Bounded Perturbation Resilience of Two Modified Relaxed CQ Algorithms for the Multiple-Sets Split Feasibility Problem

In this paper, we present some modified relaxed CQ algorithms with different kinds of step size and perturbation to solve the Multiple-sets Split Feasibility Problem (MSSFP). Under mild assumptions, we establish weak convergence and prove the bounded perturbation resilience of the proposed algorithms in Hilbert spaces. Treating appropriate inertial terms as bounded perturbations, we construct the inertial acceleration versions of the corresponding algorithms. Finally, for the LASSO problem and three experimental examples, numerical computations are given to demonstrate the efficiency of the proposed algorithms and the validity of the inertial perturbation.

On Guaranteed Optimal Robust Explanations for NLP Models

We build on abduction-based explanations for machine learning and develop a method for computing local explanations for neural network models in natural language processing (NLP). Our explanations comprise a subset of the words of the input text that satisfies two key features: optimality w.r.t. a user-defined cost function, such as the length of explanation, and robustness, in that they ensure prediction invariance for any bounded perturbation in the embedding space of the left-out words. We present two solution algorithms, respectively based on implicit hitting sets and maximum universal subsets, introducing a number of algorithmic improvements to speed up convergence of hard instances. We show how our method can be configured with different perturbation sets in the embedded space and used to detect bias in predictions by enforcing include/exclude constraints on biased terms, as well as to enhance existing heuristic-based NLP explanation frameworks such as Anchors. We evaluate our framework on three widely used sentiment analysis tasks and texts of up to 100 words from SST, Twitter and IMDB datasets, demonstrating the effectiveness of the derived explanations.

A Privacy-Preserving Mobile LBS System for Small Businesses

Small-to-medium businesses are always seeking affordable ways to advertise their products and services securely. With the emergence of mobile technology, it is possible than ever to implement innovative Location-based Advertising (LBS) systems using smartphones that preserve the privacy of mobile users. In this paper, we present a prototype implementation of such systems by developing a distributed privacy-preserving system, which has parts executing on smartphones as a mobile app, as well as a web-based application hosted on the cloud. The mobile app leverages Google Maps libraries to enhance the user experience in using the app. Mobile users can use the app to commute to their daily destinations while viewing relevant ads such as job openings in their neighborhood, discounts on favorite meals, etc. We developed a client-server privacy architecture that anonymizes the mobile user trajectories using a bounded perturbation strategy. A multi-modal sensing approach is proposed for modeling the context switching of the developed LBS system, which we represent as a Finite State Machine (FSM) model. The multi-modal sensing approach can reduce the power consumed by mobile devices by automatically detecting sensing mode changes to avoid unnecessary sensing. The developed LBS system is organized into two parts: the business side and the user side. First, the business side allows business owners to create new ads by providing the ad details, Geo-location, photos, and any other instructions. Second, the user side allows mobile users to navigate through the map to see ads while walking, driving, bicycling, or quietly sitting in their offices. Experimental results are presented to demonstrate the scalability and performance of the mobile side. Our experimental evaluation demonstrates that the mobile app incurs low processing overhead and consequently has a small energy footprint.

Uniform Exponential Stability of Perturbed Semigroups: The Dyson–Phillips Formula Versus Gil’s Approach Via Commutators

We discuss the uniform exponential stability of strongly continuous semigroups generated by operators of the form $$ A+B $$ A + B , where B is a bounded perturbation of a generator A. We compare two approaches to the problem: via the Dyson–Phillips formula and via the size of the norm of the commutator of A and B- the method recently developed by M. Gil’. We show that quite often the first approach is more powerful than the second one and, more importantly, easier to use.

Positive observers for linear positive systems in a Hilbert lattice space

In this work, we investigate the question of designing a positive observer for a class of infinite dimensional linear positive systems. We present a new observer design based on a classical Luenberger-like observer. The proposed observer is positive. That is, it ensures that the state estimates are nonnegative at any time. The existence of such positive observers is proven by a specific choice of the observer gain and using positive bounded perturbation results. We show in particular that the error of the state estimation converges exponentially to zero. Finally, the main result is applied to an isothermal tubular (bio) reactor model, namely the plug-flow (bio) reactor model. The approach is illustrated by some numerical simulations.

Averaging Attacks on Bounded Noise-based Disclosure Control Algorithms

We describe and evaluate an attack that reconstructs the histogram of any target attribute of a sensitive dataset which can only be queried through a specific class of real-world privacy-preserving algorithms which we call bounded perturbation algorithms. A defining property of such an algorithm is that it perturbs answers to the queries by adding zero-mean noise distributed within a bounded (possibly undisclosed) range. Other key properties of the algorithm include only allowing restricted queries (enforced via an online interface), suppressing answers to queries which are only satisfied by a small group of individuals (e.g., by returning a zero as an answer), and adding the same perturbation to two queries which are satisfied by the same set of individuals (to thwart differencing or averaging attacks). A real-world example of such an algorithm is the one deployed by the Australian Bureau of Statistics’ (ABS) online tool called TableBuilder, which allows users to create tables, graphs and maps of Australian census data [30]. We assume an attacker (say, a curious analyst) who is given oracle access to the algorithm via an interface. We describe two attacks on the algorithm. Both attacks are based on carefully constructing (different) queries that evaluate to the same answer. The first attack finds the hidden perturbation parameter r (if it is assumed not to be public knowledge). The second attack removes the noise to obtain the original answer of some (counting) query of choice. We also show how to use this attack to find the number of individuals in the dataset with a target attribute value a of any attribute A, and then for all attribute values ai ∈ A. None of the attacks presented here depend on any background information. Our attacks are a practical illustration of the (informal) fundamental law of information recovery which states that “overly accurate estimates of too many statistics completely destroys privacy” [9, 15].

Bounded Perturbation Resilience and Superiorization of Proximal Scaled Gradient Algorithm with Multi-Parameters

In this paper, a multi-parameter proximal scaled gradient algorithm with outer perturbations is presented in real Hilbert space. The strong convergence of the generated sequence is proved. The bounded perturbation resilience and the superiorized version of the original algorithm are also discussed. The validity and the comparison with the use or not of superiorization of the proposed algorithms were illustrated by solving the l 1 − l 2 problem.