMG signals. The proposed work presents a novel sequential master-slave architecture consisting of deep neural networks (DNNs) for classification of signs from the Indian sign language using signals recorded from multiple sEMG channels. The performance of the master-slave network is augmented by leveraging additional synthetic feature data generated by long short term memory networks. Performance of the proposed network is compared to that of a conventional DNN prior to and after the addition of synthetic data. Up to 14% improvement is observed in the conventional DNN and up to 9% improvement in master-slave network on addition of synthetic data with an average accuracy value of 93.5% asserting the suitability of the proposed approach.

In the variational relevance vector machine, the gamma distribution is representative as a hyperprior over the noise precision of automatic relevance determination prior. Instead of the gamma hyperprior, we propose to use the inverse gamma hyperprior with a shape parameter close to zero and a scale parameter not necessary close to zero. This hyperprior is associated with the concept of a weakly informative prior. The effect of this hyperprior is investigated through regression to non-homogeneous data. Because it is difficult to capture the structure of such data with a single kernel function, we apply the multiple kernel method, in which multiple kernel functions with different widths are arranged for input data. We confirm that the degrees of freedom in a model is controlled by adjusting the scale parameter and keeping the shape parameter close to zero. A candidate for selecting the scale parameter is the predictive information criterion. However the estimated model using this criterion seems to cause over-fitting. This is because the multiple kernel method makes the model a situation where the dimension of the model is larger than the data size. To select an appropriate scale parameter even in such a situation, we also propose an extended prediction information criterion. It is confirmed that a multiple kernel relevance vector regression model with good predictive accuracy can be obtained by selecting the scale parameter minimizing extended prediction information criterion.

In causal settings, such as instrumental variable settings, it is well known that estimators based on ordinary least squares (OLS) can yield biased and non-consistent estimates of the causal parameters. This is partially overcome by two-stage least squares (TSLS) estimators. These are, under weak assumptions, consistent but do not have desirable finite sample properties: in many models, for example, they do not have finite moments. The set of K-class estimators can be seen as a non-linear interpolation between OLS and TSLS and are known to have improved finite sample properties. Recently, in causal discovery, invariance properties such as the moment criterion which TSLS estimators leverage have been exploited for causal structure learning: e.g., in cases, where the causal parameter is not identifiable, some structure of the non-zero components may be identified, and coverage guarantees are available. Subsequently, anchor regression has been proposed to trade-off invariance and predictability. The resulting estimator is shown to have optimal predictive performance under bounded shift interventions. In this paper, we show that the concepts of anchor regression and K-class estimators are closely related. Establishing this connection comes with two benefits: (1) It enables us to prove robustness properties for existing K-class estimators when considering distributional shifts. And, (2), we propose a novel estimator in instrumental variable settings by minimizing the mean squared prediction error subject to the constraint that the estimator lies in an asymptotically valid confidence region of the causal parameter. We call this estimator PULSE (p-uncorrelated least squares estimator) and show that it can be computed efficiently, even though the underlying optimization problem is non-convex. We further prove that it is consistent.

Data-driven modelling and computational predictions based on maximum entropy principle (MaxEnt-principle) aim at finding as-simple-as-possible - but not simpler then necessary - models that allow to avoid the data overfitting problem. We derive a multivariate non-parametric and non-stationary formulation of the MaxEnt-principle and show that its solution can be approximated through a numerical maximisation of the sparse constrained optimization problem with regularization. Application of the resulting algorithm to popular financial benchmarks reveals memoryless models allowing for simple and qualitative descriptions of the major stock market indexes data. We compare the obtained MaxEnt-models to the heteroschedastic models from the computational econometrics (GARCH, GARCH-GJR, MS-GARCH, GARCH-PML4) in terms of the model fit, complexity and prediction quality. We compare the resulting model log-likelihoods, the values of the Bayesian Information Criterion, posterior model probabilities, the quality of the data autocorrelation function fits as well as the Value-at-Risk prediction quality. We show that all of the considered seven major financial benchmark time series (DJI, SPX, FTSE, STOXX, SMI, HSI and N225) are better described by conditionally memoryless MaxEnt-models with nonstationary regime-switching than by the common econometric models with finite memory. This analysis also reveals a sparse network of statistically-significant temporal relations for the positive and negative latent variance changes among different markets. The code is provided for open access.

Restricted Boltzmann Machine (RBM) is an energy based, undirected graphical model. It is commonly used for unsupervised and supervised machine learning. Typically, RBM is trained using contrastive divergence (CD). However, training with CD is slow and does not estimate exact gradient of log-likelihood cost function. In this work, the model expectation of gradient learning for RBM has been calculated using a quantum annealer (D-Wave 2000Q), which is much faster than Markov chain Monte Carlo (MCMC) used in CD. Training and classification results are compared with CD. The classification accuracy results indicate similar performance of both methods. Image reconstruction as well as log-likelihood calculations are used to compare the performance of quantum and classical algorithms for RBM training. It is shown that the samples obtained from quantum annealer can be used to train a RBM on a 64-bit `bars and stripes' data set with classification performance similar to a RBM trained with CD. Though training based on CD showed improved learning performance, training using a quantum annealer eliminates computationally expensive MCMC steps of CD.

People learn to discriminate between classes without explicit exposure to negative examples. On the contrary, traditional machine learning algorithms often rely on negative examples, otherwise the model would be prone to collapse and always-true predictions. Therefore, it is crucial to design the learning objective which leads the model to converge and to perform predictions unbiasedly without explicit negative signals. In this paper, we propose a Collectively loss function to learn from only Positive and Unlabeled data (cPU). We theoretically elicit the loss function from the setting of PU learning. We perform intensive experiments on the benchmark and real-world datasets. The results show that cPU consistently outperforms the current state-of-the-art PU learning methods.

In this paper we obtain the limit distribution for partial sums with a random number of terms following a class of mixed Poisson distributions. The resulting weak limit is a mixing between a normal distribution and an exponential family, which we call by normal exponential family (NEF) laws. A new stability concept is introduced and a relationship between {alpha}-stable distributions and NEF laws is established. We propose estimation of the parameters of the NEF models through the method of moments and also by the maximum likelihood method, which is performed via an Expectation-Maximization algorithm. Monte Carlo simulation studies are addressed to check the performance of the proposed estimators and an empirical illustration on financial market is presented.

We develop a general framework for data-driven approximation of input-output maps between infinite-dimensional spaces. The proposed approach is motivated by the recent successes of neural networks and deep learning, in combination with ideas from model reduction. This combination results in a neural network approximation which, in principle, is defined on infinite-dimensional spaces and, in practice, is robust to the dimension of finite-dimensional approximations of these spaces required for computation. For a class of input-output maps, and suitably chosen probability measures on the inputs, we prove convergence of the proposed approximation methodology. Numerically we demonstrate the effectiveness of the method on a class of parametric elliptic PDE problems, showing convergence and robustness of the approximation scheme with respect to the size of the discretization, and compare our method with existing algorithms from the literature.

I study the minimax-optimal design for a two-arm controlled experiment where conditional mean outcomes may vary in a given set. When this set is permutation symmetric, the optimal design is complete randomization, and using a single partition (i.e., the design that only randomizes the treatment labels for each side of the partition) has minimax risk larger by a factor of $n-1$. More generally, the optimal design is shown to be the mixed-strategy optimal design (MSOD) of Kallus (2018). Notably, even when the set of conditional mean outcomes has structure (i.e., is not permutation symmetric), being minimax-optimal for variance still requires randomization beyond a single partition. Nonetheless, since this targets precision, it may still not ensure sufficient uniformity in randomization to enable randomization (i.e., design-based) inference by Fisher's exact test to appropriately detect violations of null. I therefore propose the inference-constrained MSOD, which is minimax-optimal among all designs subject to such uniformity constraints. On the way, I discuss Johansson et al. (2020) who recently compared rerandomization of Morgan and Rubin (2012) and the pure-strategy optimal design (PSOD) of Kallus (2018). I point out some errors therein and set straight that randomization is minimax-optimal and that the "no free lunch" theorem and example in Kallus (2018) are correct.

Crowdsourcing is a popular approach to collect annotations for unlabeled data instances. It involves collecting a large number of annotations from several, often naive untrained annotators for each data instance which are then combined to estimate the ground truth. Further, annotations for constructs such as affect are often multi-dimensional with annotators rating multiple dimensions, such as valence and arousal, for each instance. Most annotation fusion schemes however ignore this aspect and model each dimension separately. In this work we address this by proposing a generative model for multi-dimensional annotation fusion, which models the dimensions jointly leading to more accurate ground truth estimates. The model we propose is applicable to both global and time series annotation fusion problems and treats the ground truth as a latent variable distorted by the annotators. The model parameters are estimated using the Expectation-Maximization algorithm and we evaluate its performance using synthetic data and real emotion corpora as well as on an artificial task with human annotations