The framework of differential privacy protects an individual's privacy while publishing query responses on congregated data. In this work, a new noise addition mechanism for differential privacy is introduced where the noise added is sampled from a hybrid density that resembles Laplace in the centre and Gaussian in the tail. With a sharper centre and light, sub-Gaussian tail, this density has the best characteristics of both distributions. We theoretically analyze the proposed mechanism, and we derive the necessary and sufficient condition in one dimension and a sufficient condition in high dimensions for the mechanism to guarantee (${\epsilon}$,${\delta}$)-differential privacy. Numerical simulations corroborate the efficacy of the proposed mechanism compared to other existing mechanisms in achieving a better trade-off between privacy and accuracy.
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This study addresses a class of linear mixed-integer programming (MILP) problems that involve uncertainty in the objective function parameters. The parameters are assumed to form a random vector, whose probability distribution can only be observed through a finite training data set. Unlike most of the related studies in the literature, we also consider uncertainty in the underlying data set. The data uncertainty is described by a set of linear constraints for each random sample, and the uncertainty in the distribution (for a fixed realization of data) is defined using a type-1 Wasserstein ball centered at the empirical distribution of the data. The overall problem is formulated as a three-level distributionally robust optimization (DRO) problem. First, we prove that the three-level problem admits a single-level MILP reformulation, if the class of loss functions is restricted to biaffine functions. Secondly, it turns out that for several particular forms of data uncertainty, the outlined problem can be solved reasonably fast by leveraging the nominal MILP problem. Finally, we conduct a computational study, where the out-of-sample performance of our model and computational complexity of the proposed MILP reformulation are explored numerically for several application domains.
In this work we introduce S-TREK, a novel local feature extractor that combines a deep keypoint detector, which is both translation and rotation equivariant by design, with a lightweight deep descriptor extractor. We train the S-TREK keypoint detector within a framework inspired by reinforcement learning, where we leverage a sequential procedure to maximize a reward directly related to keypoint repeatability. Our descriptor network is trained following a "detect, then describe" approach, where the descriptor loss is evaluated only at those locations where keypoints have been selected by the already trained detector. Extensive experiments on multiple benchmarks confirm the effectiveness of our proposed method, with S-TREK often outperforming other state-of-the-art methods in terms of repeatability and quality of the recovered poses, especially when dealing with in-plane rotations.
We study a class of Gaussian processes for which the posterior mean, for a particular choice of data, replicates a truncated Taylor expansion of any order. The data consist of derivative evaluations at the expansion point and the prior covariance kernel belongs to the class of Taylor kernels, which can be written in a certain power series form. We discuss and prove some results on maximum likelihood estimation of parameters of Taylor kernels. The proposed framework is a special case of Gaussian process regression based on data that is orthogonal in the reproducing kernel Hilbert space of the covariance kernel.
Modeling seeks to tame complexity during software development, by supporting design, analysis, and stakeholder communication. Paradoxically, experiences made by educators indicate that students often perceive modeling as adding complexity, instead of reducing it. In this position paper, I analyse modeling education from the lens of complexity science, a theoretical framework for the study of complex systems. I revisit pedagogical literature where complexity science has been used as a framework for general education and subject-specific education in disciplines such as medicine, project management, and sustainability. I revisit complexity-related challenges from modeling education literature, discuss them in the light of complexity and present recommendations for taming complexity when teaching modeling.
Modeling attacks, in which an adversary uses machine learning techniques to model a hardware-based Physically Unclonable Function (PUF) pose a great threat to the viability of these hardware security primitives. In most modeling attacks, a random subset of challenge-response-pairs (CRPs) are used as the labeled data for the machine learning algorithm. Here, for the arbiter-PUF, a delay based PUF which may be viewed as a linear threshold function with random weights (due to manufacturing imperfections), we investigate the role of active learning in Support Vector Machine (SVM) learning. We focus on challenge selection to help SVM algorithm learn ``fast'' and learn ``slow''. Our methods construct challenges rather than relying on a sample pool of challenges as in prior work. Using active learning to learn ``fast'' (less CRPs revealed, higher accuracies) may help manufacturers learn the manufactured PUFs more efficiently, or may form a more powerful attack when the attacker may query the PUF for CRPs at will. Using active learning to select challenges from which learning is ``slow'' (low accuracy despite a large number of revealed CRPs) may provide a basis for slowing down attackers who are limited to overhearing CRPs.
We review common situations in Bayesian latent variable models where the prior distribution that a researcher specifies differs from the prior distribution used during estimation. These situations can arise from the positive definite requirement on correlation matrices, from sign indeterminacy of factor loadings, and from order constraints on threshold parameters. The issue is especially problematic for reproducibility and for model checks that involve prior distributions, including prior predictive assessment and Bayes factors. In these cases, one might be assessing the wrong model, casting doubt on the relevance of the results. The most straightforward solution to the issue sometimes involves use of informative prior distributions. We explore other solutions and make recommendations for practice.
This paper describes the development of an automated knot selection method (selecting number and location of knots) for bivariate splines in a pure regression framework (SALSA2D). To demonstrate this approach we use carcass location data from Etosha National Park (ENP), Namibia to assess the spatial distribution of elephant deaths. Elephant mortality is an important component of understanding population dynamics, the overall increase or decline in populations and for disease monitoring. The presence only carcass location data were modelled using a downweighted Poisson regression (equivalent to a point-process model) and using developed method, SALSA2D, for knot selection. The result was a more realistic local/clustered intensity surface compared with an existing model averaging approach. Using the new algorithm, the carcass location data were modelled using additional environmental covariates (annual rainfall, distance to water and roads). The results showed high carcass intensity close to water holes ($<$3km) and roads ($<$2km) and in areas of the park with average rainfall ($\sim$450mm annually). Some high risk areas were identified particularly in the north east of the park and the risk of death does not always coincide with elephant distribution across the park. These findings are an important component in understanding population dynamics and drivers for population and park management. Particularly for controlling elephant numbers and/or mitigation of anthrax or other disease outbreaks.
White matter bundle segmentation is a cornerstone of modern tractography to study the brain's structural connectivity in domains such as neurological disorders, neurosurgery, and aging. In this study, we present FIESTA (FIbEr Segmentation in Tractography using Autoencoders), a reliable and robust, fully automated, and easily semi-automatically calibrated pipeline based on deep autoencoders that can dissect and fully populate white matter bundles. This pipeline is built upon previous works that demonstrated how autoencoders can be used successfully for streamline filtering, bundle segmentation, and streamline generation in tractography. Our proposed method improves bundle segmentation coverage by recovering hard-to-track bundles with generative sampling through the latent space seeding of the subject bundle and the atlas bundle. A latent space of streamlines is learned using autoencoder-based modeling combined with contrastive learning. Using an atlas of bundles in standard space (MNI), our proposed method segments new tractograms using the autoencoder latent distance between each tractogram streamline and its closest neighbor bundle in the atlas of bundles. Intra-subject bundle reliability is improved by recovering hard-to-track streamlines, using the autoencoder to generate new streamlines that increase the spatial coverage of each bundle while remaining anatomically correct. Results show that our method is more reliable than state-of-the-art automated virtual dissection methods such as RecoBundles, RecoBundlesX, TractSeg, White Matter Analysis and XTRACT. Our framework allows for the transition from one anatomical bundle definition to another with marginal calibration efforts. Overall, these results show that our framework improves the practicality and usability of current state-of-the-art bundle segmentation framework.
We propose a computationally and statistically efficient procedure for segmenting univariate data under piecewise linearity. The proposed moving sum (MOSUM) methodology detects multiple change points where the underlying signal undergoes discontinuous jumps and/or slope changes. Theoretically, it controls the family-wise error rate at a given significance level asymptotically and achieves consistency in multiple change point detection, as well as matching the minimax optimal rate of estimation when the signal is piecewise linear and continuous, all under weak assumptions permitting serial dependence and heavy-tailedness. Computationally, the complexity of the MOSUM procedure is $O(n)$ which, combined with its good performance on simulated datasets, making it highly attractive in comparison with the existing methods. We further demonstrate its good performance on a real data example on rolling element-bearing prognostics.
We bring in here a novel algebraic approach for attacking the McEliece cryptosystem. It consists in introducing a subspace of matrices representing quadratic forms. Those are associated with quadratic relationships for the component-wise product in the dual of the code used in the cryptosystem. Depending on the characteristic of the code field, this space of matrices consists only of symmetric matrices or skew-symmetric matrices. This matrix space is shown to contain unusually low-rank matrices (rank $2$ or $3$ depending on the characteristic) which reveal the secret polynomial structure of the code. Finding such matrices can then be used to recover the secret key of the scheme. We devise a dedicated approach in characteristic $2$ consisting in using a Gr\"obner basis modeling that a skew-symmetric matrix is of rank $2$. This allows to analyze the complexity of solving the corresponding algebraic system with Gr\"obner bases techniques. This computation behaves differently when applied to the skew-symmetric matrix space associated with a random code rather than with a Goppa or an alternant code. This gives a distinguisher of the latter code family. We give a bound on its complexity which turns out to interpolate nicely between polynomial and exponential depending on the code parameters. A distinguisher for alternant/Goppa codes was already known [FGO+11]. It is of polynomial complexity but works only in a narrow parameter regime. This new distinguisher is also polynomial for the parameter regime necessary for [FGO+11] but contrarily to the previous one is able to operate for virtually all code parameters relevant to cryptography. Moreover, we use this matrix space to find a polynomial time attack of the McEliece cryptosystem provided that the Goppa code is distinguishable by the method of [FGO+11] and its degree is less than $q-1$, where $q$ is the alphabet size of the code.
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