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.
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.
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.
FDN improves probabilistic regressors' adaptability to distribution shifts.
problem Overconfidence in modern probabilistic regressors under distribution shift.
method FDN uses input-conditioned distributions over network weights, trained with a Monte Carlo beta-ELBO objective.
result FDN produces predictive mixtures whose dispersion adapts to the input, providing shift-aware uncertainty.
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.
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-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 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…
Beta process is the standard nonparametric Bayesian prior for latent factor model. In this paper, we derive a structured mean-field variational inference algorithm for a beta process non-negative matrix factorization (NMF) model with Poisson likelihood. Unlike the linear Gaussian model, which is well-studied in the non…
The paper analyzes LASSO penalization for high-dimensional Beta regression models.
problem Theoretical analysis of LASSO in high-dimensional Beta regression.
method Non-convexity handling through a neighborhood framework, debiasing for confidence intervals, proximal gradient algorithm.
result Non-asymptotic bound on ℓ1-error of stationary points. Deep model learns complex latent codes without assuming factor structure.
problem Learning latent codes with complex, non-factorial distributions.
method Deep generative factor analysis with beta process prior and stochastic EM algorithm.
result Preliminary results show model can approximate complex distributions.
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 …
GRASP simplifies Bayesian regression with grouped predictors using an adaptive NBP prior.
problem Regression with grouped predictors and adaptive shrinkage.
method Normal Beta Prime (NBP) prior with tunable hyperparameters for flexible sparsity control.
result Empirical validation of robust and versatile GRASP across various sparsity and signal-to-noise ratios.
Paper develops new spot regression estimators using candlesticks for asset pricing.
problem Estimation of spot betas in asset pricing and risk management.
method Develops a new estimation and inference framework for spot regressions using high-frequency candlesticks.
result The proposed candlestick-based estimators reduce estimation risk and achieve higher power in hypothesis testing.
Enhances topic-metadata relationship modeling using Bayesian methods.
problem Estimating relationships between latent topics and metadata in topic modeling.
method Proposes modifications to the method of composition, using Beta regression and a fully Bayesian approach.
result Improves quantification of uncertainty in topic-metadata relationships.
This paper introduces a variational approximation framework using direct optimization of what is known as the {\it scale invariant Alpha-Beta divergence} (sAB divergence). This new objective encompasses most variational objectives that use the Kullback-Leibler, the R{é}nyi or the gamma divergences. It also gives access…
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 characterize the combinatorial structure of conditionally-i.i.d. sequences of negative binomial processes with a common beta process base measure. In Bayesian nonparametric applications, such processes have served as models for latent multisets of features underlying data. Analogously, random subsets arise from cond…
Proposes a non-parametric method for deep discrete latent variable models.
problem Learning sparse discrete latent representations in deep models.
method Iterative algorithm with Beta-Bernoulli process prior and local data scaling.
result Improves sparsity and scalability of deep discrete latent variable models.
We build on the work in Fackler and King 1990, and propose a more general calibration model for implied risk neutral densities. Our model allows for the joint calibration of a set of densities at different maturities and dates through a Bayesian dynamic Beta Markov Random Field. Our approach allows for possible time de…
Paper proposes an efficient algorithm for nonnegative binary matrix factorization.
problem Decomposing binary data using matrix factorization.
method Majorization-minimization algorithm with Beta prior for improved performance.
result Proposed algorithm offers excellent trade-off between performance, complexity, and interpretability.
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.
GBEST model improves survival analysis for small datasets.
problem Challenges in survival analysis, especially with small data.
method Bayesian bootstrap and Beta Stacy bootstrap methods integrated into bagging tree models.
result GBEST model outperforms classical survival models in predictive performance and stability.
Paper extends nonparametric regression bounds for dependent β-mixing samples.
problem Analyzing error in nonparametric regression with dependent data.
method Extends uniform deviation inequalities from independent to dependent β-mixing samples. result Derives generalization bounds for nonparametric regression with dependent data.
Stochastic variational inference (SVI) is emerging as the most promising candidate for scaling inference in Bayesian probabilistic models to large datasets. However, the performance of these methods has been assessed primarily in the context of Bayesian topic models, particularly latent Dirichlet allocation (LDA). Deri…
Shared Keyboard design improves phase I clinical trials by borrowing information across doses.
problem Interim decisions based on current dose data may overlook signals from neighboring doses.
method Bayesian model-assisted design using Beta kernel process with kernel-weighted pseudo-counts.
result Significant improvements in identifying maximum tolerated dose and safety.
Alternative model predicts health insurance reimbursement based on contract limitations.
problem Estimating the ratio of reimbursement to health care expenditures after deductibles and copayments.
method Proposes a Zero-One Inflated Beta regression model using GAMLSS.
result The model provides a dependency structure between reimbursement and contract limitations.
This work explains scaling laws as redundancy laws in deep learning.
problem The mathematical origins of scaling laws in deep learning models remain unclear.
method Kernel regression and analysis of data covariance spectra.
result Scaling laws can be explained as redundancy laws, revealing the learning curve's slope depends on data redundancy.
We propose a Bayesian nonparametric approach to the problem of jointly modeling multiple related time series. Our approach is based on the discovery of a set of latent, shared dynamical behaviors. Using a beta process prior, the size of the set and the sharing pattern are both inferred from data. We develop efficient M…
We propose a Bayesian nonparametric approach to the problem of jointly modeling multiple related time series. Our model discovers a latent set of dynamical behaviors shared among the sequences, and segments each time series into regions defined by a subset of these behaviors. Using a beta process prior, the size of the…
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…
We develop a Bayesian nonparametric approach to a general family of latent class problems in which individuals can belong simultaneously to multiple classes and where each class can be exhibited multiple times by an individual. We introduce a combinatorial stochastic process known as the negative binomial process (NBP)…
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…
Forward regression is a statistical model selection and estimation procedure which inductively selects covariates that add predictive power into a working statistical regression model. Once a model is selected, unknown regression parameters are estimated by least squares. This paper analyzes forward regression in high-…
CAPM interpretation is flawed; beta reflects proxy for underlying driver, not causal transmission.
problem Inconsistent interpretation of CAPM regression as contemporaneous causation.
method Formalized CAPM as a structural causal model and analyzed admissible three-node graphs.
result Contemporaneous betas act like proxies rather than mechanisms; genuine market-to-stock channel appears only at a lag.
We investigate entropy as a financial risk measure. Entropy explains the equity premium of securities and portfolios in a simpler way and, at the same time, with higher explanatory power than the beta parameter of the capital asset pricing model. For asset pricing we define the continuous entropy as an alternative meas…
The new field of adaptive data analysis seeks to provide algorithms and provable guarantees for models of machine learning that allow researchers to reuse their data, which normally falls outside of the usual statistical paradigm of static data analysis. In 2014, Dwork, Feldman, Hardt, Pitassi, Reingold and Roth introd…
Bayesian framework improves financial risk management and compliance.
problem Uncertainty in financial risk forecasting and compliance.
method Integrated Bayesian analytics framework for precise uncertainty quantification.
result Proposed DLM model produces more accurate VaR estimates compared to baseline models.
Robustness to outliers is a central issue in real-world machine learning applications. While replacing a model to a heavy-tailed one (e.g., from Gaussian to Student-t) is a standard approach for robustification, it can only be applied to simple models. In this paper, based on Zellner's optimization and variational form…
In this paper, the use of the Generalized Beta Mixture (GBM) and Horseshoe distributions as priors in the Bayesian Compressive Sensing framework is proposed. The distributions are considered in a two-layer hierarchical model, making the corresponding inference problem amenable to Expectation Maximization (EM). We prese…
While most Bayesian nonparametric models in machine learning have focused on the Dirichlet process, the beta process, or their variants, the gamma process has recently emerged as a useful nonparametric prior in its own right. Current inference schemes for models involving the gamma process are restricted to MCMC-based …
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.
Statistical modeling of nuclear data provides a novel approach to nuclear systematics complementary to established theoretical and phenomenological approaches based on quantum theory. Continuing previous studies in which global statistical modeling is pursued within the general framework of machine learning theory, we …
We discuss the foundations of factor or regression models in the light of the self-consistency condition that the market portfolio (and more generally the risk factors) is (are) constituted of the assets whose returns it is (they are) supposed to explain. As already reported in several articles, self-consistency implie…
We are concerned with obtaining well-calibrated output distributions from regression models. Such distributions allow us to quantify the uncertainty that the model has regarding the predicted target value. We introduce the novel concept of distribution calibration, and demonstrate its advantages over the existing defin…
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.
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.
In recent years, a rich variety of shrinkage priors have been proposed that have great promise in addressing massive regression problems. In general, these new priors can be expressed as scale mixtures of normals, but have more complex forms and better properties than traditional Cauchy and double exponential priors. W…