We propose a novel algebraic framework for treating probability distributions represented by their cumulants such as the mean and covariance matrix. As an example, we consider the unsupervised learning problem of finding the subspace on which several probability distributions agree. Instead of minimizing an objective f…
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48 results for “cumulative probability distribution”
We study the rank distribution, the cumulative probability, and the probability density of returns of stock prices of listed firms traded in four stock markets. We find that the rank distribution and the cumulative probability of stock prices traded in are consistent approximately with the Zipf's law or a power law. It…
In this paper we study the volatility and its probability distribution function for the cumulative production based on the experience curve hypothesis. This work presents a generalization of the study of volatility in [1], which addressed the effects of normally distributed noise in the production process. Due to its w…
Zipf's Law Distributions for Korean Stock Pricescond-mat.stat-mech
This paper investigates the rank distribution, cumulative probability, and probability density of price returns for the stocks traded in the KSE and the KOSDAQ market. This research demonstrates that the rank distribution is consistent approximately with the Zipf's law with exponent (KSE) and -1.31 (KOSDAQ),…
Conventional multiclass conditional probability estimation methods, such as Fisher's discriminate analysis and logistic regression, often require restrictive distributional model assumption. In this paper, a model-free estimation method is proposed to estimate multiclass conditional probability through a series of cond…
ECOD detects outliers without parameters, fast and simple.
problem Detecting outliers in large, high-dimensional datasets efficiently and interpretably.
method ECOD estimates empirical cumulative distribution functions per dimension, then computes tail probabilities and outlier scores.
result ECOD outperforms state-of-the-art methods in accuracy, efficiency, and scalability.
Paper converts quantiles to cumulative distribution functions to simplify risk measures.
problem Technical assumptions in risk measure calculations.
method Invention of converting integrated quantiles to integrated cumulative distribution functions.
result Avoids the need for probability density function existence.
New method corrects bias in datasets using cumulative distribution functions.
problem Varying domains and biased datasets lead to differences between training and target distributions.
method Empirical cumulative distribution function estimates of the target distribution, rigorously generalized.
result Method is more robust, not reliant on parameter tuning, and performs similarly to state-of-the-art techniques.
The paper evaluates functions of stable Lévy processes and their extrema efficiently.
problem Efficiently evaluating functions of stable Lévy processes and their extrema.
method Integral representations, conformal acceleration technique, simplified trapezoid rule.
result Efficient numerical procedures for cumulative probability distribution functions (cpdfs) are developed.
Response of Firm Agent Network to Exogenous Shockphysics.soc-ph
This paper describes an agent-based model of interacting firms, in which interacting firm agents rationally invest capital and labor in order to maximize payoff. Both transactions and production are taken into account in this model. First, the performance of individual firms on a real transaction network was simulated.…
The paper develops methods to predict the probability of achieving a user goal in a task, ensuring the system alerts when the probability falls below a threshold.
problem Ensuring an autonomous system achieves the user's goal with calibrated probability estimates.
method Invertible conformal prediction using Probability-space Conformalized Quantile Regression (PCQR) to produce well-calibrated conditional prediction intervals.
result The method produces well-calibrated probabilities that the cumulative reward will fall within a user-specified target interval, with finite-sample guarantees.
Directed acyclic graphs (DAGs) are a popular framework to express multivariate probability distributions. Acyclic directed mixed graphs (ADMGs) are generalizations of DAGs that can succinctly capture much richer sets of conditional independencies, and are especially useful in modeling the effects of latent variables im…
Power Law Distributions in Korean Household Incomescond-mat.stat-mech
We investigate the distribution function and the cumulative probability for Korean household incomes, i.e., the current, labor, and property incomes. For our case, the distribution functions are consistent with a power law. It is also showed that the probability density of income growth rates almost has the form of a e…
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 method calibrates classifier probabilities with guaranteed coverage.
problem Inaccurate probability estimates by classifiers in high-risk applications.
method Adaptive temperature scaling algorithm for conformal prediction.
result Improves calibration error measures and standard metrics across various tasks.
The probability distribution of stock price changes is studied by analyzing a database (the Trades and Quotes Database) documenting every trade for all stocks in three major US stock markets, for the two year period Jan 1994 -- Dec 1995. A sample of 40 million data points is extracted, which is substantially larger tha…
Method determines credit transition matrix from cumulative default probabilities.
problem Quantifying changes in bond credit ratings.
method Setup an ill-posed, linear inverse problem with entropy minimization.
result Method successfully determines CTM from cumulative default probabilities.
Motivated by the need for parametric families of rich and yet tractable distributions in financial mathematics, both in pricing and risk management settings, but also considering wider statistical applications, we investigate a novel technique for introducing skewness or kurtosis into a symmetric or other distribution.…
Asymptotic behavior of the Daily Increment Distribution of the IPC, the Mexican Stock Market Indexcond-mat.other
In this work, a statistical analysis of the distribution of daily fluctuations of the IPC, the Mexican Stock Market Index is presented. A sample of the IPC covering the 13-year period 04/19/1990 - 08/21/2003 was analyzed and the cumulative probability distribution of its daily logarithmic variations studied. Results sh…
Algorithm infers sampling distribution from i.i.d. samples without supervision.
problem Learning probability distributions from unlabeled data.
method Unsupervised tree boosting using additive tree ensembles and new distributional operations.
result Algorithm outperforms deep learning in multivariate density estimation.
The paper introduces a spline-based method for calibrating neural networks.
problem Ensuring neural network outputs are reliable for safety-critical applications.
method Approximating the empirical cumulative distribution function using splines to map network outputs to calibrated probabilities.
result The spline-based recalibration consistently outperforms existing methods on calibration measures.
Bayesian methods improve inference for cumulative probit models on large datasets.
problem Challenges in Bayesian inference for large cumulative probit models.
method Proposed scalable algorithms using Variational Bayes and Expectation Propagation.
result Superior computational performance and accuracy compared to MCMC.
New scoring rules for multivariate distributions and level sets.
problem Evaluating forecast accuracy for multivariate distributions and level sets.
method Theoretical framework for scoring rules, decomposition of multivariate scoring functions, numerical algorithm for computation.
result New scoring functions for multivariate distributions and level sets, including density and cumulative distribution level sets.
We present a new distributed fuzzy partitioning method to reduce the complexity of multi-way fuzzy decision trees in Big Data classification problems. The proposed algorithm builds a fixed number of fuzzy sets for all variables and adjusts their shape and position to the real distribution of training data. A two-step p…
We present a novel modulation level classification (MLC) method based on probability distribution distance functions. The proposed method uses modified Kuiper and Kolmogorov-Smirnov distances to achieve low computational complexity and outperforms the state of the art methods based on cumulants and goodness-of-fit test…
We study the volume distribution of nodal domains of random band-limited functions on generic manifolds, and find that in the high energy limit a typical instance obeys a deterministic universal law, independent of the manifold. Some of the basic qualitative properties of this law, such as its support, monotonicity and…
Online distributional prediction with latent cluster geometry
problem Predicting the full data-generating distribution in non-stationary streams
method Representing candidate laws as latent cluster geometry and using Gibbs quasi-posterior
result Achieving sublinear cumulative Wasserstein regret under bounded support and stable latent geometry
This paper proposes an active learning-based Gaussian process (AL-GP) metamodelling method to estimate the cumulative as well as complementary cumulative distribution function (CDF/CCDF) for forward uncertainty quantification (UQ) problems. Within the field of UQ, previous studies focused on developing AL-GP approaches…
This work tackles multivariate CDFs and copulas using tensor factorization.
problem Learning multivariate distributions, especially for mixed random variables, is challenging.
method Introducing a low-rank model for efficient sampling, inference, and uncertainty quantification.
result The proposed model outperforms traditional methods in various applications.
Optimizes risk-neutral probabilities for derivative pricing.
problem Deriving bounds on derivative values under multiple risk-neutral scenarios.
method Convex optimization over the set of risk-neutral probability distributions.
result Tractable finite-dimensional optimization problems for pricing.
New algorithms minimize simple and cumulative regret in contextual bandits.
problem Minimizing simple and cumulative regret in contextual bandit settings.
method Proposed new algorithms using conformal arm sets (CASs).
result Near-optimal minimax guarantees for simple regret and state-of-the-art guarantees for cumulative regret.
This work studies the chord length distribution, in the case where both ends lie on a -dimensional hypersphere (). Actually, after connecting this distribution to the recently estimated surface of a hyperspherical cap \cite{SLi11}, closed-form expressions of both the probability density function and the cu…
In this paper we revisit the integral functional of geometric Brownian motion , where , , and is a standard Brownian motion. Specifically, we calculate the Laplace transform in of the cumulative distribution function and of the probability density …
Unified approach to tensor PCA and related problems using tensor cumulants.
problem Statistical inference on invariant distributions, particularly tensor PCA.
method Definition and analysis of tensor cumulants to unify and extend previous results.
result Unified explanation of hardness and subexponential-time algorithms for tensor PCA.
We investigate the probability distribution of the volatility return intervals for the Chinese stock market. We rescale both the probability distribution and the volatility return intervals as to obtain a uniform scaling curve for different threshold value . The scali…
We propose a correlated stochastic process of which the novel non-Gaussian probability mass function is constructed by exactly solving moment generating function. The calculation of cumulants and auto-correlation shows that the process is convergent and scale invariant in the large but finite number limit. We demonstra…
The identification of relevant features, i.e., the driving variables that determine a process or the properties of a system, is an essential part of the analysis of data sets with a large number of variables. A mathematical rigorous approach to quantifying the relevance of these features is mutual information. Mutual i…
The paper develops approximations for Pearson's chi-square statistic and applies them to confidence intervals.
problem Finding confidence intervals for strictly convex functions of discrete distribution weights.
method Non-asymptotic local normal approximation for multinomial probabilities, deriving bounds and coupling inequalities.
result Developed methods to find confidence intervals for negative entropy of discrete distributions.
A new pseudo-metric uses data depth to compare probability distributions.
problem Designing a metric between probability distributions for machine learning applications.
method Extension of univariate quantiles to multivariate spaces, using data depth and Hausdorff distance.
result The pseudo-metric is robust, factorizes translations, and has good behavior under transformations.
Paper introduces symmetric divergence link models for probability distributions.
problem Symmetric divergence measures for probability distributions.
method Two general classes of link models: one for survival functions and another for cumulative probability distribution functions.
result Advantages of symmetric divergence measures over asymmetric measures for model averaging and feature assessment.
In this work we present an analytical model, based on the path-integral formalism of Statistical Mechanics, for pricing options using first-passage time problems involving both fixed and deterministically moving absorbing barriers under possible non-gaussian distributions of the underlying object. We adapt to our probl…
The paper calculates bounds for risk metrics and entropies under partial information constraints.
problem Analyzing risk metrics and entropies for unimodal, symmetric distributions with limited information.
method Develops lower and upper bounds for worst-case distortion riskmetrics and weighted entropy for unimodal, symmetric distributions with known mean and variance.
result Sharp upper bounds for distortion riskmetrics and weighted entropy for symmetric distributions.
A new graphical method compares stochastic variables visually.
problem Comparing non-deterministic measurements visually.
method Cumulative distribution function dominance measure and quantile decomposition.
result Additional conclusions missed by other methods can be inferred.
Estimates financial market impacts of COVID-19 using time-varying kernel density.
problem Estimating the impact of COVID-19 on financial markets over time.
method Time-varying kernel density estimation with Kolmogorov-Smirnov statistic.
result Determines the chronology and regional disparities of financial market impacts.
Bayesian sequence prediction is a simple technique for predicting future symbols sampled from an unknown measure on infinite sequences over a countable alphabet. While strong bounds on the expected cumulative error are known, there are only limited results on the distribution of this error. We prove tight high-probabil…
The paper simulates Lévy processes and their extremum and hitting time.
problem Simulating Lévy processes and their extremum and hitting time accurately and efficiently.
method Using characteristic functions and conditional characteristic functions, with conformal deformations and precalculated values on multi-grids.
result Accurate and fast simulation of Lévy processes and their extremum and hitting time.
New approach to Generalized Beta family using SDEs.
problem Understanding the Generalized Beta family of distributions.
method Using a mean-reverting SDE for a power of the variable, leading to a modified GB distribution.
result Provides alternative forms and cumulative distribution functions for GB distributions.
Estimates MLP expected output without sampling, using fewer FLOPs.
problem Estimating expected loss in machine learning efficiently.
method Approximate representations of activations using cumulants and Hermite expansions.
result Estimates expected output with fewer FLOPs than Monte Carlo sampling.