4 research outputs found
Computing Shapley Values in the Plane
We consider the problem of computing Shapley values for points in the plane, where each point is interpreted as a player, and the value of a coalition is defined by the area of usual geometric objects, such as the convex hull or the minimum axis-parallel bounding box.
For sets of n points in the plane, we show how to compute in roughly O(n^{3/2}) time the Shapley values for the area of the minimum axis-parallel bounding box and the area of the union of the rectangles spanned by the origin and the input points. When the points form an increasing or decreasing chain, the running time can be improved to near-linear. In all these cases, we use linearity of the Shapley values and algebraic methods.
We also show that Shapley values for the area of the convex hull or the minimum enclosing disk can be computed in O(n^2) and O(n^3) time, respectively. These problems are closely related to the model of stochastic point sets considered in computational geometry, but here we have to consider random insertion orders of the points instead of a probabilistic existence of points
Computing Shapley Values for Mean Width in 3-D
The Shapley value is a common tool in game theory to evaluate the importance
of a player in a cooperative setting. In a geometric context, it provides a way
to measure the contribution of a geometric object in a set towards some
function on the set. Recently, Cabello and Chan (SoCG 2019) presented
algorithms for computing Shapley values for a number of functions for point
sets in the plane. More formally, a coalition game consists of a set of players
and a characteristic function with . Let be a uniformly random permutation of , and be
the set of players in that appear before player in the permutation
. The Shapley value of the game is defined to be . More intuitively,
the Shapley value represents the impact of player 's appearance over all
insertion orders. We present an algorithm to compute Shapley values in 3-D,
where we treat points as players and use the mean width of the convex hull as
the characteristic function. Our algorithm runs in time and
space. Our approach is based on a new data structure for a variant of
the dynamic convolution problem , where we want to answer
dynamically. Our data structure supports updating at position ,
incrementing and decrementing and rotating by . We present a data
structure that supports operations in time and
space. Moreover, the same approach can be used to compute the Shapley values
for the mean volume of the convex hull projection onto a uniformly random -subspace in time and space for a point set in
-dimensional space ()
Towards a human-centric data economy
Spurred by widespread adoption of artificial intelligence and machine learning, “data” is becoming
a key production factor, comparable in importance to capital, land, or labour in an increasingly
digital economy. In spite of an ever-growing demand for third-party data in the B2B
market, firms are generally reluctant to share their information. This is due to the unique characteristics
of “data” as an economic good (a freely replicable, non-depletable asset holding a highly
combinatorial and context-specific value), which moves digital companies to hoard and protect
their “valuable” data assets, and to integrate across the whole value chain seeking to monopolise
the provision of innovative services built upon them. As a result, most of those valuable assets
still remain unexploited in corporate silos nowadays.
This situation is shaping the so-called data economy around a number of champions, and it is
hampering the benefits of a global data exchange on a large scale. Some analysts have estimated
the potential value of the data economy in US$2.5 trillion globally by 2025. Not surprisingly, unlocking
the value of data has become a central policy of the European Union, which also estimated
the size of the data economy in 827C billion for the EU27 in the same period. Within the scope of
the European Data Strategy, the European Commission is also steering relevant initiatives aimed
to identify relevant cross-industry use cases involving different verticals, and to enable sovereign
data exchanges to realise them.
Among individuals, the massive collection and exploitation of personal data by digital firms
in exchange of services, often with little or no consent, has raised a general concern about privacy
and data protection. Apart from spurring recent legislative developments in this direction,
this concern has raised some voices warning against the unsustainability of the existing digital
economics (few digital champions, potential negative impact on employment, growing inequality),
some of which propose that people are paid for their data in a sort of worldwide data labour
market as a potential solution to this dilemma [114, 115, 155].
From a technical perspective, we are far from having the required technology and algorithms
that will enable such a human-centric data economy. Even its scope is still blurry, and the question
about the value of data, at least, controversial. Research works from different disciplines have
studied the data value chain, different approaches to the value of data, how to price data assets,
and novel data marketplace designs. At the same time, complex legal and ethical issues with
respect to the data economy have risen around privacy, data protection, and ethical AI practices. In this dissertation, we start by exploring the data value chain and how entities trade data assets
over the Internet. We carry out what is, to the best of our understanding, the most thorough survey
of commercial data marketplaces. In this work, we have catalogued and characterised ten different
business models, including those of personal information management systems, companies born
in the wake of recent data protection regulations and aiming at empowering end users to take
control of their data. We have also identified the challenges faced by different types of entities,
and what kind of solutions and technology they are using to provide their services.
Then we present a first of its kind measurement study that sheds light on the prices of data
in the market using a novel methodology. We study how ten commercial data marketplaces categorise
and classify data assets, and which categories of data command higher prices. We also
develop classifiers for comparing data products across different marketplaces, and we study the
characteristics of the most valuable data assets and the features that specific vendors use to set
the price of their data products. Based on this information and adding data products offered by
other 33 data providers, we develop a regression analysis for revealing features that correlate with
prices of data products. As a result, we also implement the basic building blocks of a novel data
pricing tool capable of providing a hint of the market price of a new data product using as inputs
just its metadata. This tool would provide more transparency on the prices of data products in
the market, which will help in pricing data assets and in avoiding the inherent price fluctuation of
nascent markets.
Next we turn to topics related to data marketplace design. Particularly, we study how buyers
can select and purchase suitable data for their tasks without requiring a priori access to such
data in order to make a purchase decision, and how marketplaces can distribute payoffs for a
data transaction combining data of different sources among the corresponding providers, be they
individuals or firms. The difficulty of both problems is further exacerbated in a human-centric
data economy where buyers have to choose among data of thousands of individuals, and where
marketplaces have to distribute payoffs to thousands of people contributing personal data to a
specific transaction.
Regarding the selection process, we compare different purchase strategies depending on the
level of information available to data buyers at the time of making decisions. A first methodological
contribution of our work is proposing a data evaluation stage prior to datasets being selected
and purchased by buyers in a marketplace. We show that buyers can significantly improve the
performance of the purchasing process just by being provided with a measurement of the performance
of their models when trained by the marketplace with individual eligible datasets. We
design purchase strategies that exploit such functionality and we call the resulting algorithm Try
Before You Buy, and our work demonstrates over synthetic and real datasets that it can lead to
near-optimal data purchasing with only O(N) instead of the exponential execution time - O(2N)
- needed to calculate the optimal purchase. With regards to the payoff distribution problem, we focus on computing the relative value
of spatio-temporal datasets combined in marketplaces for predicting transportation demand and
travel time in metropolitan areas. Using large datasets of taxi rides from Chicago, Porto and
New York we show that the value of data is different for each individual, and cannot be approximated
by its volume. Our results reveal that even more complex approaches based on the
“leave-one-out” value, are inaccurate. Instead, more complex and acknowledged notions of value
from economics and game theory, such as the Shapley value, need to be employed if one wishes
to capture the complex effects of mixing different datasets on the accuracy of forecasting algorithms.
However, the Shapley value entails serious computational challenges. Its exact calculation
requires repetitively training and evaluating every combination of data sources and hence O(N!)
or O(2N) computational time, which is unfeasible for complex models or thousands of individuals.
Moreover, our work paves the way to new methods of measuring the value of spatio-temporal
data. We identify heuristics such as entropy or similarity to the average that show a significant
correlation with the Shapley value and therefore can be used to overcome the significant computational
challenges posed by Shapley approximation algorithms in this specific context.
We conclude with a number of open issues and propose further research directions that leverage
the contributions and findings of this dissertation. These include monitoring data transactions
to better measure data markets, and complementing market data with actual transaction prices
to build a more accurate data pricing tool. A human-centric data economy would also require
that the contributions of thousands of individuals to machine learning tasks are calculated daily.
For that to be feasible, we need to further optimise the efficiency of data purchasing and payoff
calculation processes in data marketplaces. In that direction, we also point to some alternatives
to repetitively training and evaluating a model to select data based on Try Before You Buy and
approximate the Shapley value. Finally, we discuss the challenges and potential technologies that
help with building a federation of standardised data marketplaces.
The data economy will develop fast in the upcoming years, and researchers from different
disciplines will work together to unlock the value of data and make the most out of it. Maybe
the proposal of getting paid for our data and our contribution to the data economy finally flies,
or maybe it is other proposals such as the robot tax that are finally used to balance the power
between individuals and tech firms in the digital economy. Still, we hope our work sheds light on
the value of data, and contributes to making the price of data more transparent and, eventually, to
moving towards a human-centric data economy.This work has been supported by IMDEA Networks InstitutePrograma de Doctorado en Ingeniería Telemática por la Universidad Carlos III de MadridPresidente: Georgios Smaragdakis.- Secretario: Ángel Cuevas Rumín.- Vocal: Pablo Rodríguez Rodrígue