Learning Inconsistent Preferences with Kernel Methods

We propose a probabilistic kernel approach for preferential learning from pairwise duelling data using Gaussian Processes. Different from previous methods, we do not impose a total order on the item space, hence can capture more expressive latent preferential structures such as inconsistent preferences and clusters of comparable items. Furthermore, we prove the universality of the proposed kernels, i.e. that the corresponding reproducing kernel Hilbert Space (RKHS) is dense in the space of skew-symmetric preference functions. To conclude the paper, we provide an extensive set of numerical experiments on simulated and real-world datasets showcasing the competitiveness of our proposed method with state-of-the-art

Data-driven Inverse Optimization with Imperfect Information

In data-driven inverse optimization an observer aims to learn the preferences of an agent who solves a parametric optimization problem depending on an exogenous signal. Thus, the observer seeks the agent's objective function that best explains a historical sequence of signals and corresponding optimal actions. We focus here on situations where the observer has imperfect information, that is, where the agent's true objective function is not contained in the search space of candidate objectives, where the agent suffers from bounded rationality or implementation errors, or where the observed signal-response pairs are corrupted by measurement noise. We formalize this inverse optimization problem as a distributionally robust program minimizing the worst-case risk that the {\em predicted} decision ({\em i.e.}, the decision implied by a particular candidate objective) differs from the agent's {\em actual} response to a random signal. We show that our framework offers rigorous out-of-sample guarantees for different loss functions used to measure prediction errors and that the emerging inverse optimization problems can be exactly reformulated as (or safely approximated by) tractable convex programs when a new suboptimality loss function is used. We show through extensive numerical tests that the proposed distributionally robust approach to inverse optimization attains often better out-of-sample performance than the state-of-the-art approaches

Comprehension and risk elicitation in the field: Evidence from rural Senegal

In the past decade, it has become increasingly common to use simple laboratory games and decision tasks as a device for measuring both the preferences and understanding of rural populations in the developing world. This is vitally important for policy implementation in a variety of areas. In this paper, we report the results observed using three distinct risk elicitation mechanisms, using samples drawn from the rural population in Senegal, West Africa. Whatever the intellectual merits of a particular elicitation strategy, there is little value in performing such tests if the respondents do not understand the questions involved. We test the understanding of and the level of meaningful responses to the typical Holt-Laury task, to a simple binary mechanism pioneered by Gneezy and Potters in 1997 and adapted by Charness and Gneezy in 2010, and to a nonincentivized willingness-to-risk scale à la Dohmen et al. We find a disturbingly low level of understanding with the Holt-Laury task and an unlikely-to-be-accurate pattern with the willingness-to-risk question. On the other hand, the simple binary mechanism produces results that closely match the patterns found in previous work, although the levels of risk-taking are lower than in previous studies. Our study is a cautionary note against utilizing either sophisticated risk-elicitation mechanisms at the possible cost of seriously diminished levels of comprehension or nonincentivized questions in the rural developing world.comprehension, risk elicitation, laboratory experiments in the field, rural,

Intelligent synthesis mechanism for deriving streaming priorities of multimedia content

We address the problem of integrating user preferences with network Quality of Service parameters for the streaming of media content, and suggest protocol stack configurations that satisfy user and technical requirements to the best available degree. Our approach is able to handle inconsistencies between user and networking considerations, formulating the problem of construction of tailor-made protocols as a prioritization problem, solvable using fuzzy programming

Data-Driven Shape Analysis and Processing

Data-driven methods play an increasingly important role in discovering geometric, structural, and semantic relationships between 3D shapes in collections, and applying this analysis to support intelligent modeling, editing, and visualization of geometric data. In contrast to traditional approaches, a key feature of data-driven approaches is that they aggregate information from a collection of shapes to improve the analysis and processing of individual shapes. In addition, they are able to learn models that reason about properties and relationships of shapes without relying on hard-coded rules or explicitly programmed instructions. We provide an overview of the main concepts and components of these techniques, and discuss their application to shape classification, segmentation, matching, reconstruction, modeling and exploration, as well as scene analysis and synthesis, through reviewing the literature and relating the existing works with both qualitative and numerical comparisons. We conclude our report with ideas that can inspire future research in data-driven shape analysis and processing.Comment: 10 pages, 19 figure

Towards trustworthy machine learning with kernels

Machine Learning has become an indispensable aspect of various safety-critical industries like healthcare, law, and automotive. Hence, it is crucial to ensure that our machine learning models function appropriately and instil trust among their users. This thesis focuses on improving the safety and transparency of Machine Learning by advocating for more principled uncertainty quantification and more effective explainability tools. Specifically, the use of Kernel Mean Embeddings (KME) and Gaussian Processes (GP) is prevalent in this work since they can represent probability distribution with minimal distributional assumptions and capture uncertainty well, respectively. I dedicate Chapter 2 to introduce these two methodologies. Chapter 3 demonstrates an effective use of these methods in conjunction with each other to tackle a statistical downscaling problem, in which a Deconditional Gaussian process is proposed. Chapter 4 considers a causal data fusion problem, where multiple causal graphs are combined for inference. I introduce BayesIMP, an algorithm built using KME and GPs, to draw causal conclusion while accounting for the uncertainty in the data and model. In Chapter 5, I present RKHS-SHAP to model explainability for kernel methods that utilizes Shapley values. Specifically, I propose to estimate the value function in the cooperative game using KMEs, circumventing the need for any parametric density estimations. A Shapley regulariser is also proposed to regulate the amount of contributions certain features can have to the model. Chapter 6 presents a generalised preferential Gaussian processes for modelling preference with non-rankable structure, which sets the scene for Chapter 7, where I built upon my research and propose Pref-SHAP to explain preference models

Flows and Decompositions of Games: Harmonic and Potential Games

In this paper we introduce a novel flow representation for finite games in strategic form. This representation allows us to develop a canonical direct sum decomposition of an arbitrary game into three components, which we refer to as the potential, harmonic and nonstrategic components. We analyze natural classes of games that are induced by this decomposition, and in particular, focus on games with no harmonic component and games with no potential component. We show that the first class corresponds to the well-known potential games. We refer to the second class of games as harmonic games, and study the structural and equilibrium properties of this new class of games. Intuitively, the potential component of a game captures interactions that can equivalently be represented as a common interest game, while the harmonic part represents the conflicts between the interests of the players. We make this intuition precise, by studying the properties of these two classes, and show that indeed they have quite distinct and remarkable characteristics. For instance, while finite potential games always have pure Nash equilibria, harmonic games generically never do. Moreover, we show that the nonstrategic component does not affect the equilibria of a game, but plays a fundamental role in their efficiency properties, thus decoupling the location of equilibria and their payoff-related properties. Exploiting the properties of the decomposition framework, we obtain explicit expressions for the projections of games onto the subspaces of potential and harmonic games. This enables an extension of the properties of potential and harmonic games to "nearby" games. We exemplify this point by showing that the set of approximate equilibria of an arbitrary game can be characterized through the equilibria of its projection onto the set of potential games