We propose a new blind source separation algorithm based on mixtures of alpha-stable distributions. Complex symmetric alpha-stable distributions have been recently showed to better model audio signals in the time-frequency domain than classical Gaussian distributions thanks to their larger dynamic range. However, infer…
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29 results for “alpha-stable”
Withdrawal Success Estimationq-fin.MF
Upper bound on withdrawal success for geometric Levy alpha-stable wealth process.
problem Estimating the probability of completing a withdrawal schedule.
method Constructing a log-Levy alpha-stable lower bound and applying it to a schedule of withdrawals.
result Necessary conditions on initial investment and parameters for a 95% confidence of completing withdrawals.
We consider a statistical model for pairs of traded assets, based on a Cointegrated Vector Auto Regression (CVAR) Model. We extend standard CVAR models to incorporate estimation of model parameters in the presence of price series level shifts which are not accurately modeled in the standard Gaussian error correction mo…
The study assesses how financial markets' efficiency changed during the COVID-19 crisis.
problem The impact of COVID-19 on financial market efficiency.
method Dynamic estimation method for Hurst exponent and memory parameter using alpha-stable distribution and dependence structure.
result Financial markets' efficiency varied during the COVID-19 crisis, with some indices showing less impact than others.
This paper focuses on single-channel semi-supervised speech enhancement. We learn a speaker-independent deep generative speech model using the framework of variational autoencoders. The noise model remains unsupervised because we do not assume prior knowledge of the noisy recording environment. In this context, our con…
This paper applies Thompson Sampling to asymmetric -stable bandits for financial and wireless data.
problem Optimizing exploration-exploitation in multi-armed bandits with asymmetric -stable distributions.
method Thompson Sampling applied to unknown asymmetric -stable reward distributions.
result Demonstrates effectiveness of Thompson Sampling for asymmetric -stable bandits.
Adaptive estimation of alpha-Stable distribution and Hurst exponent for nonstationary time series.
problem Nonstationary time series require adaptive models to avoid bias.
method Moving estimator with exponentially weakening weights of old values, optimized using EMA of absolute central moments.
result Continuous adaptive estimation of alpha-Stable distribution and Hurst exponent for market stability evaluation.
On non-negative solutions of stochastic Volterra equations with jumps and non-Lipschitz coefficientsmath.PR
Study on non-negative solutions for stochastic Volterra equations with jumps.
problem Existence and uniqueness of non-negative solutions for stochastic Volterra equations with jumps and non-Lipschitz coefficients.
method Developed a nonnegative approximation approach and used Yamada--Watanabe approximation technique for convergence proof.
result Established conditions for strong existence and pathwise uniqueness of non-negative solutions.
A new distribution family extends the -stable distribution with a degree of freedom parameter.
problem Lack of moments in the -stable distribution.
method Wright function framework to combine and extend distribution families.
result Generalized -stable distribution with valid moments.
Under the Basel II standards, the Operational Risk (OpRisk) advanced measurement approach is not prescriptive regarding the class of statistical model utilised to undertake capital estimation. It has however become well accepted to utlise a Loss Distributional Approach (LDA) paradigm to model the individual OpRisk loss…
It has long been agreed by academics that the inversion method is the method of choice for generating random variates, given the availability of the quantile function. However for several probability distributions arising in practice a satisfactory method of approximating these functions is not available. The main focu…
Soft diamond regularizers improve deep learning performance and sparsity.
problem Improving deep learning performance and sparsity of trained weights.
method New soft diamond synaptic weight priors based on thick-tailed symmetric alpha stable probability curves.
result Soft diamond regularizers outperform state-of-the-art methods in deep learning tasks.
We develop a modelling framework for multiple yield curves driven by continuous-state branching processes with immigration (CBI processes). Exploiting the self-exciting behavior of CBI jump processes, this approach can reproduce the relevant empirical features of spreads between different interbank rates. In particular…
This paper models cryptocurrencies using -stable distributions, outperforming other models.
problem Modeling the highly speculative and leptokurtic nature of cryptocurrencies.
method Used -stable distribution and compared it with other heavy tailed distributions. Employed maximum likelihood method for estimation.
result The -stable distribution fits cryptocurrency return data better than other models.
The total value of domestic market capitalization of the Mexican Stock Exchange was calculated at 520 billion of dollars by the end of November 2013. To manage this system and make optimum capital investments, its dynamics needs to be predicted. However, randomness within the stock indexes makes forecasting a difficult…
A fast method for estimating radar amplitude density parameters.
problem Accurate estimation of amplitude density function parameters in radar applications.
method Projecting amplitude data onto horizontal and vertical axes, then using MLE for -stale distribution parameters.
result The average of computed MLEs based on two projections is a fast and accurate estimator for amplitude distribution parameters.
The paper tackles drift identification in Lévy α-stable stochastic systems, proposing a Fourier space approach.
problem Estimating the drift field of a stochastic differential equation driven by Lévy α-stable noise.
method Fourier space approach, parameterizing the drift field using Fourier series, minimizing a loss function with gradients computed via the adjoint method.
result The method is capable of learning drift fields in qualitative and/or quantitative agreement with ground truth fields.
Efficient CNN-LSTM based Parameter Estimation of Levy Driven Stochastic Differential Equationsstat.ML
Study improves parameter estimation for SDEs driven by Levy noise.
problem Challenges in estimating parameters of SDEs with non-Gaussian noises.
method Introduces PEnet, a CNN-LSTM model for efficient parameter estimation.
result PEnet offers superior accuracy and adaptability for various SDE scenarios.
MAFLA improves sampling from heavy-tailed distributions using MH-inspired corrections.
problem Sampling from heavy-tailed and multimodal distributions when neither target nor proposal densities can be evaluated.
method Metropolis-Adjusted Fractional Langevin Algorithm (MAFLA) with Score Balance Matching.
result MAFLA significantly improves finite-time sampling accuracy over unadjusted fractional Langevin dynamics.
Study analyzes fluctuations in Mexican financial market index.
problem Understanding intra-day fluctuations in Mexican financial market index.
method Statistical analysis of high frequency tick-to-tick data, temporal aggregation, and comparison of distributions.
result Intra-day fluctuations do not follow alpha-stable distributions, suggesting autocorrelations.
Neural time-series data contain a wide variety of prototypical signal waveforms (atoms) that are of significant importance in clinical and cognitive research. One of the goals for analyzing such data is hence to extract such 'shift-invariant' atoms. Even though some success has been reported with existing algorithms, t…
This work extracts stochastic dynamical systems with -stable Lévy noise.
problem Extracting data-driven governing laws of dynamical systems with non-Gaussian noise.
method End-to-end deep learning approach for learning drift and diffusion coefficients for -stable Lévy noise.
result Effectiveness of the method confirmed by numerical experiments.
Paper proposes a self-supervised method to denoise autoregressive signals with heavy-tailed noise.
problem Denoising autoregressive signals corrupted by heavy-tailed noise.
method Self-supervised learning approach without requiring full noise distribution knowledge.
result Strong denoising performance compared to baseline methods, especially for impulsive noise.
Stochastic calculus for uncoupled continuous-time random walkscond-mat.stat-mech
The continuous-time random walk (CTRW) is a pure-jump stochastic process with several applications in physics, but also in insurance, finance and economics. A definition is given for a class of stochastic integrals driven by a CTRW, that includes the Ito and Stratonovich cases. An uncoupled CTRW with zero-mean jumps is…
Data-driven discovery of "hidden physics" -- i.e., machine learning of differential equation models underlying observed data -- has recently been approached by embedding the discovery problem into a Gaussian Process regression of spatial data, treating and discovering unknown equation parameters as hyperparameters of a…
The Bayesian Bridgestat.ME
We propose the Bayesian bridge estimator for regularized regression and classification. Two key mixture representations for the Bayesian bridge model are developed: (1) a scale mixture of normals with respect to an alpha-stable random variable; and (2) a mixture of Bartlett--Fejer kernels (or triangle densities) with r…
A neural network estimates sampling distributions for hard problems where classical methods fail.
problem Bootstrap failure in estimating sampling distributions for specific statistics.
method Neural network trained on simulated datasets using pinball loss.
result Neural network attains 95% nominal coverage and 97% improvement over classical methods on four bootstrap-failure problems.
Under the Basel II standards, the Operational Risk (OpRisk) advanced measurement approach allows a provision for reduction of capital as a result of insurance mitigation of up to 20%. This paper studies the behaviour of different insurance policies in the context of capital reduction for a range of possible extreme los…
The paper analyzes Kernel Density Estimation in high dimensions with varying data and dimensionality.
problem High-dimensional Kernel Density Estimation with growing data and dimensionality.
method Examines the behavior of Kernel Density Estimators in the regime where both data points and dimensionality grow with a fixed ratio.
result Three distinct statistical regimes are identified for Kernel-based density estimates, each with different statistical properties.