213,205 research outputs found
Adaptive approximate Bayesian computation for complex models
Approximate Bayesian computation (ABC) is a family of computational
techniques in Bayesian statistics. These techniques allow to fi t a model to
data without relying on the computation of the model likelihood. They instead
require to simulate a large number of times the model to be fi tted. A number
of re finements to the original rejection-based ABC scheme have been proposed,
including the sequential improvement of posterior distributions. This technique
allows to de- crease the number of model simulations required, but it still
presents several shortcomings which are particu- larly problematic for costly
to simulate complex models. We here provide a new algorithm to perform adaptive
approximate Bayesian computation, which is shown to perform better on both a
toy example and a complex social model.Comment: 14 pages, 5 figure
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
FUTURES-AMR: Towards an Adaptive Mesh Refinement Framework for Geosimulations
Adaptive Mesh Refinement (AMR) is a computational technique used to reduce the amount of computation and memory required in scientific simulations. Geosimulations are scientific simulations using geographic data, routinely used to predict outcomes of urbanization in urban studies. However, the lack of support for AMR techniques with geosimulations limits exploring prediction outcomes at multiple resolutions. In this paper, we propose an adaptive mesh refinement framework FUTURES-AMR, based on static user-defined policies to enable multi-resolution geosimulations. We develop a prototype for the cellular automaton based urban growth simulation FUTURES by exploiting static and dynamic mesh refinement techniques in conjunction with the Patch Growing Algorithm (PGA). While, the static refinement technique supports a statically defined fixed resolution mesh simulation at a location, the dynamic refinement technique supports dynamically refining the resolution based on simulation outcomes at runtime. Further, we develop two approaches - asynchronous AMR and synchronous AMR, suitable for parallel execution in a distributed computing environment with varying support for solution integration of the multi-resolution results. Finally, using the FUTURES-AMR framework with different policies in an urban study, we demonstrate reduced execution time, and low memory overhead for a multi-resolution simulation
On adaptive kernel intensity estimation on linear networks
In the analysis of spatial point patterns on linear networks, a critical
statistical objective is estimating the first-order intensity function,
representing the expected number of points within specific subsets of the
network. Typically, non-parametric approaches employing heating kernels are
used for this estimation. However, a significant challenge arises in selecting
appropriate bandwidths before conducting the estimation. We study an intensity
estimation mechanism that overcomes this limitation using adaptive estimators,
where bandwidths adapt to the data points in the pattern. While adaptive
estimators have been explored in other contexts, their application in linear
networks remains underexplored. We investigate the adaptive intensity estimator
within the linear network context and extend a partitioning technique based on
bandwidth quantiles to expedite the estimation process significantly. Through
simulations, we demonstrate the efficacy of this technique, showing that the
partition estimator closely approximates the direct estimator while drastically
reducing computation time. As a practical application, we employ our method to
estimate the intensity of traffic accidents in a neighbourhood in Medellin,
Colombia, showcasing its real-world relevance and efficiency.Comment: 19 pages, 7 figure
A continuous analogue of the tensor-train decomposition
We develop new approximation algorithms and data structures for representing
and computing with multivariate functions using the functional tensor-train
(FT), a continuous extension of the tensor-train (TT) decomposition. The FT
represents functions using a tensor-train ansatz by replacing the
three-dimensional TT cores with univariate matrix-valued functions. The main
contribution of this paper is a framework to compute the FT that employs
adaptive approximations of univariate fibers, and that is not tied to any
tensorized discretization. The algorithm can be coupled with any univariate
linear or nonlinear approximation procedure. We demonstrate that this approach
can generate multivariate function approximations that are several orders of
magnitude more accurate, for the same cost, than those based on the
conventional approach of compressing the coefficient tensor of a tensor-product
basis. Our approach is in the spirit of other continuous computation packages
such as Chebfun, and yields an algorithm which requires the computation of
"continuous" matrix factorizations such as the LU and QR decompositions of
vector-valued functions. To support these developments, we describe continuous
versions of an approximate maximum-volume cross approximation algorithm and of
a rounding algorithm that re-approximates an FT by one of lower ranks. We
demonstrate that our technique improves accuracy and robustness, compared to TT
and quantics-TT approaches with fixed parameterizations, of high-dimensional
integration, differentiation, and approximation of functions with local
features such as discontinuities and other nonlinearities
Kernel-density estimation and approximate Bayesian computation for flexible epidemiological model fitting in Python
Fitting complex models to epidemiological data is a challenging problem: methodologies can be inaccessible to all but specialists, there may be challenges in adequately describing uncertainty in model fitting, the complex models may take a long time to run, and it can be difficult to fully capture the heterogeneity in the data. We develop an adaptive approximate Bayesian computation scheme to fit a variety of epidemiologically relevant data with minimal hyper-parameter tuning by using an adaptive tolerance scheme. We implement a novel kernel density estimation scheme to capture both dispersed and multi-dimensional data, and directly compare this technique to standard Bayesian approaches. We then apply the procedure to a complex individual-based simulation of lymphatic filariasis, a human parasitic disease. The procedure and examples are released alongside this article as an open access library, with examples to aid researchers to rapidly fit models to data. This demonstrates that an adaptive ABC scheme with a general summary and distance metric is capable of performing model fitting for a variety of epidemiological data. It also does not require significant theoretical background to use and can be made accessible to the diverse epidemiological research community
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