3,053 research outputs found
On Automating the Doctrine of Double Effect
The doctrine of double effect () is a long-studied ethical
principle that governs when actions that have both positive and negative
effects are to be allowed. The goal in this paper is to automate
. We briefly present , and use a first-order
modal logic, the deontic cognitive event calculus, as our framework to
formalize the doctrine. We present formalizations of increasingly stronger
versions of the principle, including what is known as the doctrine of triple
effect. We then use our framework to simulate successfully scenarios that have
been used to test for the presence of the principle in human subjects. Our
framework can be used in two different modes: One can use it to build
-compliant autonomous systems from scratch, or one can use it to
verify that a given AI system is -compliant, by applying a
layer on an existing system or model. For the latter mode, the
underlying AI system can be built using any architecture (planners, deep neural
networks, bayesian networks, knowledge-representation systems, or a hybrid); as
long as the system exposes a few parameters in its model, such verification is
possible. The role of the layer here is akin to a (dynamic or
static) software verifier that examines existing software modules. Finally, we
end by presenting initial work on how one can apply our layer
to the STRIPS-style planning model, and to a modified POMDP model.This is
preliminary work to illustrate the feasibility of the second mode, and we hope
that our initial sketches can be useful for other researchers in incorporating
DDE in their own frameworks.Comment: 26th International Joint Conference on Artificial Intelligence 2017;
Special Track on AI & Autonom
Automatic Probabilistic Program Verification through Random Variable Abstraction
The weakest pre-expectation calculus has been proved to be a mature theory to
analyze quantitative properties of probabilistic and nondeterministic programs.
We present an automatic method for proving quantitative linear properties on
any denumerable state space using iterative backwards fixed point calculation
in the general framework of abstract interpretation. In order to accomplish
this task we present the technique of random variable abstraction (RVA) and we
also postulate a sufficient condition to achieve exact fixed point computation
in the abstract domain. The feasibility of our approach is shown with two
examples, one obtaining the expected running time of a probabilistic program,
and the other the expected gain of a gambling strategy.
Our method works on general guarded probabilistic and nondeterministic
transition systems instead of plain pGCL programs, allowing us to easily model
a wide range of systems including distributed ones and unstructured programs.
We present the operational and weakest precondition semantics for this programs
and prove its equivalence
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Formally justified and modular Bayesian inference for probabilistic programs
Probabilistic modelling offers a simple and coherent framework to describe the
real world in the face of uncertainty. Furthermore, by applying Bayes' rule
it is possible to use probabilistic models to make inferences about the state of
the world from partial observations. While traditionally probabilistic models
were constructed on paper, more recently the approach of probabilistic
programming enables users to write the models in executable languages resembling
computer programs and to freely mix them with deterministic code.
It has long been recognised that the semantics of programming languages is
complicated and the intuitive understanding that programmers have is often
inaccurate, resulting in difficult to understand bugs and unexpected program
behaviours. Programming languages are therefore studied in a rigorous way using
formal languages with mathematically defined semantics. Traditionally formal
semantics of probabilistic programs are defined using exact inference results,
but in practice exact Bayesian inference is not tractable and approximate
methods are used instead, posing a question of how the results of these
algorithms relate to the exact results. Correctness of such approximate methods
is usually argued somewhat less rigorously, without reference to a formal
semantics.
In this dissertation we formally develop denotational semantics for
probabilistic programs that correspond to popular sampling algorithms often used
in practice. The semantics is defined for an expressive typed lambda calculus
with higher-order functions and inductive types, extended with probabilistic
effects for sampling and conditioning, allowing continuous distributions and
unbounded likelihoods. It makes crucial use of the recently developed formalism
of quasi-Borel spaces to bring all these elements together. We provide semantics
corresponding to several variants of Markov chain Monte Carlo and Sequential
Monte Carlo methods and formally prove a notion of correctness for these
algorithms in the context of probabilistic programming.
We also show that the semantic construction can be directly mapped to an
implementation using established functional programming abstractions called
monad transformers. We develop a compact Haskell library for probabilistic
programming closely corresponding to the semantic construction, giving users a
high level of assurance in the correctness of the implementation. We also
demonstrate on a collection of benchmarks that the library offers performance
competitive with existing systems of similar scope.
An important property of our construction, both the semantics and the
implementation, is the high degree of modularity it offers. All the inference
algorithms are constructed by combining small building blocks in a setup where
the type system ensures correctness of compositions. We show that with basic
building blocks corresponding to vanilla Metropolis-Hastings and Sequential
Monte Carlo we can implement more advanced algorithms known in the literature,
such as Resample-Move Sequential Monte Carlo, Particle Marginal
Metropolis-Hastings, and Sequential Monte Carlo squared. These implementations
are very concise, reducing the effort required to produce them and the scope for
bugs. On top of that, our modular construction enables in some cases
deterministic testing of randomised inference algorithms, further increasing
reliability of the implementation.Engineering and Physical Sciences Research Council, Cambridge Trust, Cambridge-Tuebingen programm
The emergence of French statistics. How mathematics entered the world of statistics in France during the 1920s
This paper concerns the emergence of modern mathematical statistics in France
after the First World War. Emile Borel's achievements are presented, and
especially his creation of two institutions where mathematical statistics was
developed: the {\it Statistical Institute of Paris University}, (ISUP) in 1922
and above all the {\it Henri Poincar\'e Institute} (IHP) in 1928. At the IHP, a
new journal {\it Annales de l'Institut Henri Poincar\'e} was created in 1931.
We discuss the first papers in that journal dealing with mathematical
statistics
A Taxonomy of Causality-Based Biological Properties
We formally characterize a set of causality-based properties of metabolic
networks. This set of properties aims at making precise several notions on the
production of metabolites, which are familiar in the biologists' terminology.
From a theoretical point of view, biochemical reactions are abstractly
represented as causal implications and the produced metabolites as causal
consequences of the implication representing the corresponding reaction. The
fact that a reactant is produced is represented by means of the chain of
reactions that have made it exist. Such representation abstracts away from
quantities, stoichiometric and thermodynamic parameters and constitutes the
basis for the characterization of our properties. Moreover, we propose an
effective method for verifying our properties based on an abstract model of
system dynamics. This consists of a new abstract semantics for the system seen
as a concurrent network and expressed using the Chemical Ground Form calculus.
We illustrate an application of this framework to a portion of a real
metabolic pathway
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