EvoMSN tackles time series forecasting under distribution shifts by evolving multi-scale normalization.
problem Accurate long-term time series forecasting under complex distribution shifts.
method EvoMSN framework with multi-scale statistics prediction and adaptive ensembling for collaborative updating.
result Improves forecasting performance of five mainstream methods on benchmark datasets.
Proves a theorem for normal distributions on manifolds with boundary.
problem Normal distributions on manifolds with boundary require a new approach to integration.
method Introduces neat integral manifolds with boundary and conditions for integrability.
result Conditions for integrability expressed in terms of adapted collars and integrability on interior and boundary.
The paper finds the normal distribution unsuitable for modeling daily stock returns and suggests using the Laplace distribution instead.
problem The difficulty in modeling the distribution of daily stock returns, especially for extreme outliers.
method Investigation of daily stock returns of major indices using both normal and Laplace distributions.
result The normal distribution is not a good model for stock returns, even over long periods of data.
TTF improves performance of normalizing flows for heavy-tailed distributions.
problem Improving performance of normalizing flows for heavy-tailed distributions.
method Uses a Gaussian base distribution and a final transformation layer to produce heavy tails.
result Experimental results show TTF outperforms current methods, especially in high-dimensional or heavy-tailed scenarios.
Gradually Truncated Log-normal distribution - Size distribution of firms Abstract Many natural and economical phenomena are described through power law or log- normal distributions. In these cases, probability decreases very slowly with step size compared to normal distribution. Thus it is essential to cut-off these di…
Researchers study the normalizing constant of a continuous categorical distribution.
problem Understanding the normalizing constant of the continuous categorical distribution.
method Characterize numerical behavior and present theoretical and methodological advances.
result The normalizing constant can be written in closed form using elementary functions.
The paper establishes a correspondence between normal distributions and neat foliations on manifolds with boundary.
problem Understanding normal distributions on manifolds with boundary.
method Develops a theory analogous to Stefan and Sussmann's for integrable distributions, focusing on neat foliations.
result A one-to-one correspondence between neatly integrable normal distributions and neat foliations by manifolds with boundary.
In this paper, we introduce a new sparsity-promoting prior, namely, the "normal product" prior, and develop an efficient algorithm for sparse signal recovery under the Bayesian framework. The normal product distribution is the distribution of a product of two normally distributed variables with zero means and possibly …
Characterizes connections on normal distributions manifold.
problem Geometric characterization of connections on normal distributions.
method Homogeneous statistical manifold structure and Lie group analysis.
result Geometric characterization of α-connections on Lie group. Inference for normal and Monte Carlo distributions using minimum relative entropy.
problem Inference from partial information on expectations and covariances.
method Minimum relative entropy sub-manifolds, analytical formulas, Monte Carlo simulations.
result Improved numerical implementation for inference from partial information.
A new base distribution for normalizing flows allows modeling complex distributions without sacrificing invertibility.
problem Normalizing flows struggle with complex, non-trivial distributions.
method Learned rejection sampling for base distribution, combined with optimization of log-likelihood and Kullback-Leibler divergence.
result The method effectively models complicated distributions without sacrificing invertibility.
Paper proposes using truncated normal distribution for RRC model, improving detection of minority classes.
problem Improving weak classifiers in RRC models.
method Proposes using truncated normal distribution and soft confusion matrix for RRC model.
result Truncated-normal-based SCM algorithm outperforms beta distribution in discovering minority classes.
The study examines the limitations of bi-Lipschitz Normalizing Flows in approximating certain distributions.
problem The expressivity of bi-Lipschitz Normalizing Flows in approximating specific target distributions.
method Characterization of expressivity through lower bounds on Total Variation distance and discussion of potential remedies.
result Several target distributions are difficult to approximate using bi-Lipschitz Normalizing Flows, and lower bounds on their approximation are provided.
Normalizing Flows model tractable distributions for efficient sampling and evaluation.
problem Creating efficient generative models for sampling and density evaluation.
method Construct and use Normalizing Flows to learn distributions.
result Comprehensive review of current Normalizing Flow methods and future directions.
Copula-based normalizing flows improve flexibility and stability for heavy-tailed data.
problem Limited expressive power of vanilla normalizing flows.
method Generalize base distribution to copula for more accurate representation of target distribution.
result Copula-based normalizing flows improve flexibility, stability, and effectiveness for heavy-tailed data.
New distances for comparing multivariate normal distributions.
problem Comparing multivariate normal distributions efficiently and accurately.
method Approximated Fisher-Rao distance and pullback SPD cone distances.
result Efficient computation of distances between normal distributions.
A method for converting NIW parameters for better estimation.
problem Estimating parameters of multivariate normal distribution.
method Convergent procedure for converting mean parameters to natural parameters in NIW family.
result Maximum likelihood estimation of natural parameters from observed statistics.
PL-MCMC samples from normalizing flows' conditional distributions.
problem Sampling from complex conditional distributions learned by normalizing flows.
method Metropolis-Hastings implementation of PL-MCMC.
result PL-MCMC asymptotically samples from exact conditional distributions.
In this study, a numerical quadrature for the generalized inverse Gaussian distribution is derived from the Gauss-Hermite quadrature by exploiting its relationship with the normal distribution. The proposed quadrature is not Gaussian, but it exactly integrates the polynomials of both positive and negative orders. Using…
Piecewise normalizing flows improve multi-modal distribution modeling.
problem Improving accuracy in modeling multi-modal distributions.
method Divide target distribution into clusters, train flows to match standard normal base.
result Piecewise flows outperform standard approaches in accuracy.
Improves NF for complex data distributions with multiple modes.
problem Difficulty in handling data distributions with multiple isolated modes.
method Proposes a new framework using variational latent representation to improve NF.
result Significantly more powerful for generating data distributions with multiple modes.
New path-gradient estimator for continuous normalizing flows.
problem Limitation of simple Gaussian variational distributions in complex applications.
method Proposed a path-gradient estimator for continuous normalizing flows.
result Empirical evidence of superior performance of the new estimator.
The paper defines MTCov for skewed elliptical distributions.
problem No specific problem stated, but dealing with skewed elliptical distributions.
method Defined MTCov for generalized skew-elliptical distributions and compared with skewed and non-skewed normal distributions.
result Special formula for MTCov of generalized skew-elliptical distributions.
Derives pricing formulae for power binary and normal distribution standard options.
problem Developing pricing models for binary and standard options.
method Incorporates Buchen's formulae into power binary options and derives a formula for normal distribution standard options.
result Derives pricing formulae for power binary and normal distribution standard options.
Employing profits data of Japanese firms in 2003--2005, we kinematically exhibit the static log-normal distribution in the middle scale region. In the derivation, a Non-Gibrat's law under the detailed balance is adopted together with following two approximations. Firstly, the probability density function of profits gro…
Under a generalized skew normal distribution we consider the problem of European option pricing. Existence of the martingale measure is proved. An explicit expression for a given European option price is presented in terms of the cumulative distribution function of the univariate skew normal and the bivariate standard …
Entropy corrections improve GBM's predictive accuracy for non-log-normal distributions.
problem Log-normal distribution limitations in GBM predictions.
method Entropy corrections to geometric Brownian motion (GBM).
result Improved predictive accuracy for non-log-normal distributions.
New formulae identify discrete probability laws without needing normalization constants.
problem Characterizing non-normalized discrete probability distributions.
method Derive explicit formulae for mass functions using Stein's method.
result Developed tools for solving statistical problems without normalization constants.
Paper proposes efficient method to calculate Fisher-Bingham distribution normalizing constant.
problem Efficiently calculating the normalizing constant of Fisher-Bingham distributions.
method Numerical integration with continuous Euler transform to Fourier-type integral representation.
result The method is fast and accurate, applicable to high-dimensional distributions.
Paper improves normalizing flows to better capture distribution tails.
problem Difficult to learn tail behavior of distributions.
method Develops a new type of flows using flexible base distributions and data-driven linear layers.
result Improves accuracy, especially on distribution tails, and generates heavy-tailed data.
Calculation of the log-normalizer is a major computational obstacle in applications of log-linear models with large output spaces. The problem of fast normalizer computation has therefore attracted significant attention in the theoretical and applied machine learning literature. In this paper, we analyze a recently pro…
Evidential Softmax preserves multimodality in sparse probability distributions for generative models.
problem Sparse probability distributions in deep generative models make exact marginalization computationally intractable.
method Introduce ev-softmax, a sparse normalization function that preserves multimodality and can be trained with probabilistic loss functions.
result ev-softmax outperforms existing techniques in distributional accuracy and dimensionality reduction.
Develops methods for integrating multivariate normals and computing classification measures.
problem Computing performance of multivariate normal models is challenging due to lack of general analytical expressions.
method Mathematical results and open-source software for integrating and analyzing multivariate normal distributions.
result Provides tools for calculating classification errors, discriminability, and reliability.
New extensions for homogeneous distributions on deformations to the normal cone.
problem Extending homogeneous distributions on a specific geometric structure.
method Using the zoom action and Meyer's results on weakly homogeneous distributions.
result All homogeneous extensions of distributions on the DNC are described.
Inverts operator on hyperbolic surfaces, constructing invariant distributions.
problem Constructing explicit inversion formula for X-ray normal operator.
method First, inversion formula for attenuated normal operator on Poincaré disk and closed hyperbolic surfaces. Then, explicit construction of invariant distributions.
result Explicit construction of invariant distributions with prescribed pushforward.
Optimizes recommendation models using skew normal distribution.
problem Improving personalized recommendation systems.
method Develops a new optimization criterion based on skew normal distribution.
result Significantly outperforms state-of-the-art models.
Local normal forms for symmetrical contact structures on 3-manifolds.
problem Understanding symmetrical contact structures on 3-manifolds.
method Determining local normal forms for pairs of transverse contact distributions with symmetries.
result Orientable Anosov flows can be globally represented by intersecting contact distributions with maximal symmetries.
New method uses G-expectation for financial risk measurement.
problem Measuring uncertainty in financial time series.
method Introducing G-normal distribution, applying max-mean estimators, and using autoregressive models.
result G-VaR model outperforms other VaR predictors in risk prediction.
Characterizes connections on multivariate normal distributions.
problem Characterizing connections on statistical manifold of multivariate normal distributions.
method Analyzes statistical manifold (N,gF,ablaA,ablaA∗) of multivariate normal distributions. result The Amari-Chentsov connection ablaA is characterized by conjugate symmetry. The paper proposes deep normalization to improve speaker recognition performance.
problem Non-Gaussian and non-homogeneous distributions of deep speaker vectors negatively impact speaker recognition.
method Proposes a deep normalization approach based on a novel discriminative normalization flow (DNF) model.
result DNF-based normalization delivers substantial performance gains and strong generalization capability.
A new Heckman selection model uses a bivariate contaminated normal distribution for more accurate data analysis.
problem Sample selection biases in econometric data analysis.
method Introduces a Heckman selection model using a bivariate contaminated normal distribution and presents an efficient ECM algorithm for parameter estimation.
result The proposed model outperforms normal and Student's t counterparts in real data analysis and simulation studies.
Improves data normality with robust transformations.
problem Skewed data distribution.
method Modified Box-Cox and Yeo-Johnson transformations with robust parameter estimation.
result Transformed data approximates normality in the center with outliers.
New method uses batch normalization to improve OoD detection.
problem Out-of-distribution samples are not reliably detected by generative models.
method Proposes exploiting in-batch dependencies for OoD detection.
result Empirical results show improved robustness for high-dimensional images.
New normalizing flows for sphere distributions improve complexity and scale handling.
problem No straightforward normalizing flows for Fisher-Bingham distributions in higher dimensions.
method Zoom-linear-project (ZLP)-Fisher flows that gradually add complexity and handle varying scales.
result Generalizes Fisher-Bingham distributions to normalizing flows in any dimension.
Constructs portfolios based on Hellinger distance to normal, finding market invariance.
problem Finding a market invariant for portfolio construction.
method Uses Hellinger distance to normal distribution for portfolio construction and analysis.
result Minimum Hellinger distance varies drastically between markets, suggesting market invariance.
New framework explains normalizing flows' power and limitations.
problem Understanding the expressive power and limitations of normalizing flows.
method Theoretical framework for well-conditioned coupling-based normalizing flows and volume-preserving flows.
result RealNVP is distributionally universal, but volume-preserving flows are not.
In one dimension, the theory of the G-normal distribution is well-developed, and many results from the classical setting have a nonlinear counterpart. Significant challenges remain in multiple dimensions, and some of what has already been discovered is quite nonintuitive. By answering several classically-inspired que…
Normal distributions ensure asymptotic variance reduction in moment matching Monte Carlo.
problem Asymptotic variance reduction in general integration problems.
method Characterization of conditions for asymptotic variance reduction using normal distributions.
result Asymptotic variance reduction is guaranteed for normal distributions in moment matching Monte Carlo.