420,932 research outputs found
Adaptive Non-singleton Type-2 Fuzzy Logic Systems: A Way Forward for Handling Numerical Uncertainties in Real World Applications
Real world environments are characterized by high levels of linguistic and numerical uncertainties. A Fuzzy Logic System (FLS) is recognized as an adequate methodology to handle the uncertainties and imprecision available in real world environments and applications. Since the invention of fuzzy logic, it has been applied with great success to numerous real world applications such as washing machines, food processors, battery chargers, electrical vehicles, and several other domestic and industrial appliances. The first generation of FLSs were type-1 FLSs in which type-1 fuzzy sets were employed. Later, it was found that using type-2 FLSs can enable the handling of higher levels of uncertainties. Recent works have shown that interval type-2 FLSs can outperform type-1 FLSs in the applications which encompass high uncertainty levels. However, the majority of interval type-2 FLSs handle the linguistic and input numerical uncertainties using singleton interval type-2 FLSs that mix the numerical and linguistic uncertainties to be handled only by the linguistic labels type-2 fuzzy sets. This ignores the fact that if input numerical uncertainties were present, they should affect the incoming inputs to the FLS. Even in the papers that employed non-singleton type-2 FLSs, the input signals were assumed to have a predefined shape (mostly Gaussian or triangular) which might not reflect the real uncertainty distribution which can vary with the associated measurement. In this paper, we will present a new approach which is based on an adaptive non-singleton interval type-2 FLS where the numerical uncertainties will be modeled and handled by non-singleton type-2 fuzzy inputs and the linguistic uncertainties will be handled by interval type-2 fuzzy sets to represent the antecedents’ linguistic labels. The non-singleton type-2 fuzzy inputs are dynamic and they are automatically generated from data and they do not assume a specific shape about the distribution associated with the given sensor. We will present several real world experiments using a real world robot which will show how the proposed type-2 non-singleton type-2 FLS will produce a superior performance to its singleton type-1 and type-2 counterparts when encountering high levels of uncertainties.</jats:p
Multiple imputation for continuous variables using a Bayesian principal component analysis
We propose a multiple imputation method based on principal component analysis
(PCA) to deal with incomplete continuous data. To reflect the uncertainty of
the parameters from one imputation to the next, we use a Bayesian treatment of
the PCA model. Using a simulation study and real data sets, the method is
compared to two classical approaches: multiple imputation based on joint
modelling and on fully conditional modelling. Contrary to the others, the
proposed method can be easily used on data sets where the number of individuals
is less than the number of variables and when the variables are highly
correlated. In addition, it provides unbiased point estimates of quantities of
interest, such as an expectation, a regression coefficient or a correlation
coefficient, with a smaller mean squared error. Furthermore, the widths of the
confidence intervals built for the quantities of interest are often smaller
whilst ensuring a valid coverage.Comment: 16 page
Online Causal Structure Learning in the Presence of Latent Variables
We present two online causal structure learning algorithms which can track
changes in a causal structure and process data in a dynamic real-time manner.
Standard causal structure learning algorithms assume that causal structure does
not change during the data collection process, but in real-world scenarios, it
does often change. Therefore, it is inappropriate to handle such changes with
existing batch-learning approaches, and instead, a structure should be learned
in an online manner. The online causal structure learning algorithms we present
here can revise correlation values without reprocessing the entire dataset and
use an existing model to avoid relearning the causal links in the prior model,
which still fit data. Proposed algorithms are tested on synthetic and
real-world datasets, the latter being a seasonally adjusted commodity price
index dataset for the U.S. The online causal structure learning algorithms
outperformed standard FCI by a large margin in learning the changed causal
structure correctly and efficiently when latent variables were present.Comment: 16 pages, 9 figures, 2 table
Generating Bijections between HOAS and the Natural Numbers
A provably correct bijection between higher-order abstract syntax (HOAS) and
the natural numbers enables one to define a "not equals" relationship between
terms and also to have an adequate encoding of sets of terms, and maps from one
term family to another. Sets and maps are useful in many situations and are
preferably provided in a library of some sort. I have released a map and set
library for use with Twelf which can be used with any type for which a
bijection to the natural numbers exists.
Since creating such bijections is tedious and error-prone, I have created a
"bijection generator" that generates such bijections automatically together
with proofs of correctness, all in the context of Twelf.Comment: In Proceedings LFMTP 2010, arXiv:1009.218
Generalized Multivariate Extreme Value Models for Explicit Route Choice Sets
This paper analyses a class of route choice models with closed-form
probability expressions, namely, Generalized Multivariate Extreme Value (GMEV)
models. A large group of these models emerge from different utility formulas
that combine systematic utility and random error terms. Twelve models are
captured in a single discrete choice framework. The additive utility formula
leads to the known logit family, being multinomial, path-size, paired
combinatorial and link-nested. For the multiplicative formulation only the
multinomial and path-size weibit models have been identified; this study also
identifies the paired combinatorial and link-nested variations, and generalizes
the path-size variant. Furthermore, a new traveller's decision rule based on
the multiplicative utility formula with a reference route is presented. Here
the traveller chooses exclusively based on the differences between routes. This
leads to four new GMEV models. We assess the models qualitatively based on a
generic structure of route utility with random foreseen travel times, for which
we empirically identify that the variance of utility should be different from
thus far assumed for multinomial probit and logit-kernel models. The expected
travellers' behaviour and model-behaviour under simple network changes are
analysed. Furthermore, all models are estimated and validated on an
illustrative network example with long distance and short distance
origin-destination pairs. The new multiplicative models based on differences
outperform the additive models in both tests
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