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.

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.

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.

Application and use of deep learning algorithms for different healthcare applications is gaining interest at a steady pace. However, use of such algorithms can prove to be challenging as they require large amounts of training data that capture different possible variations. This makes it difficult to use them in a clinical setting since in most health applications researchers often have to work with limited data. Less data can cause the deep learning model to over-fit. In this paper, we ask how can we use data from a different environment, different use-case, with widely differing data distributions. We exemplify this use case by using single-sensor accelerometer data from healthy subjects performing activities of daily living - ADLs (source dataset), to extract features relevant to multi-sensor accelerometer gait data (target dataset) for Parkinson's disease classification. We train the pre-trained model using the source dataset and use it as a feature extractor. We show that the features extracted for the target dataset can be used to train an effective classification model. Our pre-trained source model consists of a convolutional autoencoder, and the target classification model is a simple multi-layer perceptron model. We explore two different pre-trained source models, trained using different activity groups, and analyze the influence the choice of pre-trained model has over the task of Parkinson's disease classification.

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.

The very first case of corona-virus illness was recorded on 30 January 2020, in India and the number of infected cases, including the death toll, continues to rise. In this paper, we present short-term forecasts of COVID-19 for 28 Indian states and five union territories using real-time data from 30 January to 21 April 2020. Applying Holt's second-order exponential smoothing method and autoregressive integrated moving average (ARIMA) model, we generate 10-day ahead forecasts of the likely number of infected cases and deaths in India for 22 April to 1 May 2020. Our results show that the number of cumulative cases in India will rise to 36335.63 [PI 95% (30884.56, 42918.87)], concurrently the number of deaths may increase to 1099.38 [PI 95% (959.77, 1553.76)] by 1 May 2020. Further, we have divided the country into severity zones based on the cumulative cases. According to this analysis, Maharashtra is likely to be the most affected states with around 9787.24 [PI 95% (6949.81, 13757.06)] cumulative cases by 1 May 2020. However, Kerala and Karnataka are likely to shift from the red zone (i.e. highly affected) to the lesser affected region. On the other hand, Gujarat and Madhya Pradesh will move to the red zone. These results mark the states where lockdown by 3 May 2020, can be loosened.

In the Gaussian sequence model $Y= heta_0 + varepsilon$ in $mathbb{R}^n$, we study the fundamental limit of approximating the signal $ heta_0$ by a class $Theta(d,d_0,k)$ of (generalized) splines with free knots. Here $d$ is the degree of the spline, $d_0$ is the order of differentiability at each inner knot, and $k$ is the maximal number of pieces. We show that, given any integer $dgeq 0$ and $d_0in{-1,0,ldots,d-1}$, the minimax rate of estimation over $Theta(d,d_0,k)$ exhibits the following phase transition: egin{equation*} egin{aligned} inf_{widetilde{ heta}}sup_{ hetainTheta(d,d_0, k)}mathbb{E}_ heta|widetilde{ heta} - heta|^2 asymp_d egin{cases} kloglog(16n/k), & 2leq kleq k_0,\ klog(en/k), & k geq k_0+1. end{cases} end{aligned} end{equation*} The transition boundary $k_0$, which takes the form $lfloor{(d+1)/(d-d_0) floor} + 1$, demonstrates the critical role of the regularity parameter $d_0$ in the separation between a faster $log log(16n)$ and a slower $log(en)$ rate. We further show that, once encouraging an additional '$d$-monotonicity' shape constraint (including monotonicity for $d = 0$ and convexity for $d=1$), the above phase transition is eliminated and the faster $kloglog(16n/k)$ rate can be achieved for all $k$. These results provide theoretical support for developing $ell_0$-penalized (shape-constrained) spline regression procedures as useful alternatives to $ell_1$- and $ell_2$-penalized ones.

Cooperation between different data owners may lead to an improvement in forecast quality - for instance by benefiting from spatial-temporal dependencies in geographically distributed time series. Due to business competitive factors and personal data protection questions, said data owners might be unwilling to share their data, which increases the interest in collaborative privacy-preserving forecasting. This paper analyses the state-of-the-art and unveils several shortcomings of existing methods in guaranteeing data privacy when employing Vector Autoregressive (VAR) models. The paper also provides mathematical proofs and numerical analysis to evaluate existing privacy-preserving methods, dividing them into three groups: data transformation, secure multi-party computations, and decomposition methods. The analysis shows that state-of-the-art techniques have limitations in preserving data privacy, such as a trade-off between privacy and forecasting accuracy, while the original data in iterative model fitting processes, in which intermediate results are shared, can be inferred after some iterations.

Multi-Class Incremental Learning (MCIL) aims to learn new concepts by incrementally updating a model trained on previous concepts. However, there is an inherent trade-off to effectively learning new concepts without catastrophic forgetting of previous ones. To alleviate this issue, it has been proposed to keep around a few examples of the previous concepts but the effectiveness of this approach heavily depends on the representativeness of these examples. This paper proposes a novel and automatic framework we call mnemonics, where we parameterize exemplars and make them optimizable in an end-to-end manner. We train the framework through bilevel optimizations, i.e., model-level and exemplar-level. We conduct extensive experiments on three MCIL benchmarks, CIFAR-100, ImageNet-Subset and ImageNet, and show that using mnemonics exemplars can surpass the state-of-the-art by a large margin. Interestingly and quite intriguingly, the mnemonics exemplars tend to be on the boundaries between different classes.

We study the information content of nuclear masses from the perspective of global models of nuclear binding energies. To this end, we employ a number of statistical methods and diagnostic tools, including Bayesian calibration, Bayesian model averaging, chi-square correlation analysis, principal component analysis, and empirical coverage probability. Using a Bayesian framework, we investigate the structure of the 4-parameter Liquid Drop Model by considering discrepant mass domains for calibration. We then use the chi-square correlation framework to analyze the 14-parameter Skyrme energy density functional calibrated using homogeneous and heterogeneous datasets. We show that a quite dramatic parameter reduction can be achieved in both cases. The advantage of Bayesian model averaging for improving uncertainty quantification is demonstrated. The statistical approaches used are pedagogically described; in this context this work can serve as a guide for future applications.

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.

Boosting is one of the most successful ideas in machine learning. The most well-accepted explanations for the low generalization error of boosting algorithms such as AdaBoost stem from margin theory. The study of margins in the context of boosting algorithms was initiated by Schapire, Freund, Bartlett and Lee (1998) and has inspired numerous boosting algorithms and generalization bounds. To date, the strongest known generalization (upper bound) is the $k$th margin bound of Gao and Zhou (2013). Despite the numerous generalization upper bounds that have been proved over the last two decades, nothing is known about the tightness of these bounds. In this paper, we give the first margin-based lower bounds on the generalization error of boosted classifiers. Our lower bounds nearly match the $k$th margin bound and thus almost settle the generalization performance of boosted classifiers in terms of margins.

We study the problem of parameter estimation for a non-ergodic Gaussian Vasicek-type model defined as $dX_t=(mu+ heta X_t)dt+dG_t, tgeq0$ with unknown parameters $ heta>0$ and $muinR$, where $G$ is a Gaussian process. We provide least square-type estimators $widetilde{ heta}_T$ and $widetilde{mu}_T$ respectively for the drift parameters $ heta$ and $mu$ based on continuous-time observations ${X_t, tin[0,T]}$ as $T ightarrowinfty$.

Our aim is to derive some sufficient conditions on the driving Gaussian process $G$ in order to ensure that $widetilde{ heta}_T$ and $widetilde{mu}_T$ are strongly consistent, the limit distribution of $widetilde{ heta}_T$ is a Cauchy-type distribution and $widetilde{mu}_T$ is asymptotically normal. We apply our result to fractional Vasicek, subfractional Vasicek and bifractional Vasicek processes. In addition, this work extends the result of cite{EEO} studied in the case where $mu=0$.

We present LCE, a Local Cascade Ensemble for traditional (tabular) multivariate data classification, and its extension LCEM for Multivariate Time Series (MTS) classification. LCE is a new hybrid ensemble method that combines an explicit boosting-bagging approach to handle the usual bias-variance tradeoff faced by machine learning models and an implicit divide-and-conquer approach to individualize classifier errors on different parts of the training data. Our evaluation firstly shows that the hybrid ensemble method LCE outperforms the state-of-the-art classifiers on the UCI datasets and that LCEM outperforms the state-of-the-art MTS classifiers on the UEA datasets. Furthermore, LCEM provides explainability by design and manifests robust performance when faced with challenges arising from continuous data collection (different MTS length, missing data and noise).

The $p$-tensor Curie-Weiss model is a two-parameter discrete exponential family for modeling dependent binary data, where the sufficient statistic has a linear term and a term with degree $p geq 2$. This is a special case of the tensor Ising model and the natural generalization of the matrix Curie-Weiss model, which provides a convenient mathematical abstraction for capturing, not just pairwise, but higher-order dependencies. In this paper we provide a complete description of the limiting properties of the maximum likelihood (ML) estimates of the natural parameters, given a single sample from the $p$-tensor Curie-Weiss model, for $p geq 3$, complementing the well-known results in the matrix ($p=2$) case (Comets and Gidas (1991)). Our results unearth various new phase transitions and surprising limit theorems, such as the existence of a 'critical' curve in the parameter space, where the limiting distribution of the ML estimates is a mixture with both continuous and discrete components. The number of mixture components is either two or three, depending on, among other things, the sign of one of the parameters and the parity of $p$. Another interesting revelation is the existence of certain 'special' points in the parameter space where the ML estimates exhibit a superefficiency phenomenon, converging to a non-Gaussian limiting distribution at rate $N^{frac{3}{4}}$. We discuss how these results can be used to construct confidence intervals for the model parameters and, as a byproduct of our analysis, obtain limit theorems for the sample mean, which provide key insights into the statistical properties of the model.

Disaggregation regression has become an important tool in spatial disease mapping for making fine-scale predictions of disease risk from aggregated response data. By including high resolution covariate information and modelling the data generating process on a fine scale, it is hoped that these models can accurately learn the relationships between covariates and response at a fine spatial scale. However, validating these high resolution predictions can be a challenge, as often there is no data observed at this spatial scale. In this study, disaggregation regression was performed on simulated data in various settings and the resulting fine-scale predictions are compared to the simulated ground truth. Performance was investigated with varying numbers of data points, sizes of aggregated areas and levels of model misspecification. The effectiveness of cross validation on the aggregate level as a measure of fine-scale predictive performance was also investigated. Predictive performance improved as the number of observations increased and as the size of the aggregated areas decreased. When the model was well-specified, fine-scale predictions were accurate even with small numbers of observations and large aggregated areas. Under model misspecification predictive performance was significantly worse for large aggregated areas but remained high when response data was aggregated over smaller regions. Cross-validation correlation on the aggregate level was a moderately good predictor of fine-scale predictive performance. While the simulations are unlikely to capture the nuances of real-life response data, this study gives insight into the effectiveness of disaggregation regression in different contexts.

We introduce an optimized physics-informed neural network (PINN) trained to solve the problem of identifying and characterizing a surface breaking crack in a metal plate. PINNs are neural networks that can combine data and physics in the learning process by adding the residuals of a system of Partial Differential Equations to the loss function. Our PINN is supervised with realistic ultrasonic surface acoustic wave data acquired at a frequency of 5 MHz. The ultrasonic surface wave data is represented as a surface deformation on the top surface of a metal plate, measured by using the method of laser vibrometry. The PINN is physically informed by the acoustic wave equation and its convergence is sped up using adaptive activation functions. The adaptive activation function uses a scalable hyperparameter in the activation function, which is optimized to achieve best performance of the network as it changes dynamically the topology of the loss function involved in the optimization process. The usage of adaptive activation function significantly improves the convergence, notably observed in the current study. We use PINNs to estimate the speed of sound of the metal plate, which we do with an error of 1\%, and then, by allowing the speed of sound to be space dependent, we identify and characterize the crack as the positions where the speed of sound has decreased. Our study also shows the effect of sub-sampling of the data on the sensitivity of sound speed estimates. More broadly, the resulting model shows a promising deep neural network model for ill-posed inverse problems.

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.

As an important type of reinforcement learning algorithms, actor-critic (AC) and natural actor-critic (NAC) algorithms are often executed in two ways for finding optimal policies. In the first nested-loop design, actor's one update of policy is followed by an entire loop of critic's updates of the value function, and the finite-sample analysis of such AC and NAC algorithms have been recently well established. The second two time-scale design, in which actor and critic update simultaneously but with different learning rates, has much fewer tuning parameters than the nested-loop design and is hence substantially easier to implement. Although two time-scale AC and NAC have been shown to converge in the literature, the finite-sample convergence rate has not been established. In this paper, we provide the first such non-asymptotic convergence rate for two time-scale AC and NAC under Markovian sampling and with actor having general policy class approximation. We show that two time-scale AC requires the overall sample complexity at the order of $mathcal{O}(epsilon^{-2.5}log^3(epsilon^{-1}))$ to attain an $epsilon$-accurate stationary point, and two time-scale NAC requires the overall sample complexity at the order of $mathcal{O}(epsilon^{-4}log^2(epsilon^{-1}))$ to attain an $epsilon$-accurate global optimal point. We develop novel techniques for bounding the bias error of the actor due to dynamically changing Markovian sampling and for analyzing the convergence rate of the linear critic with dynamically changing base functions and transition kernel.

In the field of numerical weather prediction (NWP), the probabilistic distribution of the future state of the atmosphere is sampled with Monte-Carlo-like simulations, called ensembles. These ensembles have deficiencies (such as conditional biases) that can be corrected thanks to statistical post-processing methods. Several ensembles exist and may be corrected with different statistiscal methods. A further step is to combine these raw or post-processed ensembles. The theory of prediction with expert advice allows us to build combination algorithms with theoretical guarantees on the forecast performance. This article adapts this theory to the case of probabilistic forecasts issued as step-wise cumulative distribution functions (CDF). The theory is applied to wind speed forecasting, by combining several raw or post-processed ensembles, considered as CDFs. The second goal of this study is to explore the use of two forecast performance criteria: the Continous ranked probability score (CRPS) and the Jolliffe-Primo test. Comparing the results obtained with both criteria leads to reconsidering the usual way to build skillful probabilistic forecasts, based on the minimization of the CRPS. Minimizing the CRPS does not necessarily produce reliable forecasts according to the Jolliffe-Primo test. The Jolliffe-Primo test generally selects reliable forecasts, but could lead to issuing suboptimal forecasts in terms of CRPS. It is proposed to use both criterion to achieve reliable and skillful probabilistic forecasts.

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.

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.

This paper proposes a stochastic variant of the stable matching model from Rasulkhani and Chow [1] which allows microtransit operators to evaluate their operation policy and resource allocations. The proposed model takes into account the stochastic nature of users' travel utility perception, resulting in a probabilistic stable operation cost allocation outcome to design ticket price and ridership forecasting. We applied the model for the operation policy evaluation of a microtransit service in Luxembourg and its border area. The methodology for the model parameters estimation and calibration is developed. The results provide useful insights for the operator and the government to improve the ridership of the service.

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 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.

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.

This paper revisits the problem of computing empirical cumulative distribution functions (ECDF) efficiently on large, multivariate datasets. Computing an ECDF at one evaluation point requires $mathcal{O}(N)$ operations on a dataset composed of $N$ data points. Therefore, a direct evaluation of ECDFs at $N$ evaluation points requires a quadratic $mathcal{O}(N^2)$ operations, which is prohibitive for large-scale problems. Two fast and exact methods are proposed and compared. The first one is based on fast summation in lexicographical order, with a $mathcal{O}(N{log}N)$ complexity and requires the evaluation points to lie on a regular grid. The second one is based on the divide-and-conquer principle, with a $mathcal{O}(Nlog(N)^{(d-1){vee}1})$ complexity and requires the evaluation points to coincide with the input points. The two fast algorithms are described and detailed in the general $d$-dimensional case, and numerical experiments validate their speed and accuracy. Secondly, the paper establishes a direct connection between cumulative distribution functions and kernel density estimation (KDE) for a large class of kernels. This connection paves the way for fast exact algorithms for multivariate kernel density estimation and kernel regression. Numerical tests with the Laplacian kernel validate the speed and accuracy of the proposed algorithms. A broad range of large-scale multivariate density estimation, cumulative distribution estimation, survival function estimation and regression problems can benefit from the proposed numerical methods.

An accurate and prompt diagnosis of pediatric pneumonia is imperative for successful treatment intervention. One approach to diagnose pneumonia cases is using radiographic data. In this article, we propose a novel parsimonious scalar-on-image classification model adopting the ideas of functional data analysis. Our main idea is to treat images as functional measurements and exploit underlying covariance structures to select basis functions; these bases are then used in approximating both image profiles and corresponding regression coefficient. We re-express the regression model into a standard generalized linear model where the functional principal component scores are treated as covariates. We apply the method to (1) classify pneumonia against healthy and viral against bacterial pneumonia patients, and (2) test the null effect about the association between images and responses. Extensive simulation studies show excellent numerical performance in terms of classification, hypothesis testing, and efficient computation.

Class imbalance is an inherent characteristic of multi-label data that hinders most multi-label learning methods. One efficient and flexible strategy to deal with this problem is to employ sampling techniques before training a multi-label learning model. Although existing multi-label sampling approaches alleviate the global imbalance of multi-label datasets, it is actually the imbalance level within the local neighbourhood of minority class examples that plays a key role in performance degradation. To address this issue, we propose a novel measure to assess the local label imbalance of multi-label datasets, as well as two multi-label sampling approaches based on the local label imbalance, namely MLSOL and MLUL. By considering all informative labels, MLSOL creates more diverse and better labeled synthetic instances for difficult examples, while MLUL eliminates instances that are harmful to their local region. Experimental results on 13 multi-label datasets demonstrate the effectiveness of the proposed measure and sampling approaches for a variety of evaluation metrics, particularly in the case of an ensemble of classifiers trained on repeated samples of the original data.

Ridge regression (RR) is a regularization technique that penalizes the L2-norm of the coefficients in linear regression. One of the challenges of using RR is the need to set a hyperparameter ($alpha$) that controls the amount of regularization. Cross-validation is typically used to select the best $alpha$ from a set of candidates. However, efficient and appropriate selection of $alpha$ can be challenging, particularly where large amounts of data are analyzed. Because the selected $alpha$ depends on the scale of the data and predictors, it is not straightforwardly interpretable. Here, we propose to reparameterize RR in terms of the ratio $gamma$ between the L2-norms of the regularized and unregularized coefficients. This approach, called fractional RR (FRR), has several benefits: the solutions obtained for different $gamma$ are guaranteed to vary, guarding against wasted calculations, and automatically span the relevant range of regularization, avoiding the need for arduous manual exploration. We provide an algorithm to solve FRR, as well as open-source software implementations in Python and MATLAB (https://github.com/nrdg/fracridge). We show that the proposed method is fast and scalable for large-scale data problems, and delivers results that are straightforward to interpret and compare across models and datasets.

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.

Current explanation techniques towards a transparent Convolutional Neural Network (CNN) mainly focuses on building connections between the human-understandable input features with models' prediction, overlooking an alternative representation of the input, the frequency components decomposition. In this work, we present an analysis of the connection between the distribution of frequency components in the input dataset and the reasoning process the model learns from the data. We further provide quantification analysis about the contribution of different frequency components toward the model's prediction. We show that the vulnerability of the model against tiny distortions is a result of the model is relying on the high-frequency features, the target features of the adversarial (black and white-box) attackers, to make the prediction. We further show that if the model develops stronger association between the low-frequency component with true labels, the model is more robust, which is the explanation of why adversarially trained models are more robust against tiny distortions.

The next seminar in the 2017–18 History of Pre-Modern Medicine seminar series takes place on Tuesday 7 November. Speaker: Dr Michael Brown (University of Roehampton), ‘Anxiety and compassion: emotions and the surgical encounter in early 19th-century Britain’ The historical study of the… Continue reading

The next seminar in the 2017–18 History of Pre-Modern Medicine seminar series takes place on Tuesday 21 November. Speaker: Professor Roberta Gilchrist (University of Reading), ‘The archaeology of monastic healing: spirit, mind and body’ This paper highlights the potential of archaeology to… Continue reading

The next seminar in the 2017–18 History of Pre-Modern Medicine seminar series takes place on Tuesday 16 January. Speaker: Dr Catherine Rider (University of Exeter) Medieval Ideas about Infertility and Old Age Abstract: When they discussed fertility and reproductive disorders it was common… Continue reading

Broadcasting Health and Disease: Bodies, markets and television, 1950s–1980s An ERC BodyCapital international conference to be held at the Wellcome Trust, 19–21 February 2018 In the television age, health and the body have been broadcasted in many ways: in short… Continue reading