One of the common tasks in unsupervised learning is dimensionality reduction, where the goal is to find meaningful low-dimensional structures hidden in high-dimensional data. Sometimes referred to as manifold learning, this problem is closely related to the problem of localization, which aims at embedding a weighted graph into a low-dimensional Euclidean space. Several methods have been proposed for localization, and also manifold learning. Nonetheless, the robustness property of most of them is little understood. In this paper, we obtain perturbation bounds for classical scaling and trilateration, which are then applied to derive performance bounds for Isomap, Landmark Isomap, and Maximum Variance Unfolding. A new perturbation bound for procrustes analysis plays a key role.

We present new practical local differentially private heavy hitters algorithms achieving optimal or near-optimal worst-case error and running time -- TreeHist and Bitstogram. In both algorithms, server running time is $ ilde O(n)$ and user running time is $ ilde O(1)$, hence improving on the prior state-of-the-art result of Bassily and Smith [STOC 2015] requiring $O(n^{5/2})$ server time and $O(n^{3/2})$ user time. With a typically large number of participants in local algorithms (in the millions), this reduction in time complexity, in particular at the user side, is crucial for making locally private heavy hitters algorithms usable in practice. We implemented Algorithm TreeHist to verify our theoretical analysis and compared its performance with the performance of Google's RAPPOR code.

We study the identity testing problem in the context of spin systems or undirected graphical models, where it takes the following form: given the parameter specification of the model $M$ and a sampling oracle for the distribution $mu_{M^*}$ of an unknown model $M^*$, can we efficiently determine if the two models $M$ and $M^*$ are the same? We consider identity testing for both soft-constraint and hard-constraint systems. In particular, we prove hardness results in two prototypical cases, the Ising model and proper colorings, and explore whether identity testing is any easier than structure learning. For the ferromagnetic (attractive) Ising model, Daskalakis et al. (2018) presented a polynomial-time algorithm for identity testing. We prove hardness results in the antiferromagnetic (repulsive) setting in the same regime of parameters where structure learning is known to require a super-polynomial number of samples. Specifically, for $n$-vertex graphs of maximum degree $d$, we prove that if $|eta| d = omega(log{n})$ (where $eta$ is the inverse temperature parameter), then there is no polynomial running time identity testing algorithm unless $RP=NP$. In the hard-constraint setting, we present hardness results for identity testing for proper colorings. Our results are based on the presumed hardness of #BIS, the problem of (approximately) counting independent sets in bipartite graphs.

Sufficient dimension reduction (SDR) is a very useful concept for exploratory analysis and data visualization in regression, especially when the number of covariates is large. Many SDR methods have been proposed for regression with a continuous response, where the central subspace (CS) is the target of estimation. Various conditions, such as the linearity condition and the constant covariance condition, are imposed so that these methods can estimate at least a portion of the CS. In this paper we study SDR for regression and discriminant analysis with categorical response. Motivated by the exploratory analysis and data visualization aspects of SDR, we propose a new geometric framework to reformulate the SDR problem in terms of manifold optimization and introduce a new concept called Maximum Separation Subspace (MASES). The MASES naturally preserves the “sufficiency” in SDR without imposing additional conditions on the predictor distribution, and directly inspires a semi-parametric estimator. Numerical studies show MASES exhibits superior performance as compared with competing SDR methods in specific settings.

Parametrised state space models in the form of recurrent networks are often used in machine learning to learn from data streams exhibiting temporal dependencies. To break the black box nature of such models it is important to understand the dynamical features of the input-driving time series that are formed in the state space. We propose a framework for rigorous analysis of such state representations in vanishing memory state space models such as echo state networks (ESN). In particular, we consider the state space a temporal feature space and the readout mapping from the state space a kernel machine operating in that feature space. We show that: (1) The usual ESN strategy of randomly generating input-to-state, as well as state coupling leads to shallow memory time series representations, corresponding to cross-correlation operator with fast exponentially decaying coefficients; (2) Imposing symmetry on dynamic coupling yields a constrained dynamic kernel matching the input time series with straightforward exponentially decaying motifs or exponentially decaying motifs of the highest frequency; (3) Simple ring (cycle) high-dimensional reservoir topology specified only through two free parameters can implement deep memory dynamic kernels with a rich variety of matching motifs. We quantify richness of feature representations imposed by dynamic kernels and demonstrate that for dynamic kernel associated with cycle reservoir topology, the kernel richness undergoes a phase transition close to the edge of stability.

Motivated by modern applications in which one constructs graphical models based on a very large number of features, this paper introduces a new class of cluster-based graphical models, in which variable clustering is applied as an initial step for reducing the dimension of the feature space. We employ model assisted clustering, in which the clusters contain features that are similar to the same unobserved latent variable. Two different cluster-based Gaussian graphical models are considered: the latent variable graph, corresponding to the graphical model associated with the unobserved latent variables, and the cluster-average graph, corresponding to the vector of features averaged over clusters. Our study reveals that likelihood based inference for the latent graph, not analyzed previously, is analytically intractable. Our main contribution is the development and analysis of alternative estimation and inference strategies, for the precision matrix of an unobservable latent vector Z. We replace the likelihood of the data by an appropriate class of empirical risk functions, that can be specialized to the latent graphical model and to the simpler, but under-analyzed, cluster-average graphical model. The estimators thus derived can be used for inference on the graph structure, for instance on edge strength or pattern recovery. Inference is based on the asymptotic limits of the entry-wise estimates of the precision matrices associated with the conditional independence graphs under consideration. While taking the uncertainty induced by the clustering step into account, we establish Berry-Esseen central limit theorems for the proposed estimators. It is noteworthy that, although the clusters are estimated adaptively from the data, the central limit theorems regarding the entries of the estimated graphs are proved under the same conditions one would use if the clusters were known in advance. As an illustration of the usage of these newly developed inferential tools, we show that they can be reliably used for recovery of the sparsity pattern of the graphs we study, under FDR control, which is verified via simulation studies and an fMRI data analysis. These experimental results confirm the theoretically established difference between the two graph structures. Furthermore, the data analysis suggests that the latent variable graph, corresponding to the unobserved cluster centers, can help provide more insight into the understanding of the brain connectivity networks relative to the simpler, average-based, graph.

We consider the standard model of distributed optimization of a sum of functions $F(mathbf z) = sum_{i=1}^n f_i(mathbf z)$, where node $i$ in a network holds the function $f_i(mathbf z)$. We allow for a harsh network model characterized by asynchronous updates, message delays, unpredictable message losses, and directed communication among nodes. In this setting, we analyze a modification of the Gradient-Push method for distributed optimization, assuming that (i) node $i$ is capable of generating gradients of its function $f_i(mathbf z)$ corrupted by zero-mean bounded-support additive noise at each step, (ii) $F(mathbf z)$ is strongly convex, and (iii) each $f_i(mathbf z)$ has Lipschitz gradients. We show that our proposed method asymptotically performs as well as the best bounds on centralized gradient descent that takes steps in the direction of the sum of the noisy gradients of all the functions $f_1(mathbf z), ldots, f_n(mathbf z)$ at each step.

A new strategy for probabilistic graphical modeling is developed that draws parallels to community detection analysis. The method jointly estimates an undirected graph and homogeneous communities of nodes. The structure of the communities is taken into account when estimating the graph and at the same time, the structure of the graph is accounted for when estimating communities of nodes. The procedure uses a joint group graphical lasso approach with community detection-based grouping, such that some groups of edges co-occur in the estimated graph. The grouping structure is unknown and is estimated based on community detection algorithms. Theoretical derivations regarding graph convergence and sparsistency, as well as accuracy of community recovery are included, while the method's empirical performance is illustrated in an fMRI context, as well as with simulated examples.

Graphical models are commonly used to represent conditional dependence relationships between variables. There are multiple methods available for exploring them from high-dimensional data, but almost all of them rely on the assumption that the observations are independent and identically distributed. At the same time, observations connected by a network are becoming increasingly common, and tend to violate these assumptions. Here we develop a Gaussian graphical model for observations connected by a network with potentially different mean vectors, varying smoothly over the network. We propose an efficient estimation algorithm and demonstrate its effectiveness on both simulated and real data, obtaining meaningful and interpretable results on a statistics coauthorship network. We also prove that our method estimates both the inverse covariance matrix and the corresponding graph structure correctly under the assumption of network “cohesion”, which refers to the empirically observed phenomenon of network neighbors sharing similar traits.

Mohsen Maleki, Arezo Hajrajabi, Reinaldo B. Arellano-Valle.

Source: Brazilian Journal of Probability and Statistics, Volume 34, Number 2, 273--290.

Abstract:
In this paper, we study the finite mixtures of autoregressive processes assuming that the distribution of innovations (errors) belongs to the class of scale mixture of skew-normal (SMSN) distributions. The SMSN distributions allow a simultaneous modeling of the existence of outliers, heavy tails and asymmetries in the distribution of innovations. Therefore, a statistical methodology based on the SMSN family allows us to use a robust modeling on some non-linear time series with great flexibility, to accommodate skewness, heavy tails and heterogeneity simultaneously. The existence of convenient hierarchical representations of the SMSN distributions facilitates also the implementation of an ECME-type of algorithm to perform the likelihood inference in the considered model. Simulation studies and the application to a real data set are finally presented to illustrate the usefulness of the proposed model.

Glaura C. Franco, Helio S. Migon, Marcos O. Prates.

Source: Brazilian Journal of Probability and Statistics, Volume 33, Number 4, 756--781.

Abstract:
Observation and parameter driven models are commonly used in the literature to analyse time series of counts. In this paper, we study the characteristics of a variety of models and point out the main differences and similarities among these procedures, concerning parameter estimation, model fitting and forecasting. Alternatively to the literature, all inference was performed under the Bayesian paradigm. The models are fitted with a latent AR($p$) process in the mean, which accounts for autocorrelation in the data. An extensive simulation study shows that the estimates for the covariate parameters are remarkably similar across the different models. However, estimates for autoregressive coefficients and forecasts of future values depend heavily on the underlying process which generates the data. A real data set of bankruptcy in the United States is also analysed.

Rodrigo Citton P. dos Reis, Enrico A. Colosimo, Gustavo L. Gilardoni.

Source: Brazilian Journal of Probability and Statistics, Volume 33, Number 2, 374--396.

Abstract:
In the data analysis from multiple repairable systems, it is usual to observe both different truncation times and heterogeneity among the systems. Among other reasons, the latter is caused by different manufacturing lines and maintenance teams of the systems. In this paper, a hierarchical model is proposed for the statistical analysis of multiple repairable systems under different truncation times. A reparameterization of the power law process is proposed in order to obtain a quasi-conjugate bayesian analysis. An empirical Bayes approach is used to estimate model hyperparameters. The uncertainty in the estimate of these quantities are corrected by using a parametric bootstrap approach. The results are illustrated in a real data set of failure times of power transformers from an electric company in Brazil.

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.

Kevin McGoff, Sayan Mukherjee, Natesh Pillai.

Source: Statistics Surveys, Volume 9, 209--252.

Abstract:
The topic of statistical inference for dynamical systems has been studied widely across several fields. In this survey we focus on methods related to parameter estimation for nonlinear dynamical systems. Our objective is to place results across distinct disciplines in a common setting and highlight opportunities for further research.

Oleksandr Sverdlov, Weng Kee Wong, Yevgen Ryeznik.

Source: Statistics Surveys, Volume 8, 2--44.

Abstract:
Adaptive clinical trials are becoming increasingly popular research designs for clinical investigation. Adaptive designs are particularly useful in phase I cancer studies where clinical data are scant and the goals are to assess the drug dose-toxicity profile and to determine the maximum tolerated dose while minimizing the number of study patients treated at suboptimal dose levels. In the current work we give an overview of adaptive design methods for phase I cancer trials. We find that modern statistical literature is replete with novel adaptive designs that have clearly defined objectives and established statistical properties, and are shown to outperform conventional dose finding methods such as the 3+3 design, both in terms of statistical efficiency and in terms of minimizing the number of patients treated at highly toxic or nonefficacious doses. We discuss statistical, logistical, and regulatory aspects of these designs and present some links to non-commercial statistical software for implementing these methods in practice.

Jeffrey Picka

Source: Statist. Surv., Volume 6, 74--112.

Abstract:
This paper gives an overview of statistical inference for disordered sphere packing processes. These processes are used extensively in physics and engineering in order to represent the internal structure of composite materials, packed bed reactors, and powders at rest, and are used as initial arrangements of grains in the study of avalanches and other problems involving powders in motion. Packing processes are spatial processes which are neither stationary nor ergodic. Classical spatial statistical models and procedures cannot be applied to these processes, but alternative models and procedures can be developed based on ideas from statistical physics. Most of the development of models and statistics for sphere packings has been undertaken by scientists and engineers. This review summarizes their results from an inferential perspective.

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.

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.

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.

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.

Factor analysis is a flexible technique for assessment of multivariate dependence and codependence. Besides being an exploratory tool used to reduce the dimensionality of multivariate data, it allows estimation of common factors that often have an interesting theoretical interpretation in real problems. However, standard factor analysis is only applicable when the variables are scaled, which is often inappropriate, for example, in data obtained from questionnaires in the field of psychology,where the variables are often categorical. In this framework, we propose a factor model for the analysis of multivariate ordered and non-ordered polychotomous data. The inference procedure is done under the Bayesian approach via Markov chain Monte Carlo methods. Two Monte-Carlo simulation studies are presented to investigate the performance of this approach in terms of estimation bias, precision and assessment of the number of factors. We also illustrate the proposed method to analyze participants' responses to the Motivational State Questionnaire dataset, developed to study emotions in laboratory and field settings.

Harnessing data to discover the underlying governing laws or equations that describe the behavior of complex physical systems can significantly advance our modeling, simulation and understanding of such systems in various science and engineering disciplines. Recent advances in sparse identification show encouraging success in distilling closed-form governing equations from data for a wide range of nonlinear dynamical systems. However, the fundamental bottleneck of this approach lies in the robustness and scalability with respect to data scarcity and noise. This work introduces a novel physics-informed deep learning framework to discover governing partial differential equations (PDEs) from scarce and noisy data for nonlinear spatiotemporal systems. In particular, this approach seamlessly integrates the strengths of deep neural networks for rich representation learning, automatic differentiation and sparse regression to approximate the solution of system variables, compute essential derivatives, as well as identify the key derivative terms and parameters that form the structure and explicit expression of the PDEs. The efficacy and robustness of this method are demonstrated on discovering a variety of PDE systems with different levels of data scarcity and noise. The resulting computational framework shows the potential for closed-form model discovery in practical applications where large and accurate datasets are intractable to capture.

Hierarchical abstraction and curiosity-driven exploration are two common paradigms in current reinforcement learning approaches to break down difficult problems into a sequence of simpler ones and to overcome reward sparsity. However, there is a lack of approaches that combine these paradigms, and it is currently unknown whether curiosity also helps to perform the hierarchical abstraction. As a novelty and scientific contribution, we tackle this issue and develop a method that combines hierarchical reinforcement learning with curiosity. Herein, we extend a contemporary hierarchical actor-critic approach with a forward model to develop a hierarchical notion of curiosity. We demonstrate in several continuous-space environments that curiosity approximately doubles the learning performance and success rates for most of the investigated benchmarking problems.

The notion of incremental learning is to train an ANN algorithm in stages, as and when newer training data arrives. Incremental learning is becoming widespread in recent times with the advent of deep learning. Noise in the training data reduces the accuracy of the algorithm. In this paper, we make an empirical study of the effect of noise in the training phase. We numerically show that the accuracy of the algorithm is dependent more on the location of the error than the percentage of error. Using Perceptron, Feed Forward Neural Network and Radial Basis Function Neural Network, we show that for the same percentage of error, the accuracy of the algorithm significantly varies with the location of error. Furthermore, our results show that the dependence of the accuracy with the location of error is independent of the algorithm. However, the slope of the degradation curve decreases with more sophisticated algorithms

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.

Hyperbolic balance laws with uncertain (random) parameters and inputs are ubiquitous in science and engineering. Quantification of uncertainty in predictions derived from such laws, and reduction of predictive uncertainty via data assimilation, remain an open challenge. That is due to nonlinearity of governing equations, whose solutions are highly non-Gaussian and often discontinuous. To ameliorate these issues in a computationally efficient way, we use the method of distributions, which here takes the form of a deterministic equation for spatiotemporal evolution of the cumulative distribution function (CDF) of the random system state, as a means of forward uncertainty propagation. Uncertainty reduction is achieved by recasting the standard loss function, i.e., discrepancy between observations and model predictions, in distributional terms. This step exploits the equivalence between minimization of the square error discrepancy and the Kullback-Leibler divergence. The loss function is regularized by adding a Lagrangian constraint enforcing fulfillment of the CDF equation. Minimization is performed sequentially, progressively updating the parameters of the CDF equation as more measurements are assimilated.

Hierarchical Agglomerative Clustering (HAC) algorithms are extensively utilized in modern data science and machine learning, and seek to partition the dataset into clusters while generating a hierarchical relationship between the data samples themselves. HAC algorithms are employed in a number of applications, such as biology, natural language processing, and recommender systems. Thus, it is imperative to ensure that these algorithms are fair-- even if the dataset contains biases against certain protected groups, the cluster outputs generated should not be discriminatory against samples from any of these groups. However, recent work in clustering fairness has mostly focused on center-based clustering algorithms, such as k-median and k-means clustering. Therefore, in this paper, we propose fair algorithms for performing HAC that enforce fairness constraints 1) irrespective of the distance linkage criteria used, 2) generalize to any natural measures of clustering fairness for HAC, 3) work for multiple protected groups, and 4) have competitive running times to vanilla HAC. To the best of our knowledge, this is the first work that studies fairness for HAC algorithms. We also propose an algorithm with lower asymptotic time complexity than HAC algorithms that can rectify existing HAC outputs and make them subsequently fair as a result. Moreover, we carry out extensive experiments on multiple real-world UCI datasets to demonstrate the working of our algorithms.

We present the R package mgm for the estimation of k-order mixed graphical models (MGMs) and mixed vector autoregressive (mVAR) models in high-dimensional data. These are a useful extensions of graphical models for only one variable type, since data sets consisting of mixed types of variables (continuous, count, categorical) are ubiquitous. In addition, we allow to relax the stationarity assumption of both models by introducing time-varying versions of MGMs and mVAR models based on a kernel weighting approach. Time-varying models offer a rich description of temporally evolving systems and allow to identify external influences on the model structure such as the impact of interventions. We provide the background of all implemented methods and provide fully reproducible examples that illustrate how to use the package.

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 13 February. Speaker: Dr William Tullett (Institute of Historical Research, University of London) Smell and medical efficacy in 18th-century England Abstract: In recent years a growing scholarship… Continue reading

The last seminar in the 2017–18 History of Pre-Modern Medicine seminar series takes place on Tuesday 27 February. Speaker: Dr Dror Weil (Max Planck Institute for the History of Science, Berlin) Bodies translated: the circulation of Arabo-Persian physiological theories in late… Continue reading