6,153 research outputs found
Sequential Density Estimation via Nonlinear Continuous Weighted Finite Automata
Weighted finite automata (WFAs) have been widely applied in many fields. One
of the classic problems for WFAs is probability distribution estimation over
sequences of discrete symbols. Although WFAs have been extended to deal with
continuous input data, namely continuous WFAs (CWFAs), it is still unclear how
to approximate density functions over sequences of continuous random variables
using WFA-based models, due to the limitation on the expressiveness of the
model as well as the tractability of approximating density functions via CWFAs.
In this paper, we propose a nonlinear extension to the CWFA model to first
improve its expressiveness, we refer to it as the nonlinear continuous WFAs
(NCWFAs). Then we leverage the so-called RNADE method, which is a well-known
density estimator based on neural networks, and propose the RNADE-NCWFA model.
The RNADE-NCWFA model computes a density function by design. We show that this
model is strictly more expressive than the Gaussian HMM model, which CWFA
cannot approximate. Empirically, we conduct a synthetic experiment using
Gaussian HMM generated data. We focus on evaluating the model's ability to
estimate densities for sequences of varying lengths (longer length than the
training data). We observe that our model performs the best among the compared
baseline methods
A weighted pair graph representation for reconstructibility of Boolean control networks
A new concept of weighted pair graphs (WPGs) is proposed to represent a new
reconstructibility definition for Boolean control networks (BCNs), which is a
generalization of the reconstructibility definition given in [Fornasini &
Valcher, TAC2013, Def. 4]. Based on the WPG representation, an effective
algorithm for determining the new reconstructibility notion for BCNs is
designed with the help of the theories of finite automata and formal languages.
We prove that a BCN is not reconstructible iff its WPG has a complete subgraph.
Besides, we prove that a BCN is reconstructible in the sense of [Fornasini &
Valcher, TAC2013, Def. 4] iff its WPG has no cycles, which is simpler to be
checked than the condition in [Fornasini & Valcher, TAC2013, Thm. 4].Comment: 20 pages, 10 figures, accepted by SIAM Journal on Control and
Optimizatio
Algebra, coalgebra, and minimization in polynomial differential equations
We consider reasoning and minimization in systems of polynomial ordinary
differential equations (ode's). The ring of multivariate polynomials is
employed as a syntax for denoting system behaviours. We endow this set with a
transition system structure based on the concept of Lie-derivative, thus
inducing a notion of L-bisimulation. We prove that two states (variables) are
L-bisimilar if and only if they correspond to the same solution in the ode's
system. We then characterize L-bisimilarity algebraically, in terms of certain
ideals in the polynomial ring that are invariant under Lie-derivation. This
characterization allows us to develop a complete algorithm, based on building
an ascending chain of ideals, for computing the largest L-bisimulation
containing all valid identities that are instances of a user-specified
template. A specific largest L-bisimulation can be used to build a reduced
system of ode's, equivalent to the original one, but minimal among all those
obtainable by linear aggregation of the original equations. A computationally
less demanding approximate reduction and linearization technique is also
proposed.Comment: 27 pages, extended and revised version of FOSSACS 2017 pape
Computation of distances for regular and context-free probabilistic languages
Several mathematical distances between probabilistic languages have been investigated in the literature, motivated by applications in language modeling, computational biology, syntactic pattern matching and machine learning. In most cases, only pairs of probabilistic regular languages were considered. In this paper we extend the previous results to pairs of languages generated by a probabilistic context-free grammar and a probabilistic finite automaton.PostprintPeer reviewe
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