723 research outputs found
A Practical Method to Estimate Information Content in the Context of 4D-Var Data Assimilation. I: Methodology
Data assimilation obtains improved estimates of the state of a physical system
by combining imperfect model results with sparse and noisy observations of reality.
Not all observations used in data assimilation are equally valuable. The ability to
characterize the usefulness of different data points is important for analyzing the
effectiveness of the assimilation system, for data pruning, and for the design of future
sensor systems.
This paper focuses on the four dimensional variational (4D-Var) data assimilation
framework. Metrics from information theory are used to quantify the contribution
of observations to decreasing the uncertainty with which the system state is known.
We establish an interesting relationship between different information-theoretic metrics
and the variational cost function/gradient under Gaussian linear assumptions.
Based on this insight we derive an ensemble-based computational procedure to estimate
the information content of various observations in the context of 4D-Var. The
approach is illustrated on linear and nonlinear test problems. In the companion paper
[Singh et al.(2011)] the methodology is applied to a global chemical data assimilation
problem
Throughput-Distortion Computation Of Generic Matrix Multiplication: Toward A Computation Channel For Digital Signal Processing Systems
The generic matrix multiply (GEMM) function is the core element of
high-performance linear algebra libraries used in many
computationally-demanding digital signal processing (DSP) systems. We propose
an acceleration technique for GEMM based on dynamically adjusting the
imprecision (distortion) of computation. Our technique employs adaptive scalar
companding and rounding to input matrix blocks followed by two forms of packing
in floating-point that allow for concurrent calculation of multiple results.
Since the adaptive companding process controls the increase of concurrency (via
packing), the increase in processing throughput (and the corresponding increase
in distortion) depends on the input data statistics. To demonstrate this, we
derive the optimal throughput-distortion control framework for GEMM for the
broad class of zero-mean, independent identically distributed, input sources.
Our approach converts matrix multiplication in programmable processors into a
computation channel: when increasing the processing throughput, the output
noise (error) increases due to (i) coarser quantization and (ii) computational
errors caused by exceeding the machine-precision limitations. We show that,
under certain distortion in the GEMM computation, the proposed framework can
significantly surpass 100% of the peak performance of a given processor. The
practical benefits of our proposal are shown in a face recognition system and a
multi-layer perceptron system trained for metadata learning from a large music
feature database.Comment: IEEE Transactions on Signal Processing (vol. 60, 2012
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