Proposes logistic-beta process for modeling dependent probabilities with beta marginals.
problem Limited work on flexible and computationally convenient stochastic process extensions for dependent random probabilities.
method Introduces logistic-beta process with logistic transformation and beta marginals, capable of modeling dependence in discrete and continuous domains.
result Logistic-beta processes enable effective posterior inference and design of computationally tractable dependent Bayesian nonparametric models.
Study examines time-varying betas and their volatility in bank interest income and expense margins.
problem Understanding the variability of bank betas and their impact on net interest margins.
method Used state-space methods to estimate time-varying betas and conditional volatility.
result Substantial variation in interest income and expense betas, leading to varying net interest margin coefficients.
The paper improves conformal prediction by analyzing the beta law of conditional coverage.
problem Improving finite-sample marginal coverage guarantees for non-i.i.d. data.
method The method uses Wasserstein distances to quantify deviations from the beta law of conditional coverage.
result The framework provides direct bounds on marginal coverage gaps and bad-calibration probabilities.
A beta-negative binomial (BNB) process is proposed, leading to a beta-gamma-Poisson process, which may be viewed as a "multi-scoop" generalization of the beta-Bernoulli process. The BNB process is augmented into a beta-gamma-gamma-Poisson hierarchical structure, and applied as a nonparametric Bayesian prior for an infi…
Beta diffusion generates bounded data using multiplicative transitions.
problem Generating data within specific ranges.
method Integrates demasking and denoising with scaled and shifted beta distributions.
result KLUBs are more effective for optimizing beta diffusion compared to negative ELBOs.
Study efficient algorithms for one-shot federated conformal prediction.
problem Valid prediction sets in one-shot federated learning.
method Quantile-of-quantiles family of estimators and split conformal prediction.
result No significant loss in coverage and length compared to centralized setting.
A method to compute divergences between decomposable models, useful in supervised learning.
problem Computing exact divergences between high-dimensional distributions is intractable.
method Proposes an approach to compute exact alpha-beta divergences between marginal and conditional distributions of decomposable models.
result Tractable computation of marginal and conditional alpha-beta divergences.
Paper proposes a new uncertainty measure for active learning in neural networks.
problem Efficiently selecting informative data points in limited labeled data scenarios.
method BalEntAcq, a new uncertainty measure based on balanced entropy, approximated by Beta distributions.
result BalEntAcq outperforms existing uncertainty measures in active learning.
The beta-negative binomial process (BNBP), an integer-valued stochastic process, is employed to partition a count vector into a latent random count matrix. As the marginal probability distribution of the BNBP that governs the exchangeable random partitions of grouped data has not yet been developed, current inference f…
The study tests a functional-form restriction on risk exposure dynamics using margin debt data.
problem Understanding risk exposure dynamics under capital constraints and slack.
method Testing a regime-conditional functional-form restriction on aggregate risk-exposure dynamics implied by VaR-constrained intermediary models.
result The contraction and growth of exposures under capital constraints and slack are observed and tested.
Group factor analysis (GFA) methods have been widely used to infer the common structure and the group-specific signals from multiple related datasets in various fields including systems biology and neuroimaging. To date, most available GFA models require Gibbs sampling or slice sampling to perform inference, which prev…
Proposes a new factor to improve BAB strategies by recognizing bad-beta assets.
problem Investors often misprice assets based on beta, ignoring bad-beta.
method Double-sorting on beta and bad-beta to create a new factor.
result The Betting Against Bad Beta factor improves BAB strategies.
New f-Betas for portfolio optimization using f-divergence risk measures.
problem Optimizing portfolio performance under varying market conditions.
method Derive f-Betas and Hellinger-Betas, using f-divergence risk measures.
result Demonstrated new Beta metrics provide better performance under stress.
New method for interpreting non-linear models using forward marginal effects.
problem Interpreting non-linear models' feature effects is challenging.
method Introducing forward marginal effects and partitioning feature space for better interpretation.
result Improved interpretation of non-linear prediction functions.
The seemingly disjoint problems of count and mixture modeling are united under the negative binomial (NB) process. A gamma process is employed to model the rate measure of a Poisson process, whose normalization provides a random probability measure for mixture modeling and whose marginalization leads to an NB process f…
Machine learning improves beta forecasts, enhancing equity valuation and portfolio performance.
problem Improving beta forecasts for better equity valuation and portfolio performance.
method Using machine learning on a large cross-section of US stocks with various firm characteristics.
result Machine learning improves out-of-sample performance of asymmetric beta measures.
The beta-Bernoulli process provides a Bayesian nonparametric prior for models involving collections of binary-valued features. A draw from the beta process yields an infinite collection of probabilities in the unit interval, and a draw from the Bernoulli process turns these into binary-valued features. Recent work has …
We show that the stick-breaking construction of the beta process due to Paisley, et al. (2010) can be obtained from the characterization of the beta process as a Poisson process. Specifically, we show that the mean measure of the underlying Poisson process is equal to that of the beta process. We use this underlying re…
In this paper, the geometric meaning of (alpha,beta)-norms is made clear. On this basis, we introduce a new class of Finsler metrics called general (alpha,beta)-metrics, which are defined by a Riemannian metric and an 1-form. These metrics not only generalize original (alpha,beta)-metrics naturally, but also include so…
Study beta function for convex billiard maps, linking spectral invariants.
problem Understanding spectral invariants of convex billiard maps.
method Birkhoff normal form via constructive generating functions, explicit beta function formula.
result Linked spectral invariants to beta function for convex billiard maps.
Beta-SOD detects and corrects noisy object re-identification using cosine similarity and Beta mixtures.
problem Noisy object re-identification in image datasets.
method Reframed Re-ID as a similarity task, using Siamese networks and Beta mixture models.
result Superior performance in noisy conditions compared to state-of-the-art methods.
We present a reactive beta model that includes the leverage effect to allow hedge fund managers to target a near-zero beta for market neutral strategies. For this purpose, we derive a metric of correlation with leverage effect to identify the relation between the market beta and volatility changes. An empirical test ba…
This is a short description of graphic lambda calculus, with special emphasis on a duality suggested by the two different appearances of knot diagrams, in lambda calculus and emergent algebra sectors of the graphic lambda calculus respectively. This duality leads to the introduction of the dual of the graphic beta move…
Bayesian Beta regression for proportions in high dimensions with theoretical guarantees.
problem Modeling bounded continuous responses in high-dimensional settings with theoretical guarantees.
method Proposes a Bayesian approach using a tempered posterior with Horseshoe prior for shrinkage and variable selection.
result Demonstrates improved estimation accuracy and model interpretability in high-dimensional scenarios.
NeuralBeta uses deep learning to estimate beta, outperforming traditional methods.
problem Limitations of traditional beta estimation methods in capturing dynamic beta behavior.
method Neural networks with a new output layer for interpretability.
result NeuralBeta outperforms benchmark methods in dynamic beta estimation.
We describe the underlying probabilistic interpretation of alpha and beta divergences. We first show that beta divergences are inherently tied to Tweedie distributions, a particular type of exponential family, known as exponential dispersion models. Starting from the variance function of a Tweedie model, we outline how…
Study explores geometric structure and prior for beta-logistic distribution.
problem Understanding the geometric structure and prior distributions of the beta-logistic distribution.
method Exploring dual geometric structure and uncovering α-parallel prior. result The beta-logistic distribution admits an α-parallel prior for any real number α. The paper proves optimizability implies inequalities for sampling.
problem Optimizing functions via Gradient Flow and sampling from Gibbs measures.
method Gradient Flow and Lyapunov potentials to establish inequalities.
result Optimizability via Gradient Flow implies Poincaré and Log-Sobolev Inequalities.
Unified framework for scale-invariant representation learning using MAPCA.
problem Learning invariant representations in data.
method Metric-Aware Principal Component Analysis (MAPCA) based on generalized eigenproblem.
result MAPCA provides a unified geometric language for various self-supervised learning objectives.
This paper generalizes beta divergence beyond its classical form associated with power variance functions of Tweedie models. Generalized form is represented by a compact definite integral as a function of variance function of the exponential dispersion model. This compact integral form simplifies derivations of many pr…
The Brylinski beta function is extended for coaxial layers on submanifolds.
problem Extending the Brylinski beta function to coaxial layers on submanifolds.
method Analytic continuation and computation of residues for the function.
result The Brylinski beta function has an analytic continuation with simple poles.
Smart beta, also known as strategic beta or factor investing, is the idea of selecting an investment portfolio in a simple rule-based manner that systematically captures market inefficiencies, thereby enhancing risk-adjusted returns above capitalization-weighted benchmarks. We explore the idea of applying a smart strat…
We develop quantile regression models in order to derive risk margin and to evaluate capital in non-life insurance applications. By utilizing the entire range of conditional quantile functions, especially higher quantile levels, we detail how quantile regression is capable of providing an accurate estimation of risk ma…
A beta function for double layers is defined and analyzed.
problem Defining and analyzing a beta function for double layers.
method Holomorphic function definition and analytic continuation.
result Residues of the beta function are integrals of invariants.
We derive and approximate the conjugate prior of Dirichlet and beta distributions.
problem Intractability of conjugate prior for Dirichlet and beta distributions.
method Derive conjugate prior, define closed-form approximation, and provide algorithm.
result Closed-form approximation enables fully tractable Bayesian treatment.
This paper computes exact posterior distributions of mixture weights in hierarchical Bayesian models.
problem Uncertainty in class membership or data-generating processes in heterogeneous data.
method Exact marginalization of mixture weights using dynamic programming and FFT for two components, and joint dynamic program for K >= 3 components.
result Exact posterior distributions of mixture weights are finite mixtures of Beta distributions, providing credible intervals and per-observation local false-discovery rates.
Beta is a widely used quantity in investment analysis. We review the common interpretations that are applied to beta in finance and show that the standard method of estimation - least squares regression - is inconsistent with these interpretations. We present the case for an alternative beta estimator which is more app…
Study analyzes AI's impact on firms, markets, and workers using large language model data.
problem Understanding AI's effect on firms, markets, and workers.
method Used 380 trillion tokens from 400+ large language models to analyze AI's impact.
result Firms with higher AI exposure earn higher returns, creating an AI premium.
We consider a shrinking flow of smooth, closed, uniformly convex hypersurfaces in (n+1)-dimensional Euclidean space with speed fu^{alpha}{sigma}_n^{beta}, where u is the support function of the hypersurface, alpha, beta are two constants, and beta>0, sigma_n is the n-th symmetric polynomial of the principle curvature r…
A new beta-VAE based regression model accelerates oilfield optimization studies.
problem Computational expense of full-physics reservoir simulations.
method beta-VAE for interpretable latent space representation, probabilistic dense layers for uncertainty quantification.
result Interpretable latent representation and quantified uncertainty for optimization decisions.
This paper studies the Fisher-Rao geometry on the parameter space of beta distributions. We derive the geodesic equations and the sectional curvature, and prove that it is negative. This leads to uniqueness for the Riemannian centroid in that space. We use this Riemannian structure to study canonical moments, an intrin…
Paper introduces a new text clustering model using Beta-Liouville priors.
problem Clustering short text data.
method Develops a hierarchical mixture model with Beta-Liouville priors for short text clustering.
result The Beta-Liouville distribution offers a more flexible correlation structure for short text clustering.
Betas are possibly the most frequently applied tool to analyze how securities relate to the market. While in very widespread use, betas only express dynamics derived from second moment statistics. Financial returns data often deviate from normal assumptions in the sense that they have significant third and fourth order…
Magnitude of manifolds linked to Riesz energies and beta functions.
problem Magnitude invariant and its geometric significance.
method Relating magnitude invariant to Brylinski's beta function and pseudodifferential analysis.
result Precise relation between magnitude invariant and beta function for closed manifolds.
We construct a one-dimensional deformation retract of the unordered k-point configuration space of a star S. This retract suggests an explicit set of free generators Beta_k for the corresponding braid group of the star B_k and shows that the natural map from B_k-1 to B_k sends Beta_k-1 to Beta_k injectively.
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.
BS-VAE separates decoder variance and beta to improve VAE performance.
problem Blurriness in VAE outputs and difficulty in analyzing model performance.
method Explicitly separates beta and decoder variance in Beta-Sigma VAE.
result Superior performance in natural image synthesis and controllable parameters.
New estimator reveals intraday betas mainly driven by correlations.
problem Intraday fluctuations in market betas due to time-varying volatility.
method Proposes a novel subsampled quadrant estimator for high-frequency financial data.
result Intraday variation in betas primarily driven by intraday variation in correlations.