1,756 research outputs found
Online Natural Gradient as a Kalman Filter
We cast Amari's natural gradient in statistical learning as a specific case
of Kalman filtering. Namely, applying an extended Kalman filter to estimate a
fixed unknown parameter of a probabilistic model from a series of observations,
is rigorously equivalent to estimating this parameter via an online stochastic
natural gradient descent on the log-likelihood of the observations.
In the i.i.d. case, this relation is a consequence of the "information
filter" phrasing of the extended Kalman filter. In the recurrent (state space,
non-i.i.d.) case, we prove that the joint Kalman filter over states and
parameters is a natural gradient on top of real-time recurrent learning (RTRL),
a classical algorithm to train recurrent models.
This exact algebraic correspondence provides relevant interpretations for
natural gradient hyperparameters such as learning rates or initialization and
regularization of the Fisher information matrix.Comment: 3rd version: expanded intr
Observing and Verifying the Quantum Trajectory of a Mechanical Resonator
Continuous weak measurement allows localizing open quantum systems in state
space, and tracing out their quantum trajectory as they evolve in time.
Efficient quantum measurement schemes have previously enabled recording quantum
trajectories of microwave photon and qubit states. We apply these concepts to a
macroscopic mechanical resonator, and follow the quantum trajectory of its
motional state conditioned on a continuous optical measurement record. Starting
with a thermal mixture, we eventually obtain coherent states of 78%
purity--comparable to a displaced thermal state of occupation 0.14. We
introduce a retrodictive measurement protocol to directly verify state purity
along the trajectory, and furthermore observe state collapse and decoherence.
This opens the door to measurement-based creation of advanced quantum states,
and potential tests of gravitational decoherence models.Comment: 20 pages, 4 figure
Probabilistic Methodology and Techniques for Artefact Conception and Development
The purpose of this paper is to make a state of the art on probabilistic methodology and techniques for artefact conception and development. It is the 8th deliverable of the BIBA (Bayesian Inspired Brain and Artefacts) project. We first present the incompletness problem as the central difficulty that both living creatures and artefacts have to face: how can they perceive, infer, decide and act efficiently with incomplete and uncertain knowledge?. We then introduce a generic probabilistic formalism called Bayesian Programming. This formalism is then used to review the main probabilistic methodology
and techniques. This review is organized in 3 parts: first the probabilistic models from Bayesian networks to Kalman filters and from sensor fusion to CAD systems, second the inference techniques and finally the learning and model acquisition and comparison methodologies. We conclude with the perspectives of the BIBA project as they rise from this state of the art
The Constant Information Radar
abstract: The constant information radar, or CIR, is a tracking radar that modulates target revisit time by maintaining a fixed mutual information measure. For highly dynamic targets that deviate significantly from the path predicted by the tracking motion model, the CIR adjusts by illuminating the target more frequently than it would for well-modeled targets. If SNR is low, the radar delays revisit to the target until the state entropy overcomes noise uncertainty. As a result, we show that the information measure is highly dependent on target entropy and target measurement covariance. A constant information measure maintains a fixed spectral efficiency to support the RF convergence of radar and communications. The result is a radar implementing a novel target scheduling algorithm based on information instead of heuristic or ad hoc methods. The CIR mathematically ensures that spectral use is justified
Finite-time thermodynamics of port-Hamiltonian systems
In this paper, we identify a class of time-varying port-Hamiltonian systems
that is suitable for studying problems at the intersection of statistical
mechanics and control of physical systems. Those port-Hamiltonian systems are
able to modify their internal structure as well as their interconnection with
the environment over time. The framework allows us to prove the First and
Second laws of thermodynamics, but also lets us apply results from optimal and
stochastic control theory to physical systems. In particular, we show how to
use linear control theory to optimally extract work from a single heat source
over a finite time interval in the manner of Maxwell's demon. Furthermore, the
optimal controller is a time-varying port-Hamiltonian system, which can be
physically implemented as a variable linear capacitor and transformer. We also
use the theory to design a heat engine operating between two heat sources in
finite-time Carnot-like cycles of maximum power, and we compare those two heat
engines.Comment: To appear in Physica D (accepted July 2013
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