29 research outputs found
Variational approach for learning Markov processes from time series data
Inference, prediction and control of complex dynamical systems from time
series is important in many areas, including financial markets, power grid
management, climate and weather modeling, or molecular dynamics. The analysis
of such highly nonlinear dynamical systems is facilitated by the fact that we
can often find a (generally nonlinear) transformation of the system coordinates
to features in which the dynamics can be excellently approximated by a linear
Markovian model. Moreover, the large number of system variables often change
collectively on large time- and length-scales, facilitating a low-dimensional
analysis in feature space. In this paper, we introduce a variational approach
for Markov processes (VAMP) that allows us to find optimal feature mappings and
optimal Markovian models of the dynamics from given time series data. The key
insight is that the best linear model can be obtained from the top singular
components of the Koopman operator. This leads to the definition of a family of
score functions called VAMP-r which can be calculated from data, and can be
employed to optimize a Markovian model. In addition, based on the relationship
between the variational scores and approximation errors of Koopman operators,
we propose a new VAMP-E score, which can be applied to cross-validation for
hyper-parameter optimization and model selection in VAMP. VAMP is valid for
both reversible and nonreversible processes and for stationary and
non-stationary processes or realizations
Distributed Algorithms for Learning and Cognitive Medium Access with Logarithmic Regret
The problem of distributed learning and channel access is considered in a
cognitive network with multiple secondary users. The availability statistics of
the channels are initially unknown to the secondary users and are estimated
using sensing decisions. There is no explicit information exchange or prior
agreement among the secondary users. We propose policies for distributed
learning and access which achieve order-optimal cognitive system throughput
(number of successful secondary transmissions) under self play, i.e., when
implemented at all the secondary users. Equivalently, our policies minimize the
regret in distributed learning and access. We first consider the scenario when
the number of secondary users is known to the policy, and prove that the total
regret is logarithmic in the number of transmission slots. Our distributed
learning and access policy achieves order-optimal regret by comparing to an
asymptotic lower bound for regret under any uniformly-good learning and access
policy. We then consider the case when the number of secondary users is fixed
but unknown, and is estimated through feedback. We propose a policy in this
scenario whose asymptotic sum regret which grows slightly faster than
logarithmic in the number of transmission slots.Comment: Submitted to IEEE JSAC on Advances in Cognitive Radio Networking and
Communications, Dec. 2009, Revised May 201
A two-level Markov model for packet loss in UDP/IP-based real-time video applications targeting residential users
The packet loss characteristics of Internet paths that include residential broadband links are not well understood, and there are no good models for their behaviour. This compli- cates the design of real-time video applications targeting home users, since it is difficult to choose appropriate error correction and concealment algorithms without a good model for the types of loss observed. Using measurements of residential broadband networks in the UK and Finland, we show that existing models for packet loss, such as the Gilbert model and simple hidden Markov models, do not effectively model the loss patterns seen in this environment. We present a new two-level Markov model for packet loss that can more accurately describe the characteristics of these links, and quantify the effectiveness of this model. We demonstrate that our new packet loss model allows for improved application design, by using it to model the performance of forward error correction on such links
Multi-Satellite DVB-RCS System with RCST based on Software Defined Radio
Abstract-Multi-mode satellite terminals are actually the most desired devices on the market, thanks to their flexibility and suitability. A multi-mode radio communication terminal is a terminal allowing two or more transmission mode. In the last few years many research resources have been invested in the study of this new type of terminal. In this work, we define a multi-mode terminal as a terminal capable of communicating both with a Bent-Pipe (BP) satellite and with an On-Board Processor (OBP) satellite and dynamically setting its transmission parameters (e.g. transmission power and code rate). In order to realize this multimode functionality, the most suitable technology is the Software Defined Radio (SDR). The SDR is a set of Hardware and Software technologies that allow one to obtain reconfigurable architectures for network and wireless terminals. The goal of our work is to plan a satellite system based on Digital Video Broadcast with the Return Channel Satellite (DVB-RCS) standard in which the Return Channel Satellite Terminals (RCSTs) are able to adapt it to the channel state, configuring the transmission chain via software, respecting a certain Quality of Service (QoS) constraint on the Packet Error Rate (PER)
Deep learning Markov and Koopman models with physical constraints
The long-timescale behavior of complex dynamical systems can be described by
linear Markov or Koopman models in a suitable latent space. Recent variational
approaches allow the latent space representation and the linear dynamical model
to be optimized via unsupervised machine learning methods. Incorporation of
physical constraints such as time-reversibility or stochasticity into the
dynamical model has been established for a linear, but not for arbitrarily
nonlinear (deep learning) representations of the latent space. Here we develop
theory and methods for deep learning Markov and Koopman models that can bear
such physical constraints. We prove that the model is an universal approximator
for reversible Markov processes and that it can be optimized with either
maximum likelihood or the variational approach of Markov processes (VAMP). We
demonstrate that the model performs equally well for equilibrium and
systematically better for biased data compared to existing approaches, thus
providing a tool to study the long-timescale processes of dynamical systems