Encrypted statistical machine learning: new privacy preserving methods

We present two new statistical machine learning methods designed to learn on fully homomorphic encrypted (FHE) data. The introduction of FHE schemes following Gentry (2009) opens up the prospect of privacy preserving statistical machine learning analysis and modelling of encrypted data without compromising security constraints. We propose tailored algorithms for applying extremely random forests, involving a new cryptographic stochastic fraction estimator, and na\"{i}ve Bayes, involving a semi-parametric model for the class decision boundary, and show how they can be used to learn and predict from encrypted data. We demonstrate that these techniques perform competitively on a variety of classification data sets and provide detailed information about the computational practicalities of these and other FHE methods.Comment: 39 page

Complexity Hierarchies Beyond Elementary

We introduce a hierarchy of fast-growing complexity classes and show its suitability for completeness statements of many non elementary problems. This hierarchy allows the classification of many decision problems with a non-elementary complexity, which occur naturally in logic, combinatorics, formal languages, verification, etc., with complexities ranging from simple towers of exponentials to Ackermannian and beyond.Comment: Version 3 is the published version in TOCT 8(1:3), 2016. I will keep updating the catalogue of problems from Section 6 in future revision

Detection of Uniform and Non-Uniform Differential Item Functioning by Item Focussed Trees

Detection of differential item functioning by use of the logistic modelling approach has a long tradition. One big advantage of the approach is that it can be used to investigate non-uniform DIF as well as uniform DIF. The classical approach allows to detect DIF by distinguishing between multiple groups. We propose an alternative method that is a combination of recursive partitioning methods (or trees) and logistic regression methodology to detect uniform and non-uniform DIF in a nonparametric way. The output of the method are trees that visualize in a simple way the structure of DIF in an item showing which variables are interacting in which way when generating DIF. In addition we consider a logistic regression method in which DIF can by induced by a vector of covariates, which may include categorical but also continuous covariates. The methods are investigated in simulation studies and illustrated by two applications.Comment: 32 pages, 13 figures, 7 table

Ackermannian and Primitive-Recursive Bounds with Dickson's Lemma

Dickson's Lemma is a simple yet powerful tool widely used in termination proofs, especially when dealing with counters or related data structures. However, most computer scientists do not know how to derive complexity upper bounds from such termination proofs, and the existing literature is not very helpful in these matters. We propose a new analysis of the length of bad sequences over (N^k,\leq) and explain how one may derive complexity upper bounds from termination proofs. Our upper bounds improve earlier results and are essentially tight

Tree species selection for land rehabilitation in Ethiopia: from fragmented knowledge to an integrated multi-criteria decision approach

Dryland regions worldwide are increasingly suffering from losses of soil and biodiversity as a consequence of land degradation. Integrated conservation, rehabilitation and community-based management of natural resources are therefore of vital importance. Local planting efforts should focus on species performing a wide range of functions. Too often however, unsuitable tree species are planted when both ecological suitability for the targeted area or preferences of local stakeholders are not properly taken into account during selection. To develop a decision support tool for multi-purpose species selection, first information needs to be pooled on species-specific ranges, characteristics and functions for a set of potentially valuable species. In this study such database has been developed for the highly degraded northern Ethiopian highlands, using a unique combination of information sources, and with particular attention for local ecological knowledge and preferences. A set of candidate tree species and potentially relevant criteria, a flexible input database with species performance scores upon these criteria, and a ready-to-use multi-criteria decision support tool are presented. Two examples of species selection under different scenarios have been worked out in detail, with highest scores obtained for Cordia africana and Dodonaea angustifolia, as well as Eucalyptus spp., Acacia abyssinica, Acacia saligna, Olea europaea and Faidherbia albida. Sensitivity to criteria weights, and reliability and lack of knowledge on particular species attributes remain constraints towards applicability, particularly when many species are jointly evaluated. Nonetheless, the amount and diversity of the knowledge pooled in the presented database is high, covering 91 species and 45 attributes