150 research outputs found
ASP-based Discovery of Semi-Markovian Causal Models under Weaker Assumptions
In recent years the possibility of relaxing the so-called Faithfulness assumption in automated causal discovery has been investigated. The investigation showed (1) that the Faithfulness assumption can be weakened in various ways that in an important sense preserve its power, and (2) that weakening of Faithfulness may help to speed up methods based on Answer Set Programming. However, this line of work has so far only considered the discovery of causal models without latent variables. In this paper, we study weakenings of Faithfulness for constraint-based discovery of semi-Markovian causal models, which accommodate the possibility of latent variables, and show that both (1) and (2) remain the case in this more realistic setting
Learning Adjustment Sets from Observational and Limited Experimental Data
Estimating causal effects from observational data is not always possible due
to confounding. Identifying a set of appropriate covariates (adjustment set)
and adjusting for their influence can remove confounding bias; however, such a
set is typically not identifiable from observational data alone. Experimental
data do not have confounding bias, but are typically limited in sample size and
can therefore yield imprecise estimates. Furthermore, experimental data often
include a limited set of covariates, and therefore provide limited insight into
the causal structure of the underlying system. In this work we introduce a
method that combines large observational and limited experimental data to
identify adjustment sets and improve the estimation of causal effects. The
method identifies an adjustment set (if possible) by calculating the marginal
likelihood for the experimental data given observationally-derived prior
probabilities of potential adjustmen sets. In this way, the method can make
inferences that are not possible using only the conditional dependencies and
independencies in all the observational and experimental data. We show that the
method successfully identifies adjustment sets and improves causal effect
estimation in simulated data, and it can sometimes make additional inferences
when compared to state-of-the-art methods for combining experimental and
observational data.Comment: 10 pages, 5 figure
Causal Razors
When performing causal discovery, assumptions have to be made on how the true
causal mechanism corresponds to the underlying joint probability distribution.
These assumptions are labeled as causal razors in this work. We review numerous
causal razors that appeared in the literature, and offer a comprehensive
logical comparison of them. In particular, we scrutinize an unpopular causal
razor, namely parameter minimality, in multinomial causal models and its
logical relations with other well-studied causal razors. Our logical result
poses a dilemma in selecting a reasonable scoring criterion for score-based
casual search algorithms.Comment: 29 pages for the main paper. 14 pages for the supplementary material
Learning Optimal Causal Graphs with Exact Search
Peer reviewe
Enabling Runtime Verification of Causal Discovery Algorithms with Automated Conditional Independence Reasoning (Extended Version)
Causal discovery is a powerful technique for identifying causal relationships
among variables in data. It has been widely used in various applications in
software engineering. Causal discovery extensively involves conditional
independence (CI) tests. Hence, its output quality highly depends on the
performance of CI tests, which can often be unreliable in practice. Moreover,
privacy concerns arise when excessive CI tests are performed.
Despite the distinct nature between unreliable and excessive CI tests, this
paper identifies a unified and principled approach to addressing both of them.
Generally, CI statements, the outputs of CI tests, adhere to Pearl's axioms,
which are a set of well-established integrity constraints on conditional
independence. Hence, we can either detect erroneous CI statements if they
violate Pearl's axioms or prune excessive CI statements if they are logically
entailed by Pearl's axioms. Holistically, both problems boil down to reasoning
about the consistency of CI statements under Pearl's axioms (referred to as CIR
problem).
We propose a runtime verification tool called CICheck, designed to harden
causal discovery algorithms from reliability and privacy perspectives. CICheck
employs a sound and decidable encoding scheme that translates CIR into SMT
problems. To solve the CIR problem efficiently, CICheck introduces a four-stage
decision procedure with three lightweight optimizations that actively prove or
refute consistency, and only resort to costly SMT-based reasoning when
necessary. Based on the decision procedure to CIR, CICheck includes two
variants: ED-CICheck and ED-CICheck, which detect erroneous CI tests (to
enhance reliability) and prune excessive CI tests (to enhance privacy),
respectively. [abridged due to length limit
The Minimal Modal Interpretation of Quantum Theory
We introduce a realist, unextravagant interpretation of quantum theory that
builds on the existing physical structure of the theory and allows experiments
to have definite outcomes, but leaves the theory's basic dynamical content
essentially intact. Much as classical systems have specific states that evolve
along definite trajectories through configuration spaces, the traditional
formulation of quantum theory asserts that closed quantum systems have specific
states that evolve unitarily along definite trajectories through Hilbert
spaces, and our interpretation extends this intuitive picture of states and
Hilbert-space trajectories to the case of open quantum systems as well. We
provide independent justification for the partial-trace operation for density
matrices, reformulate wave-function collapse in terms of an underlying
interpolating dynamics, derive the Born rule from deeper principles, resolve
several open questions regarding ontological stability and dynamics, address a
number of familiar no-go theorems, and argue that our interpretation is
ultimately compatible with Lorentz invariance. Along the way, we also
investigate a number of unexplored features of quantum theory, including an
interesting geometrical structure---which we call subsystem space---that we
believe merits further study. We include an appendix that briefly reviews the
traditional Copenhagen interpretation and the measurement problem of quantum
theory, as well as the instrumentalist approach and a collection of
foundational theorems not otherwise discussed in the main text.Comment: 73 pages + references, 9 figures; cosmetic changes, added figure,
updated references, generalized conditional probabilities with attendant
changes to the sections on the EPR-Bohm thought experiment and Lorentz
invariance; for a concise summary, see the companion letter at
arXiv:1405.675
- …