377,439 research outputs found
Causal Discovery for Relational Domains: Representation, Reasoning, and Learning
Many domains are currently experiencing the growing trend to record and analyze massive, observational data sets with increasing complexity. A commonly made claim is that these data sets hold potential to transform their corresponding domains by providing previously unknown or unexpected explanations and enabling informed decision-making. However, only knowledge of the underlying causal generative process, as opposed to knowledge of associational patterns, can support such tasks.
Most methods for traditional causal discovery—the development of algorithms that learn causal structure from observational data—are restricted to representations that require limiting assumptions on the form of the data. Causal discovery has almost exclusively been applied to directed graphical models of propositional data that assume a single type of entity with independence among instances. However, most real-world domains are characterized by systems that involve complex interactions among multiple types of entities. Many state-of-the-art methods in statistics and machine learning that address such complex systems focus on learning associational models, and they are oftentimes mistakenly interpreted as causal. The intersection between causal discovery and machine learning in complex systems is small.
The primary objective of this thesis is to extend causal discovery to such complex systems. Specifically, I formalize a relational representation and model that can express the causal and probabilistic dependencies among the attributes of interacting, heterogeneous entities. I show that the traditional method for reasoning about statistical independence from model structure fails to accurately derive conditional independence facts from relational models. I introduce a new theory—relational d-separation—and a novel, lifted representation—the abstract ground graph—that supports a sound, complete, and computationally efficient method for algorithmically deriving conditional independencies from probabilistic models of relational data. The abstract ground graph representation also presents causal implications that enable the detection of causal direction for bivariate relational dependencies without parametric assumptions. I leverage these implications and the theoretical framework of relational d-separation to develop a sound and complete algorithm—the relational causal discovery (RCD) algorithm—that learns causal structure from relational data
Large-Scale Kernel Methods for Independence Testing
Representations of probability measures in reproducing kernel Hilbert spaces
provide a flexible framework for fully nonparametric hypothesis tests of
independence, which can capture any type of departure from independence,
including nonlinear associations and multivariate interactions. However, these
approaches come with an at least quadratic computational cost in the number of
observations, which can be prohibitive in many applications. Arguably, it is
exactly in such large-scale datasets that capturing any type of dependence is
of interest, so striking a favourable tradeoff between computational efficiency
and test performance for kernel independence tests would have a direct impact
on their applicability in practice. In this contribution, we provide an
extensive study of the use of large-scale kernel approximations in the context
of independence testing, contrasting block-based, Nystrom and random Fourier
feature approaches. Through a variety of synthetic data experiments, it is
demonstrated that our novel large scale methods give comparable performance
with existing methods whilst using significantly less computation time and
memory.Comment: 29 pages, 6 figure
Reasoning about Independence in Probabilistic Models of Relational Data
We extend the theory of d-separation to cases in which data instances are not
independent and identically distributed. We show that applying the rules of
d-separation directly to the structure of probabilistic models of relational
data inaccurately infers conditional independence. We introduce relational
d-separation, a theory for deriving conditional independence facts from
relational models. We provide a new representation, the abstract ground graph,
that enables a sound, complete, and computationally efficient method for
answering d-separation queries about relational models, and we present
empirical results that demonstrate effectiveness.Comment: 61 pages, substantial revisions to formalisms, theory, and related
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Quantum Probability Theory
The mathematics of classical probability theory was subsumed into classical
measure theory by Kolmogorov in 1933. Quantum theory as nonclassical
probability theory was incorporated into the beginnings of noncommutative
measure theory by von Neumann in the early thirties, as well. To precisely this
end, von Neumann initiated the study of what are now called von Neumann
algebras and, with Murray, made a first classification of such algebras into
three types. The nonrelativistic quantum theory of systems with finitely many
degrees of freedom deals exclusively with type I algebras. However, for the
description of further quantum systems, the other types of von Neumann algebras
are indispensable. The paper reviews quantum probability theory in terms of
general von Neumann algebras, stressing the similarity of the conceptual
structure of classical and noncommutative probability theories and emphasizing
the correspondence between the classical and quantum concepts, though also
indicating the nonclassical nature of quantum probabilistic predictions. In
addition, differences between the probability theories in the type I, II and
III settings are explained. A brief description is given of quantum systems for
which probability theory based on type I algebras is known to be insufficient.
These illustrate the physical significance of the previously mentioned
differences.Comment: 28 pages, LaTeX, typos removed and some minor modifications for
clarity and accuracy made. This is the version to appear in Studies in the
History and Philosophy of Modern Physic
Modes of Political Representation: Toward a New Typology
The mandate-independence controversy still features prominently in studies of political representation even though the problems with its theoretical foundation and empirical operationalization have long been recognized. This article proposes an alternative typology of modes of representation. By combining type of control (ex ante or ex post) with direction of the interactions (bottom-up or top-down), our study captures the most important aspects of the relationship between voters and representatives. We demonstrate how the typology can be used in a survey instrument by comparing the attitudes toward representation of Dutch members of Parliament with the attitudes held by voters, and by relating the views of the members to their behavior
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