1,082 research outputs found
Modeling a Sensor to Improve its Efficacy
Robots rely on sensors to provide them with information about their
surroundings. However, high-quality sensors can be extremely expensive and
cost-prohibitive. Thus many robotic systems must make due with lower-quality
sensors. Here we demonstrate via a case study how modeling a sensor can improve
its efficacy when employed within a Bayesian inferential framework. As a test
bed we employ a robotic arm that is designed to autonomously take its own
measurements using an inexpensive LEGO light sensor to estimate the position
and radius of a white circle on a black field. The light sensor integrates the
light arriving from a spatially distributed region within its field of view
weighted by its Spatial Sensitivity Function (SSF). We demonstrate that by
incorporating an accurate model of the light sensor SSF into the likelihood
function of a Bayesian inference engine, an autonomous system can make improved
inferences about its surroundings. The method presented here is data-based,
fairly general, and made with plug-and play in mind so that it could be
implemented in similar problems.Comment: 18 pages, 8 figures, submitted to the special issue of "Sensors for
Robotics
Quantum computers can search arbitrarily large databases by a single query
This paper shows that a quantum mechanical algorithm that can query
information relating to multiple items of the database, can search a database
in a single query (a query is defined as any question to the database to which
the database has to return a (YES/NO) answer). A classical algorithm will be
limited to the information theoretic bound of at least O(log N) queries (which
it would achieve by using a binary search).Comment: Several enhancements to the original pape
Maximum Joint Entropy and Information-Based Collaboration of Automated Learning Machines
We are working to develop automated intelligent agents, which can act and
react as learning machines with minimal human intervention. To accomplish this,
an intelligent agent is viewed as a question-asking machine, which is designed
by coupling the processes of inference and inquiry to form a model-based
learning unit. In order to select maximally-informative queries, the
intelligent agent needs to be able to compute the relevance of a question. This
is accomplished by employing the inquiry calculus, which is dual to the
probability calculus, and extends information theory by explicitly requiring
context. Here, we consider the interaction between two question-asking
intelligent agents, and note that there is a potential information redundancy
with respect to the two questions that the agents may choose to pose. We show
that the information redundancy is minimized by maximizing the joint entropy of
the questions, which simultaneously maximizes the relevance of each question
while minimizing the mutual information between them. Maximum joint entropy is
therefore an important principle of information-based collaboration, which
enables intelligent agents to efficiently learn together.Comment: 8 pages, 1 figure, to appear in the proceedings of MaxEnt 2011 held
in Waterloo, Canad
The Spatial Sensitivity Function of a Light Sensor
The Spatial Sensitivity Function (SSF) is used to quantify a detector's
sensitivity to a spatially-distributed input signal. By weighting the incoming
signal with the SSF and integrating, the overall scalar response of the
detector can be estimated. This project focuses on estimating the SSF of a
light intensity sensor consisting of a photodiode. This light sensor has been
used previously in the Knuth Cyberphysics Laboratory on a robotic arm that
performs its own experiments to locate a white circle in a dark field (Knuth et
al., 2007). To use the light sensor to learn about its surroundings, the
robot's inference software must be able to model and predict the light sensor's
response to a hypothesized stimulus. Previous models of the light sensor
treated it as a point sensor and ignored its spatial characteristics. Here we
propose a parametric approach where the SSF is described by a mixture of
Gaussians (MOG). By performing controlled calibration experiments with known
stimulus inputs, we used nested sampling to estimate the SSF of the light
sensor using an MOG model with the number of Gaussians ranging from one to
five. By comparing the evidence computed for each MOG model, we found that one
Gaussian is sufficient to describe the SSF to the accuracy we require. Future
work will involve incorporating this more accurate SSF into the Bayesian
machine learning software for the robotic system and studying how this detailed
information about the properties of the light sensor will improve robot's
ability to learn.Comment: Published in MaxEnt 200
Origins of the Combinatorial Basis of Entropy
The combinatorial basis of entropy, given by Boltzmann, can be written , where is the dimensionless entropy, is the
number of entities and is number of ways in which a given
realization of a system can occur (its statistical weight). This can be
broadened to give generalized combinatorial (or probabilistic) definitions of
entropy and cross-entropy: and , where is the probability of a given
realization, is a convenient transformation function, is a
scaling parameter and an arbitrary constant. If or
satisfy the multinomial weight or distribution, then using
and , and asymptotically
converge to the Shannon and Kullback-Leibler functions. In general, however,
or need not be multinomial, nor may they approach an
asymptotic limit. In such cases, the entropy or cross-entropy function can be
{\it defined} so that its extremization ("MaxEnt'' or "MinXEnt"), subject to
the constraints, gives the ``most probable'' (``MaxProb'') realization of the
system. This gives a probabilistic basis for MaxEnt and MinXEnt, independent of
any information-theoretic justification.
This work examines the origins of the governing distribution ....
(truncated)Comment: MaxEnt07 manuscript, version 4 revise
Origin of Complex Quantum Amplitudes and Feynman's Rules
Complex numbers are an intrinsic part of the mathematical formalism of
quantum theory, and are perhaps its most mysterious feature. In this paper, we
show that the complex nature of the quantum formalism can be derived directly
from the assumption that a pair of real numbers is associated with each
sequence of measurement outcomes, with the probability of this sequence being a
real-valued function of this number pair. By making use of elementary symmetry
conditions, and without assuming that these real number pairs have any other
algebraic structure, we show that these pairs must be manipulated according to
the rules of complex arithmetic. We demonstrate that these complex numbers
combine according to Feynman's sum and product rules, with the modulus-squared
yielding the probability of a sequence of outcomes.Comment: v2: Clarifications, and minor corrections and modifications. Results
unchanged. v3: Minor changes to introduction and conclusio
Formalizing Size-Optimal Sorting Networks: Extracting a Certified Proof Checker
Since the proof of the four color theorem in 1976, computer-generated proofs
have become a reality in mathematics and computer science. During the last
decade, we have seen formal proofs using verified proof assistants being used
to verify the validity of such proofs.
In this paper, we describe a formalized theory of size-optimal sorting
networks. From this formalization we extract a certified checker that
successfully verifies computer-generated proofs of optimality on up to 8
inputs. The checker relies on an untrusted oracle to shortcut the search for
witnesses on more than 1.6 million NP-complete subproblems.Comment: IMADA-preprint-c
Improved quantum algorithms for the ordered search problem via semidefinite programming
One of the most basic computational problems is the task of finding a desired
item in an ordered list of N items. While the best classical algorithm for this
problem uses log_2 N queries to the list, a quantum computer can solve the
problem using a constant factor fewer queries. However, the precise value of
this constant is unknown. By characterizing a class of quantum query algorithms
for ordered search in terms of a semidefinite program, we find new quantum
algorithms for small instances of the ordered search problem. Extending these
algorithms to arbitrarily large instances using recursion, we show that there
is an exact quantum ordered search algorithm using 4 log_{605} N \approx 0.433
log_2 N queries, which improves upon the previously best known exact algorithm.Comment: 8 pages, 4 figure
Bayesian Evidence and Model Selection
In this paper we review the concepts of Bayesian evidence and Bayes factors,
also known as log odds ratios, and their application to model selection. The
theory is presented along with a discussion of analytic, approximate and
numerical techniques. Specific attention is paid to the Laplace approximation,
variational Bayes, importance sampling, thermodynamic integration, and nested
sampling and its recent variants. Analogies to statistical physics, from which
many of these techniques originate, are discussed in order to provide readers
with deeper insights that may lead to new techniques. The utility of Bayesian
model testing in the domain sciences is demonstrated by presenting four
specific practical examples considered within the context of signal processing
in the areas of signal detection, sensor characterization, scientific model
selection and molecular force characterization.Comment: Arxiv version consists of 58 pages and 9 figures. Features theory,
numerical methods and four application
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