Dynamic Bayesian Combination of Multiple Imperfect Classifiers

Classifier combination methods need to make best use of the outputs of multiple, imperfect classifiers to enable higher accuracy classifications. In many situations, such as when human decisions need to be combined, the base decisions can vary enormously in reliability. A Bayesian approach to such uncertain combination allows us to infer the differences in performance between individuals and to incorporate any available prior knowledge about their abilities when training data is sparse. In this paper we explore Bayesian classifier combination, using the computationally efficient framework of variational Bayesian inference. We apply the approach to real data from a large citizen science project, Galaxy Zoo Supernovae, and show that our method far outperforms other established approaches to imperfect decision combination. We go on to analyse the putative community structure of the decision makers, based on their inferred decision making strategies, and show that natural groupings are formed. Finally we present a dynamic Bayesian classifier combination approach and investigate the changes in base classifier performance over time.Comment: 35 pages, 12 figure

Matching Code and Law: Achieving Algorithmic Fairness with Optimal Transport

Increasingly, discrimination by algorithms is perceived as a societal and legal problem. As a response, a number of criteria for implementing algorithmic fairness in machine learning have been developed in the literature. This paper proposes the Continuous Fairness Algorithm (CFA$\theta$) which enables a continuous interpolation between different fairness definitions. More specifically, we make three main contributions to the existing literature. First, our approach allows the decision maker to continuously vary between specific concepts of individual and group fairness. As a consequence, the algorithm enables the decision maker to adopt intermediate ``worldviews'' on the degree of discrimination encoded in algorithmic processes, adding nuance to the extreme cases of ``we're all equal'' (WAE) and ``what you see is what you get'' (WYSIWYG) proposed so far in the literature. Second, we use optimal transport theory, and specifically the concept of the barycenter, to maximize decision maker utility under the chosen fairness constraints. Third, the algorithm is able to handle cases of intersectionality, i.e., of multi-dimensional discrimination of certain groups on grounds of several criteria. We discuss three main examples (credit applications; college admissions; insurance contracts) and map out the legal and policy implications of our approach. The explicit formalization of the trade-off between individual and group fairness allows this post-processing approach to be tailored to different situational contexts in which one or the other fairness criterion may take precedence. Finally, we evaluate our model experimentally.Comment: Vastly extended new version, now including computational experiment

RISK MANAGEMENT THROUGH INSURANCE AND ENVIRONMENTAL EXTERNALITIES FROM AGRICULTURAL INPUT USE: AN ITALIAN CASE STUDY

The biological nature of agricultural production processes induce a higher degree of uncertainty surrounding the economic performance of farm enterprises. This has contributed to the development and acceptance of forms of public intervention aimed at reducing income variability that have no parallel in other sectors of the economy. In particular, subsidized crop insurance are a widely used tool. The impact of these programs on the decisions of production generates effects on input use, land use and thus, indirectly, environmental outcomes. The importance of this issue has grown in parallel with the growth in importance of the collective role of agriculture sector that has addressed the recent guidelines adopted by many developed countries. To examine the effects of public risk management programs on optimal nitrogen fertilizer use and land allocation to crops, this study carried out an empirical analysis by developing a mathematical programming model of a representative wheat-tomato farm in Apulia southern region of Italy. The model endogenizes nitrogen fertilizer rates and land allocation, as well as the insurance coverage levels, participation in insurance programs and the Environmental Payment (EP). This study utilized direct expected utility maximizing non-linear programming in combination with a simulation approach. Results show that with current crop insurance programs, the optimal nitrogen fertilizer rate slightly increases and the optimal acreage substantially increases for tomato whereas decrease for wheat. Assuming that the environmental negative effects of crop insurance are positively related to nitrogen fertilizer use, this type of public intervention implies negative environmental effects.Uncertainty, Risk Management, Crop Insurance, Input Use Decisions, Environmental Externalities, Mathematical Programming., Agricultural and Food Policy, Environmental Economics and Policy, Research Methods/ Statistical Methods, Risk and Uncertainty, Q10, Q14,

Development of Interactive Support Systems for Multiobjective Decision Analysis under Uncertainty

This paper presents interactive multiobjective decision analysis support systems, called MIDASS, which is a newly developed interactive computer program for strategic use of expected utility theory. Decision analysis based on expected utility hypothesis is an established prescriptive approach for supporting business decisions under uncertainty, which embodies an effective procedure for seeking the best choice among alternatives. It is usually difficult, however, for the decision maker (DM) to apply it for the strategic use in the realistic business situations. MIDASS provides an integrated interactive computer system for supporting multiobjective decision analysis under uncertainty, which assists to derive an acceptable business solution for DM with the construction of his/her expected multiattribute utility fuction (EMUF).expected multiobjective decision analysis, MIDASS, expected multiattribute utility function (EMUF), intelligent decision support systems (IDSS).

Improved Program Planning Approaches Generates Large Benefits in High Risk Crop Farming

This paper examines whether there is room for the improvement of farm program decisions through the incorporation of mathematical optimization in the practical planning process. Probing the potential for improvement, we investigate the cases of four German cash crop farms over the last six years. The formal planning approach includes a systematic time series analysis of farmspecific single gross margins and a stochastic optimization model. In order to avoid solutions that simply exceed the farmer's risk tolerance, the apparently accepted variance of the observed program's total gross margin which represents an observable reflection of the individual farmer's risk attitude is used as an upper bound in the optimization. For each of the 24 planning occasions, the formal model is used in a quasi ex-ante approach that provides optimized alternative programs. The total gross margins that could have been realized if the formally optimized programs had been implemented are then ex-post compared to those that were actually realized. We find that the farmers could have increased their total gross margins significantly if - instead of using simple routines and rules of thumb - they had used the more sophisticated formal planning model. However, we also find that the superiority of formalized planning approaches depends on the quality of statistical analysis and the resulting forecasting model. Using our approach for practical decision support implies that farmers first specify their "own" production programs without the formal planning aid. Then, an alternative program can be provided which leads to superior expected total gross margins without exceeding the farmer's accepted total gross margin variance.production program planning, optimization, uncertainty, static distributions, stochastic processes, Crop Production/Industries, C1, C61, M11, Q12,