6,058 research outputs found
The OS* Algorithm: a Joint Approach to Exact Optimization and Sampling
Most current sampling algorithms for high-dimensional distributions are based
on MCMC techniques and are approximate in the sense that they are valid only
asymptotically. Rejection sampling, on the other hand, produces valid samples,
but is unrealistically slow in high-dimension spaces. The OS* algorithm that we
propose is a unified approach to exact optimization and sampling, based on
incremental refinements of a functional upper bound, which combines ideas of
adaptive rejection sampling and of A* optimization search. We show that the
choice of the refinement can be done in a way that ensures tractability in
high-dimension spaces, and we present first experiments in two different
settings: inference in high-order HMMs and in large discrete graphical models.Comment: 21 page
A Nonparametric Bayesian Approach to Uncovering Rat Hippocampal Population Codes During Spatial Navigation
Rodent hippocampal population codes represent important spatial information
about the environment during navigation. Several computational methods have
been developed to uncover the neural representation of spatial topology
embedded in rodent hippocampal ensemble spike activity. Here we extend our
previous work and propose a nonparametric Bayesian approach to infer rat
hippocampal population codes during spatial navigation. To tackle the model
selection problem, we leverage a nonparametric Bayesian model. Specifically, to
analyze rat hippocampal ensemble spiking activity, we apply a hierarchical
Dirichlet process-hidden Markov model (HDP-HMM) using two Bayesian inference
methods, one based on Markov chain Monte Carlo (MCMC) and the other based on
variational Bayes (VB). We demonstrate the effectiveness of our Bayesian
approaches on recordings from a freely-behaving rat navigating in an open field
environment. We find that MCMC-based inference with Hamiltonian Monte Carlo
(HMC) hyperparameter sampling is flexible and efficient, and outperforms VB and
MCMC approaches with hyperparameters set by empirical Bayes
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
On the Performance of Short Block Codes over Finite-State Channels in the Rare-Transition Regime
As the mobile application landscape expands, wireless networks are tasked
with supporting different connection profiles, including real-time traffic and
delay-sensitive communications. Among many ensuing engineering challenges is
the need to better understand the fundamental limits of forward error
correction in non-asymptotic regimes. This article characterizes the
performance of random block codes over finite-state channels and evaluates
their queueing performance under maximum-likelihood decoding. In particular,
classical results from information theory are revisited in the context of
channels with rare transitions, and bounds on the probabilities of decoding
failure are derived for random codes. This creates an analysis framework where
channel dependencies within and across codewords are preserved. Such results
are subsequently integrated into a queueing problem formulation. For instance,
it is shown that, for random coding on the Gilbert-Elliott channel, the
performance analysis based on upper bounds on error probability provides very
good estimates of system performance and optimum code parameters. Overall, this
study offers new insights about the impact of channel correlation on the
performance of delay-aware, point-to-point communication links. It also
provides novel guidelines on how to select code rates and block lengths for
real-time traffic over wireless communication infrastructures
Discriminative Segmental Cascades for Feature-Rich Phone Recognition
Discriminative segmental models, such as segmental conditional random fields
(SCRFs) and segmental structured support vector machines (SSVMs), have had
success in speech recognition via both lattice rescoring and first-pass
decoding. However, such models suffer from slow decoding, hampering the use of
computationally expensive features, such as segment neural networks or other
high-order features. A typical solution is to use approximate decoding, either
by beam pruning in a single pass or by beam pruning to generate a lattice
followed by a second pass. In this work, we study discriminative segmental
models trained with a hinge loss (i.e., segmental structured SVMs). We show
that beam search is not suitable for learning rescoring models in this
approach, though it gives good approximate decoding performance when the model
is already well-trained. Instead, we consider an approach inspired by
structured prediction cascades, which use max-marginal pruning to generate
lattices. We obtain a high-accuracy phonetic recognition system with several
expensive feature types: a segment neural network, a second-order language
model, and second-order phone boundary features
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