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Optimal Transport for Fairness: Archival Data Repair using Small Research Data Sets
Mar 20, 2024
With the advent of the AI Act and other regulations, there is now an urgent need for algorithms that repair unfairness in training data. In this paper, we define fairness in terms of conditional independence between protected attributes ($S$) and features ($X$), given unprotected attributes ($U$). We address the important setting in which torrents of archival data need to be repaired, using only a small proportion of these data, which are $S|U$-labelled (the research data). We use the latter to design optimal transport (OT)-based repair plans on interpolated supports. This allows {\em off-sample}, labelled, archival data to be repaired, subject to stationarity assumptions. It also significantly reduces the size of the supports of the OT plans, with correspondingly large savings in the cost of their design and of their {\em sequential\/} application to the off-sample data. We provide detailed experimental results with simulated and benchmark real data (the Adult data set). Our performance figures demonstrate effective repair -- in the sense of quenching conditional dependence -- of large quantities of off-sample, labelled (archival) data.
Fully Probabilistic Design for Optimal Transport
Dec 19, 2022The goal of this paper is to introduce a new theoretical framework for Optimal Transport (OT), using the terminology and techniques of Fully Probabilistic Design (FPD). Optimal Transport is the canonical method for comparing probability measures and has been successfully applied in a wide range of areas (computer vision Rubner et al. [2004], computer graphics Solomon et al. [2015], natural language processing Kusner et al. [2015], etc.). However, we argue that the current OT framework suffers from two shortcomings: first, it is hard to induce generic constraints and probabilistic knowledge in the OT problem; second, the current formalism does not address the question of uncertainty in the marginals, lacking therefore the mechanisms to design robust solutions. By viewing the OT problem as the optimal design of a probability density function with marginal constraints, we prove that OT is an instance of the more generic FPD framework. In this new setting, we can furnish the OT framework with the necessary mechanisms for processing probabilistic constraints and deriving uncertainty quantifiers, hence establishing a new extended framework, called FPD-OT. Our main contribution in this paper is to establish the connection between OT and FPD, providing new theoretical insights for both. This will lay the foundations for the application of FPD-OT in a subsequent work, notably in processing more sophisticated knowledge constraints, as well as in designing robust solutions in the case of uncertain marginals.
Closed-Loop View of the Regulation of AI: Equal Impact across Repeated Interactions
Sep 03, 2022
There has been much recent interest in the regulation of AI. We argue for a view based on civil-rights legislation, built on the notions of equal treatment and equal impact. In a closed-loop view of the AI system and its users, the equal treatment concerns one pass through the loop. Equal impact, in our view, concerns the long-run average behaviour across repeated interactions. In order to establish the existence of the average and its properties, one needs to study the ergodic properties of the closed-loop and its unique stationary measure.
Reinforcement Learning with Algorithms from Probabilistic Structure Estimation
Mar 15, 2021
Reinforcement learning (RL) algorithms aim to learn optimal decisions in unknown environments through experience of taking actions and observing the rewards gained. In some cases, the environment is not influenced by the actions of the RL agent, in which case the problem can be modeled as a contextual multi-armed bandit and lightweight \emph{myopic} algorithms can be employed. On the other hand, when the RL agent's actions affect the environment, the problem must be modeled as a Markov decision process and more complex RL algorithms are required which take the future effects of actions into account. Moreover, in many modern RL settings, it is unknown from the outset whether or not the agent's actions will impact the environment and it is often not possible to determine which RL algorithm is most fitting. In this work, we propose to avoid this dilemma entirely and incorporate a choice mechanism into our RL framework. Rather than assuming a specific problem structure, we use a probabilistic structure estimation procedure based on a likelihood-ratio (LR) test to make a more informed selection of learning algorithm. We derive a sufficient condition under which myopic policies are optimal, present an LR test for this condition, and derive a bound on the regret of our framework. We provide examples of real-world scenarios where our framework is needed and provide extensive simulations to validate our approach.
I-nteract 2.0: A Cyber-Physical System to Design 3D Models using Mixed Reality Technologies and Deep Learning for Additive Manufacturing
Oct 21, 2020
I-nteract is a cyber-physical system that enables real-time interaction with both virtual and real artifacts to design 3D models for additive manufacturing by leveraging on mixed reality technologies. This paper presents novel advances in the development of the interaction platform I-nteract to generate 3D models using both constructive solid geometry and artificial intelligence. The system also enables the user to adjust the dimensions of the 3D models with respect to their physical workspace. The effectiveness of the system is demonstrated by generating 3D models of furniture (e.g., chairs and tables) and fitting them into the physical space in a mixed reality environment.
Bayesian Classifier for Route Prediction with Markov Chains
Aug 31, 2018
We present here a general framework and a specific algorithm for predicting the destination, route, or more generally a pattern, of an ongoing journey, building on the recent work of [Y. Lassoued, J. Monteil, Y. Gu, G. Russo, R. Shorten, and M. Mevissen, "Hidden Markov model for route and destination prediction," in IEEE International Conference on Intelligent Transportation Systems, 2017]. In the presented framework, known journey patterns are modelled as stochastic processes, emitting the road segments visited during the journey, and the ongoing journey is predicted by updating the posterior probability of each journey pattern given the road segments visited so far. In this contribution, we use Markov chains as models for the journey patterns, and consider the prediction as final, once one of the posterior probabilities crosses a predefined threshold. Despite the simplicity of both, examples run on a synthetic dataset demonstrate high accuracy of the made predictions.
r-Extreme Signalling for Congestion Control
Mar 31, 2016
In many "smart city" applications, congestion arises in part due to the nature of signals received by individuals from a central authority. In the model of Marecek et al. [arXiv:1406.7639, Int. J. Control 88(10), 2015], each agent uses one out of multiple resources at each time instant. The per-use cost of a resource depends on the number of concurrent users. A central authority has up-to-date knowledge of the congestion across all resources and uses randomisation to provide a scalar or an interval for each resource at each time. In this paper, the interval to broadcast per resource is obtained by taking the minima and maxima of costs observed within a time window of length r, rather than by randomisation. We show that the resulting distribution of agents across resources also converges in distribution, under plausible assumptions about the evolution of the population over time.
Pricing Vehicle Sharing with Proximity Information
Jan 25, 2016
For vehicle sharing schemes, where drop-off positions are not fixed, we propose a pricing scheme, where the price depends in part on the distance between where a vehicle is being dropped off and where the closest shared vehicle is parked. Under certain restrictive assumptions, we show that this pricing leads to a socially optimal spread of the vehicles within a region.