12,204 research outputs found
Recommended from our members
Software tools for stochastic programming: A Stochastic Programming Integrated Environment (SPInE)
SP models combine the paradigm of dynamic linear programming with
modelling of random parameters, providing optimal decisions which hedge
against future uncertainties. Advances in hardware as well as software
techniques and solution methods have made SP a viable optimisation tool.
We identify a growing need for modelling systems which support the creation
and investigation of SP problems. Our SPInE system integrates a number of
components which include a flexible modelling tool (based on stochastic
extensions of the algebraic modelling languages AMPL and MPL), stochastic
solvers, as well as special purpose scenario generators and database tools.
We introduce an asset/liability management model and illustrate how SPInE
can be used to create and process this model as a multistage SP application
Learning probability distributions generated by finite-state machines
We review methods for inference of probability distributions generated by probabilistic automata and related models for sequence generation. We focus on methods that can be proved to learn in the inference
in the limit and PAC formal models. The methods we review are state merging and state splitting methods for probabilistic deterministic automata and the recently developed spectral method for nondeterministic probabilistic automata. In both cases, we derive them from a high-level algorithm described in terms of the Hankel matrix of the distribution to be learned, given as an oracle, and then describe how to adapt that algorithm to account for the error introduced by a finite sample.Peer ReviewedPostprint (author's final draft
Experimental Biological Protocols with Formal Semantics
Both experimental and computational biology is becoming increasingly
automated. Laboratory experiments are now performed automatically on
high-throughput machinery, while computational models are synthesized or
inferred automatically from data. However, integration between automated tasks
in the process of biological discovery is still lacking, largely due to
incompatible or missing formal representations. While theories are expressed
formally as computational models, existing languages for encoding and
automating experimental protocols often lack formal semantics. This makes it
challenging to extract novel understanding by identifying when theory and
experimental evidence disagree due to errors in the models or the protocols
used to validate them. To address this, we formalize the syntax of a core
protocol language, which provides a unified description for the models of
biochemical systems being experimented on, together with the discrete events
representing the liquid-handling steps of biological protocols. We present both
a deterministic and a stochastic semantics to this language, both defined in
terms of hybrid processes. In particular, the stochastic semantics captures
uncertainties in equipment tolerances, making it a suitable tool for both
experimental and computational biologists. We illustrate how the proposed
protocol language can be used for automated verification and synthesis of
laboratory experiments on case studies from the fields of chemistry and
molecular programming
Rational stochastic languages
The goal of the present paper is to provide a systematic and comprehensive
study of rational stochastic languages over a semiring K \in {Q, Q +, R, R+}. A
rational stochastic language is a probability distribution over a free monoid
\Sigma^* which is rational over K, that is which can be generated by a
multiplicity automata with parameters in K. We study the relations between the
classes of rational stochastic languages S rat K (\Sigma). We define the notion
of residual of a stochastic language and we use it to investigate properties of
several subclasses of rational stochastic languages. Lastly, we study the
representation of rational stochastic languages by means of multiplicity
automata.Comment: 35 page
Probabilistic abstract interpretation: From trace semantics to DTMC’s and linear regression
In order to perform probabilistic program analysis we need to consider probabilistic languages or languages with a probabilistic semantics, as well as a corresponding framework for the analysis which is able to accommodate probabilistic properties and properties of probabilistic computations. To this purpose we investigate the relationship between three different types of probabilistic semantics for a core imperative language, namely Kozen’s Fixpoint Semantics, our Linear Operator Semantics and probabilistic versions of Maximal Trace Semantics. We also discuss the relationship between Probabilistic Abstract Interpretation (PAI) and statistical or linear regression analysis. While classical Abstract Interpretation, based on Galois connection, allows only for worst-case analyses, the use of the Moore-Penrose pseudo inverse in PAI opens the possibility of exploiting statistical and noisy observations in order to analyse and identify various system properties
Toric grammars: a new statistical approach to natural language modeling
We propose a new statistical model for computational linguistics. Rather than
trying to estimate directly the probability distribution of a random sentence
of the language, we define a Markov chain on finite sets of sentences with many
finite recurrent communicating classes and define our language model as the
invariant probability measures of the chain on each recurrent communicating
class. This Markov chain, that we call a communication model, recombines at
each step randomly the set of sentences forming its current state, using some
grammar rules. When the grammar rules are fixed and known in advance instead of
being estimated on the fly, we can prove supplementary mathematical properties.
In particular, we can prove in this case that all states are recurrent states,
so that the chain defines a partition of its state space into finite recurrent
communicating classes. We show that our approach is a decisive departure from
Markov models at the sentence level and discuss its relationships with Context
Free Grammars. Although the toric grammars we use are closely related to
Context Free Grammars, the way we generate the language from the grammar is
qualitatively different. Our communication model has two purposes. On the one
hand, it is used to define indirectly the probability distribution of a random
sentence of the language. On the other hand it can serve as a (crude) model of
language transmission from one speaker to another speaker through the
communication of a (large) set of sentences
- …