17,564 research outputs found
The Neural Particle Filter
The robust estimation of dynamically changing features, such as the position
of prey, is one of the hallmarks of perception. On an abstract, algorithmic
level, nonlinear Bayesian filtering, i.e. the estimation of temporally changing
signals based on the history of observations, provides a mathematical framework
for dynamic perception in real time. Since the general, nonlinear filtering
problem is analytically intractable, particle filters are considered among the
most powerful approaches to approximating the solution numerically. Yet, these
algorithms prevalently rely on importance weights, and thus it remains an
unresolved question how the brain could implement such an inference strategy
with a neuronal population. Here, we propose the Neural Particle Filter (NPF),
a weight-less particle filter that can be interpreted as the neuronal dynamics
of a recurrently connected neural network that receives feed-forward input from
sensory neurons and represents the posterior probability distribution in terms
of samples. Specifically, this algorithm bridges the gap between the
computational task of online state estimation and an implementation that allows
networks of neurons in the brain to perform nonlinear Bayesian filtering. The
model captures not only the properties of temporal and multisensory integration
according to Bayesian statistics, but also allows online learning with a
maximum likelihood approach. With an example from multisensory integration, we
demonstrate that the numerical performance of the model is adequate to account
for both filtering and identification problems. Due to the weightless approach,
our algorithm alleviates the 'curse of dimensionality' and thus outperforms
conventional, weighted particle filters in higher dimensions for a limited
number of particles
Entropy of Overcomplete Kernel Dictionaries
In signal analysis and synthesis, linear approximation theory considers a
linear decomposition of any given signal in a set of atoms, collected into a
so-called dictionary. Relevant sparse representations are obtained by relaxing
the orthogonality condition of the atoms, yielding overcomplete dictionaries
with an extended number of atoms. More generally than the linear decomposition,
overcomplete kernel dictionaries provide an elegant nonlinear extension by
defining the atoms through a mapping kernel function (e.g., the gaussian
kernel). Models based on such kernel dictionaries are used in neural networks,
gaussian processes and online learning with kernels.
The quality of an overcomplete dictionary is evaluated with a diversity
measure the distance, the approximation, the coherence and the Babel measures.
In this paper, we develop a framework to examine overcomplete kernel
dictionaries with the entropy from information theory. Indeed, a higher value
of the entropy is associated to a further uniform spread of the atoms over the
space. For each of the aforementioned diversity measures, we derive lower
bounds on the entropy. Several definitions of the entropy are examined, with an
extensive analysis in both the input space and the mapped feature space.Comment: 10 page
Past, Present, and Future of Simultaneous Localization And Mapping: Towards the Robust-Perception Age
Simultaneous Localization and Mapping (SLAM)consists in the concurrent
construction of a model of the environment (the map), and the estimation of the
state of the robot moving within it. The SLAM community has made astonishing
progress over the last 30 years, enabling large-scale real-world applications,
and witnessing a steady transition of this technology to industry. We survey
the current state of SLAM. We start by presenting what is now the de-facto
standard formulation for SLAM. We then review related work, covering a broad
set of topics including robustness and scalability in long-term mapping, metric
and semantic representations for mapping, theoretical performance guarantees,
active SLAM and exploration, and other new frontiers. This paper simultaneously
serves as a position paper and tutorial to those who are users of SLAM. By
looking at the published research with a critical eye, we delineate open
challenges and new research issues, that still deserve careful scientific
investigation. The paper also contains the authors' take on two questions that
often animate discussions during robotics conferences: Do robots need SLAM? and
Is SLAM solved
Sparse Volterra and Polynomial Regression Models: Recoverability and Estimation
Volterra and polynomial regression models play a major role in nonlinear
system identification and inference tasks. Exciting applications ranging from
neuroscience to genome-wide association analysis build on these models with the
additional requirement of parsimony. This requirement has high interpretative
value, but unfortunately cannot be met by least-squares based or kernel
regression methods. To this end, compressed sampling (CS) approaches, already
successful in linear regression settings, can offer a viable alternative. The
viability of CS for sparse Volterra and polynomial models is the core theme of
this work. A common sparse regression task is initially posed for the two
models. Building on (weighted) Lasso-based schemes, an adaptive RLS-type
algorithm is developed for sparse polynomial regressions. The identifiability
of polynomial models is critically challenged by dimensionality. However,
following the CS principle, when these models are sparse, they could be
recovered by far fewer measurements. To quantify the sufficient number of
measurements for a given level of sparsity, restricted isometry properties
(RIP) are investigated in commonly met polynomial regression settings,
generalizing known results for their linear counterparts. The merits of the
novel (weighted) adaptive CS algorithms to sparse polynomial modeling are
verified through synthetic as well as real data tests for genotype-phenotype
analysis.Comment: 20 pages, to appear in IEEE Trans. on Signal Processin
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