Differentially private MIMO filtering for event streams

Rigorous privacy-preserving mechanisms that can process and analyze dynamic data streams in real-time are required to encourage a wider adoption of many large-scale monitoring and control systems recording the detailed activities of their users, such as intelligent transportation systems, smart grids or smart buildings. Motivated by scenarios where signals originate from many sensors capturing privacy-sensitive events about individuals and several statistics of interest need to be continuously published in real-time, we consider the problem of designing multi-input multi-output (MIMO) systems processing event streams while providing certain differential privacy guarantees on the input signals. We show how to construct and optimize MIMO extensions of the zero-forcing mechanism, which we previously proposed for single-input single-output systems. Some of these extensions can take a statistical model of the input signals into account. We illustrate our privacy-preserving filter design methodology in two examples: privately monitoring and forecasting occupancy in a building equipped with multiple motion detection sensors; and analyzing the activity of a Markov chain model of a simple shared processing server

A dynamic game model of collective choice in multi-agent systems

Inspired by successful biological collective decision mechanisms such as honey bees searching for a new colony or the collective navigation of fish schools, we consider a scenario where a large number of agents engaged in a dynamic game have to make a choice among a finite set of different potential target destinations. Each individual both influences and is influenced by the group's decision, as represented by the mean trajectory of all agents. Agents are assumed linear and coupled through a modified form of quadratic cost, whereby the terminal cost captures the discrete choice component of the problem. Following the mean field games methodology, we identify sufficient conditions under which allocations of destination choices over agents lead to self replication of the overall mean trajectory under the best response by the agents. Importantly, we establish that when the number of agents increases sufficiently, (i) the best response strategies to the self replicating mean trajectories qualify as epsilon-Nash equilibria of the population game; (ii) these epsilon-Nash strategies can be computed solely based on the knowledge of the joint probability distribution of the initial conditions, dynamics parameters and destination preferences, now viewed as random variables. Our results are illustrated through numerical simulations

A motion planning strategy for the active vision-based mapping of ground-level structures

This paper presents a strategy to guide a mobile ground robot equipped with a camera or depth sensor, in order to autonomously map the visible part of a bounded 3-D structure. We describe motion planning algorithms that determine appropriate successive viewpoints and attempt to fill holes automatically in a point cloud produced by the sensing and perception layer. The emphasis is on accurately reconstructing a 3-D model of a structure of moderate size rather than mapping large open environments, with applications for example in architecture, construction, and inspection. The proposed algorithms do not require any initialization in the form of a mesh model or a bounding box, and the paths generated are well adapted to situations where the vision sensor is used simultaneously for mapping and for localizing the robot, in the absence of additional absolute positioning system. We analyze the coverage properties of our policy, and compare its performance with the classic frontier-based exploration algorithm. We illustrate its efficacy for different structure sizes, levels of localization accuracy, and range of the depth sensor, and validate our design on a real-world experiment

Autoregressive neural networks with exogenous variables for indoor temperature prediction in buildings

Thermal models of buildings are helpful to forecast their energy use and to enhance the control of their mechanical systems. However, these models are building-specific and require a tedious, error-prone and time-consuming development effort relying on skilled building energy modelers. Compared to white-box and gray-box models, data-driven (black-box) models require less development time and a minimal amount of information about the building characteristics. In this paper, autoregressive neural network models are compared to gray-box and black-box linear models to simulate indoor temperatures. These models are trained, validated and compared to actual experimental data obtained for an existing commercial building in Montreal (QC, Canada) equipped with roof top units for air conditioning. Results show that neural networks mimic more accurately the thermal behavior of the building when limited information is available, compared to gray-box and black-box linear models. The gray-box model does not perform adequately due to its under-parameterized nature, while the linear models cannot capture non-linear phenomena such as radiative heat transfer and occupancy. Therefore, the neural network models outperform the alternative models in the presented application, reaching a coefficient of determination R2 up to 0.824 and a root mean square error down to 1.11 °C, including the error propagation over time for a 1-week period with a 5-minute time-step. When considering a 50-hour time horizon, the best neural networks reach a much lower root mean square error of around 0.6 °C, which is suitable for applications such as model predictive control

On differentially private filtering for event streams

Rigorous privacy mechanisms that can cope with dynamic data are required to encourage a wider adoption of large-scale monitoring and decision systems relying on end-user information. A promising approach to develop these mechanisms is to specify quantitative privacy requirements at design time rather than as an afterthought, and to rely on signal processing techniques to achieve satisfying trade-offs between privacy and performance specifications. This paper discusses, from the signal processing point of view, an event stream analysis problem introduced in the database and cryptography literature. A discrete-valued input signal describes the occurrence of events contributed by end-users, and a system is supposed to provide some output signal based on this information, while preserving the privacy of the participants. The notion of privacy adopted here is that of event-level differential privacy, which provides strong privacy guarantees and has important operational advantages. Several mechanisms are described to provide differentially private output signals while minimizing the impact on performance. These mechanisms demonstrate the benefits of leveraging system theoretic techniques to provide privacy guarantees for dynamic systems.Comment: arXiv admin note: text overlap with arXiv:1207.430

On Some Extensions of Fictitious Play

This report considers extensions of fictitious play, a well-known model of learning in games. We review stochastic fictitious play as introduced in [FK93] as an attempt to solve some issues associated with standard fictitious play. Since the original paper on stochastic fictitious play, the traditional way of studying the convergence of this algorithm is via the theory of stochastic approximation algorithms. This leads to the study of an ODE which captures the mean dynamics of the system. For this continuous-time system, we review some convergence results, as well as ideas from the control theory litterature aimed at stabilizing Shapley’s game, for which it is known that standard fictitious play does not converge. W