The Experts below are selected from a list of 40176 Experts worldwide ranked by ideXlab platform

Rafal Weron - One of the best experts on this subject based on the ideXlab platform.

Joanna Janczura - One of the best experts on this subject based on the ideXlab platform.

  • ci_powertail Matlab Function to test for dragon kings vs black swans
    HSC Software, 2012
    Co-Authors: Joanna Janczura, Rafal Weron
    Abstract:

    [CI_LO,CI_HI]=CI_POWERTAIL(DATA,ALPHA,TAIL) calculates confidence intervals of significance level ALPHA for a power law fitted to the right tail of the empirical distrubution Function (edf) of the observations in DATA. Only observations lying in the interval [TAIL(1)-quantile of DATA,TAIL(2)-quantile of DATA] are used to obtain the least squares fit. CI_POWERTAIL(DATA,ALPHA,TAIL,CLT) allows to choose between the exact but slower to compute (binomial law based; CLT=0) and asymptotic (Gaussian law based; CLT=1, default) confidence intervals. CI_POWERTAIL(DATA,ALPHA,TAIL,CLT,1) plots the power law and the intervals in the current figure. Observations lying outside the curves spanned by the confidence intervals are likely to be (i.e. with probability 1-ALPHA) 'dragon kings', i.e. deviations from power law events (commonly known as 'black swans'). Note, that Taleb (2007) calls these 'tractable scientifically' events 'Mandelbrotian gray swans', to distinguish them from the 'totally intractable' black swans.

  • ci_weibulltail Matlab Function to test for dragon kings in weibull type tails
    HSC Software, 2012
    Co-Authors: Joanna Janczura, Rafal Weron
    Abstract:

    [CI_LO,CI_HI]=CI_WEIBULLTAIL(DATA,ALPHA,TAIL) calculates confidence intervals of significance level ALPHA for a Weibull law (i.e. a stretched exponential law) fitted to the right tail of the empirical distrubution Function (edf) of the observations in DATA. Only observations lying in the interval [TAIL(1)-quantile of DATA,TAIL(2)-quantile of DATA] are used to obtain the least squares fit. CI_WEIBULLTAIL(DATA,ALPHA,TAIL,CLT) allows to choose between the exact but slower to compute (binomial law based; CLT=0) and asymptotic (Gaussian law based; CLT=1, default) confidence intervals. CI_WEIBULLTAIL(DATA,ALPHA,TAIL,CLT,1) plots the Weibull law and the intervals in the current figure. Observations lying outside the curves spanned by the confidence intervals are likely to be (i.e. with probability 1-ALPHA) 'dragon kings', i.e. deviations from Weibull law.

  • e_hmm Matlab Function to calculate electromagnetic field emf intensity using a hidden markov model hmm filter
    HSC Software, 2012
    Co-Authors: Joanna Janczura, Rafal Weron
    Abstract:

    E=E_HMM(DATA) returns the EMF intensity calculated for the EMF vector in DATA. E_HMM(DATA,PLOT,FREQ,D) additionally allows to plot (PLOT=1) the filtering results for frequencies FREQ and panel specified by D (D=0 for the central panel, D=1 for the left panel, D=2 for the right panel).

  • mrs3ir_est Matlab Function to estimate parameters of a markov regime switching mrs model with 3 independent regimes
    Research Papers in Economics, 2011
    Co-Authors: Joanna Janczura, Rafal Weron
    Abstract:

    [KSI_TT,PARAM,P]=MRS3IR_EST(DATA,MODEL) returns smoothed inferences KSI_TT, estimated parameters PARAM and transition matrix P of a Markov regime-switching (MRS) model with 3 independent regimes: (i) an AR(1) process in the base regime X(t+1)=phi_1*X(t)+c_1+sigma_1*|X(t)|^g_1*N(0,1), (ii) a Gaussian (MODEL='G'), lognormal ('LN'), Pareto ('P'), Weibull ('W') or exponential ('E') distributed spike regime, (iii) and a shifted 'inverse lognormal' price drop regime, fitted to time series DATA. The first column (KSI_TT) or row (PARAM, P) contains results for the base regime, the second column/row for the spike regime and the third column/row for the drop regime.

  • ps2r_est Matlab Function to estimate parameters of a 2 regime parameter switching ps model
    Research Papers in Economics, 2011
    Co-Authors: Joanna Janczura, Rafal Weron
    Abstract:

    [KSI_TT,PARAM,P]=PS2R_EST(DATA) returns smoothed inferences KSI_TT, estimated parameters PARAM and transition matrix P of a 2-regime parameter switching (PS) model, i.e. a 2-regime Markov regime-switching (MRS) model with both regimes driven by AR(1) processes of the form: X(t+1)=phi_i*X(t)+c_i+sigma_i*|X(t)|^g_i*N(0,1). The first column (KSI_TT) or row (PARAM, P) contains results for the base regime and the second column/row for the spike regime.

Pranesh Srikara - One of the best experts on this subject based on the ideXlab platform.

  • Random Matrices Generating Large Growth in LU Factorization with Pivoting
    2020
    Co-Authors: Higham, Desmond J., Higham, Nicholas J., Pranesh Srikara
    Abstract:

    We identify a class of random, dense $n\times n$ matrices for which LU factorization with any form of pivoting produces a growth factor typically of size at least $n/(4 \log n)$ for large $n$. The condition number of the matrices can be arbitrarily chosen and large growth also happens for the transpose. No previous matrices with all these properties were known. The matrices can be generated by the Matlab Function \verb"gallery('randsvd',..)", and they are formed as the product of two random orthogonal matrices from the Haar distribution with a diagonal matrix having only one diagonal entry different from $1$, which lies between $0$ and $1$ (the ``one small singular value'' case). Our explanation for the large growth uses the fact that the maximum absolute value of any element of a Haar distributed orthogonal matrix tends to be relatively small for large $n$. We verify the behavior numerically, finding that for partial pivoting the actual growth is significantly larger than the lower bound, and much larger than the growth observed for random matrices with elements from the uniform $[0,1$] or standard normal distributions. We show more generally that a rank-$1$ perturbation to an orthogonal matrix producing large growth for any form of pivoting also generates large growth under reasonable assumptions. Finally, we demonstrate that GMRES-based iterative refinement can provide stable solutions to $Ax = b$ when large growth occurs in low precision LU factors, even when standard iterative refinement cannot

  • Random Matrices Generating Large Growth in LU Factorization with Pivoting
    2020
    Co-Authors: Higham, Desmond J., Higham, Nicholas J., Pranesh Srikara
    Abstract:

    We identify a class of random, dense $n\times n$ matrices for which LU factorization with any form of pivoting produces a growth factor of at least $n/(4 \log n)$ for large $n$ with high probability. The condition number of the matrices can be arbitrarily chosen and large growth also happens for the transpose. No previous matrices with all these properties were known. The matrices can be generated by the Matlab Function \verb"gallery('randsvd',..)", and they are formed as the product of two random orthogonal matrices from the Haar distribution with a diagonal matrix having only one diagonal entry different from $1$, which lies between $0$ and $1$ (the ``one small singular value'' case). Our explanation for the large growth uses the fact that the maximum absolute value of any element of a Haar distributed orthogonal matrix tends to be relatively small for large $n$. We verify the behavior numerically, finding that for partial pivoting the actual growth is significantly larger than the lower bound, and much larger than the growth observed for random matrices with elements from the uniform $[0,1$] or standard normal distributions. We show more generally that a rank-$1$ perturbation to an orthogonal matrix producing large growth for any form of pivoting also generates large growth under reasonable assumptions. Finally, we demonstrate that GMRES-based iterative refinement can provide stable solutions to $Ax = b$ when large growth occurs in low precision LU factors, even when standard iterative refinement cannot

  • SIMULATING LOW PRECISION FLOATING-POINT ARITHMETIC
    2019
    Co-Authors: Higham, Nicholas J., Pranesh Srikara
    Abstract:

    The half precision (fp16) floating-point format, defined in the 2008 revision of the IEEE standard for floating-point arithmetic, and a more recently proposed half precision format bfloat16, are increasingly available in GPUs and other accelerators. While the support for low precision arithmetic is mainly motivated by machine learning applications, general purpose numerical algorithms can benefit from it, too, gaining in speed, energy usage, and reduced communication costs. Since the appropriate hardware is not always available, and one may wish to experiment with new arithmetics not yet implemented in hardware, software simulations of low precision arithmetic are needed. We discuss how to simulate low precision arithmetic using arithmetic of higher precision. We examine the correctness of such simulations and explain via rounding error analysis why a natural method of simulation can provide results that are more accurate than actual computations at low precision. We provide a Matlab Function chop that can be used to efficiently simulate fp16, bfloat16, and other low precision arithmetics, with or without the representation of subnormal numbers and with the options of round to nearest, directed rounding, stochastic rounding, and random bit flips in the significand. We demonstrate the advantages of this approach over defining a new Matlab class and overloading operators

  • SIMULATING LOW PRECISION FLOATING-POINT ARITHMETIC
    2019
    Co-Authors: Higham, Nicholas J., Pranesh Srikara
    Abstract:

    The half precision (fp16) floating-point format, defined in the 2008 revision of the IEEE standard for floating-point arithmetic, and a more recently proposed half precision format bfloat16, are increasingly available in GPUs and other accelerators. While the support for low precision arithmetic is mainly motivated by machine learning applications, general purpose numerical algorithms can benefit from it, too, gaining in speed, energy usage, and reduced communication costs. Since the appropriate hardware is not always available, and one may wish to experiment with new arithmetics not yet implemented in hardware, software simulations of low precision arithmetic are needed. We discuss how to simulate low precision arithmetic using arithmetic of higher precision. We examine the correctness of such simulations and explain via rounding error analysis why a natural method of simulation can provide results that are more accurate than actual computations at low precision. We provide a Matlab Function chop that can be used to efficiently simulate fp16 and bfloat16 arithmetics, with or without the representation of subnormal numbers and with the options of round to nearest, directed rounding, stochastic rounding, and random bit flips in the significand. We demonstrate the advantages of this approach over defining a new Matlab class and overloading operators

Rafał Weron - One of the best experts on this subject based on the ideXlab platform.

Higham, Nicholas J. - One of the best experts on this subject based on the ideXlab platform.

  • Random Matrices Generating Large Growth in LU Factorization with Pivoting
    2020
    Co-Authors: Higham, Desmond J., Higham, Nicholas J., Pranesh Srikara
    Abstract:

    We identify a class of random, dense $n\times n$ matrices for which LU factorization with any form of pivoting produces a growth factor typically of size at least $n/(4 \log n)$ for large $n$. The condition number of the matrices can be arbitrarily chosen and large growth also happens for the transpose. No previous matrices with all these properties were known. The matrices can be generated by the Matlab Function \verb"gallery('randsvd',..)", and they are formed as the product of two random orthogonal matrices from the Haar distribution with a diagonal matrix having only one diagonal entry different from $1$, which lies between $0$ and $1$ (the ``one small singular value'' case). Our explanation for the large growth uses the fact that the maximum absolute value of any element of a Haar distributed orthogonal matrix tends to be relatively small for large $n$. We verify the behavior numerically, finding that for partial pivoting the actual growth is significantly larger than the lower bound, and much larger than the growth observed for random matrices with elements from the uniform $[0,1$] or standard normal distributions. We show more generally that a rank-$1$ perturbation to an orthogonal matrix producing large growth for any form of pivoting also generates large growth under reasonable assumptions. Finally, we demonstrate that GMRES-based iterative refinement can provide stable solutions to $Ax = b$ when large growth occurs in low precision LU factors, even when standard iterative refinement cannot

  • Random Matrices Generating Large Growth in LU Factorization with Pivoting
    2020
    Co-Authors: Higham, Desmond J., Higham, Nicholas J., Pranesh Srikara
    Abstract:

    We identify a class of random, dense $n\times n$ matrices for which LU factorization with any form of pivoting produces a growth factor of at least $n/(4 \log n)$ for large $n$ with high probability. The condition number of the matrices can be arbitrarily chosen and large growth also happens for the transpose. No previous matrices with all these properties were known. The matrices can be generated by the Matlab Function \verb"gallery('randsvd',..)", and they are formed as the product of two random orthogonal matrices from the Haar distribution with a diagonal matrix having only one diagonal entry different from $1$, which lies between $0$ and $1$ (the ``one small singular value'' case). Our explanation for the large growth uses the fact that the maximum absolute value of any element of a Haar distributed orthogonal matrix tends to be relatively small for large $n$. We verify the behavior numerically, finding that for partial pivoting the actual growth is significantly larger than the lower bound, and much larger than the growth observed for random matrices with elements from the uniform $[0,1$] or standard normal distributions. We show more generally that a rank-$1$ perturbation to an orthogonal matrix producing large growth for any form of pivoting also generates large growth under reasonable assumptions. Finally, we demonstrate that GMRES-based iterative refinement can provide stable solutions to $Ax = b$ when large growth occurs in low precision LU factors, even when standard iterative refinement cannot

  • SIMULATING LOW PRECISION FLOATING-POINT ARITHMETIC
    2019
    Co-Authors: Higham, Nicholas J., Pranesh Srikara
    Abstract:

    The half precision (fp16) floating-point format, defined in the 2008 revision of the IEEE standard for floating-point arithmetic, and a more recently proposed half precision format bfloat16, are increasingly available in GPUs and other accelerators. While the support for low precision arithmetic is mainly motivated by machine learning applications, general purpose numerical algorithms can benefit from it, too, gaining in speed, energy usage, and reduced communication costs. Since the appropriate hardware is not always available, and one may wish to experiment with new arithmetics not yet implemented in hardware, software simulations of low precision arithmetic are needed. We discuss how to simulate low precision arithmetic using arithmetic of higher precision. We examine the correctness of such simulations and explain via rounding error analysis why a natural method of simulation can provide results that are more accurate than actual computations at low precision. We provide a Matlab Function chop that can be used to efficiently simulate fp16, bfloat16, and other low precision arithmetics, with or without the representation of subnormal numbers and with the options of round to nearest, directed rounding, stochastic rounding, and random bit flips in the significand. We demonstrate the advantages of this approach over defining a new Matlab class and overloading operators

  • SIMULATING LOW PRECISION FLOATING-POINT ARITHMETIC
    2019
    Co-Authors: Higham, Nicholas J., Pranesh Srikara
    Abstract:

    The half precision (fp16) floating-point format, defined in the 2008 revision of the IEEE standard for floating-point arithmetic, and a more recently proposed half precision format bfloat16, are increasingly available in GPUs and other accelerators. While the support for low precision arithmetic is mainly motivated by machine learning applications, general purpose numerical algorithms can benefit from it, too, gaining in speed, energy usage, and reduced communication costs. Since the appropriate hardware is not always available, and one may wish to experiment with new arithmetics not yet implemented in hardware, software simulations of low precision arithmetic are needed. We discuss how to simulate low precision arithmetic using arithmetic of higher precision. We examine the correctness of such simulations and explain via rounding error analysis why a natural method of simulation can provide results that are more accurate than actual computations at low precision. We provide a Matlab Function chop that can be used to efficiently simulate fp16 and bfloat16 arithmetics, with or without the representation of subnormal numbers and with the options of round to nearest, directed rounding, stochastic rounding, and random bit flips in the significand. We demonstrate the advantages of this approach over defining a new Matlab class and overloading operators