A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
The paper discusses the impact of prior densities on Bayesian model selection.
Develops a new algorithm to calibrate signed datasets to specified marginals.
Bayesian models use hyperparameters to indirectly assign priors, and this work shows how these priors can be derived from maximum entropy principles.
This paper shows that the implicit bias of gradient descent on linearly separable data is exactly characterized by the optimal solution of a dual optimization problem given by a smoothed margin, even for general losses. This is in contrast to prior results, which are often tailored to exponentially-tailed losses. For t…
The paper proposes a method to improve Bayesian inference for periodic data using data-driven priors.
Bayesian evidence helps compare models but can overfit.
Recent reports have described that the equivalent sample size (ESS) in a Dirichlet prior plays an important role in learning Bayesian networks. This paper provides an asymptotic analysis of the marginal likelihood score for a Bayesian network. Results show that the ratio of the ESS and sample size determine the penalty…
Develops methods for constructing likelihoods and priors for Bayesian networks.
In Bayesian statistics, the marginal likelihood, also known as the evidence, is used to evaluate model fit as it quantifies the joint probability of the data under the prior. In contrast, non-Bayesian models are typically compared using cross-validation on held-out data, either through -fold partitioning or leave-$p…
Bayesian network structure learning is often performed in a Bayesian setting, evaluating candidate structures using their posterior probabilities for a given data set. Score-based algorithms then use those posterior probabilities as an objective function and return the maximum a posteriori network as the learned model.…
Exploration is critical to a reinforcement learning agent's performance in its given environment. Prior exploration methods are often based on using heuristic auxiliary predictions to guide policy behavior, lacking a mathematically-grounded objective with clear properties. In contrast, we recast exploration as a proble…
The lack of interpretability often makes black-box models difficult to be applied to many practical domains. For this reason, the current work, from the black-box model input port, proposes to incorporate data-based prior information into the black-box soft-margin SVM model to enhance its interpretability. The concept …
Gradient descent and SGD achieve low test error in specific network weight regimes.
The hyperparameters in Gaussian process regression (GPR) model with a specified kernel are often estimated from the data via the maximum marginal likelihood. Due to the non-convexity of marginal likelihood with respect to the hyperparameters, the optimization may not converge to the global maxima. A common approach to …
Bayesian network structure learning is often performed in a Bayesian setting, by evaluating candidate structures using their posterior probabilities for a given data set. Score-based algorithms then use those posterior probabilities as an objective function and return the maximum a posteriori network as the learned mod…
Bayesian deep learning improves accuracy and calibration without sacrificing scalability.
A new approach for instance-optimal learning that bypasses impossibility results.
Method estimates joint probability density from samples using low-rank decomposition and random projections.
Unified binary and multiclass margin-based classification methods.
In the absence of prior knowledge, ordinal embedding methods obtain new representation for items in a low-dimensional Euclidean space via a set of quadruple-wise comparisons. These ordinal comparisons often come from human annotators, and sufficient comparisons induce the success of classical approaches. However, colle…
Develops methods for constructing parameter priors in DAG models.
PDGMM-VAE uses adaptive priors for better ICA recovery.
Thermodynamic integration (TI) for computing marginal likelihoods is based on an inverse annealing path from the prior to the posterior distribution. In many cases, the resulting estimator suffers from high variability, which particularly stems from the prior regime. When comparing complex models with differences in a …
We present a non-parametric Bayesian latent variable model capable of learning dependency structures across dimensions in a multivariate setting. Our approach is based on flexible Gaussian process priors for the generative mappings and interchangeable Dirichlet process priors to learn the structure. The introduction of…
Researchers derive exact priors for finite Bayesian neural networks.
In this paper we address the problem of learning the structure of a Bayesian network in domains with continuous variables. This task requires a procedure for comparing different candidate structures. In the Bayesian framework, this is done by evaluating the {em marginal likelihood/} of the data given a candidate struct…
Efficiently estimates marginal posteriors for complex simulations.
Nested sampling improved for arbitrary priors.
Gaussian process regression is a popular method for non-parametric probabilistic modeling of functions. The Gaussian process prior is characterized by so-called hyperparameters, which often have a large influence on the posterior model and can be difficult to tune. This work provides a method for numerical marginalizat…
Statistical inference can be computationally prohibitive in ultrahigh-dimensional linear models. Correlation-based variable screening, in which one leverages marginal correlations for removal of irrelevant variables from the model prior to statistical inference, can be used to overcome this challenge. Prior works on co…
We introduce new definitions of universal and superuniversal computable codes, which are based on a code's ability to approximate Kolmogorov complexity within the prescribed margin for all individual sequences from a given set. Such sets of sequences may be singled out almost surely with respect to certain probability …
We analyze a new robust method for the reconstruction of probability distributions of observed data in the presence of output outliers. It is based on a so-called gradient conjugate prior (GCP) network which outputs the parameters of a prior. By rigorously studying the dynamics of the GCP learning process, we derive an…
There are three principle paradigms of statistical inference: (i) Bayesian, (ii) information-based and (iii) frequentist inference. We describe an objective prior (the weighting or -prior) which unifies objective Bayes and information-based inference. The -prior is chosen to make the marginal probability an unbia…
BSTabDiff: Block-Subunit Diffusion Priors for HDLSS Tabular Data Generation
In variational autoencoders, the prior on the latent codes is often treated as an afterthought, but the prior shapes the kind of latent representation that the model learns. If the goal is to learn a representation that is interpretable and useful, then the prior should reflect the ways in which the high-level fact…
Bayesian inference in state-space models is challenging due to high-dimensional state trajectories. A viable approach is particle Markov chain Monte Carlo, combining MCMC and sequential Monte Carlo to form "exact approximations" to otherwise intractable MCMC methods. The performance of the approximation is limited to t…
We propose a Bayesian approximate inference method for learning the dependence structure of a Gaussian graphical model. Using pseudo-likelihood, we derive an analytical expression to approximate the marginal likelihood for an arbitrary graph structure without invoking any assumptions about decomposability. The majority…
Deep neural network (DNN) regression models are widely used in applications requiring state-of-the-art predictive accuracy. However, until recently there has been little work on accurate uncertainty quantification for predictions from such models. We add to this literature by outlining an approach to constructing predi…
A new method learns hierarchical EBM models with diffusion schemes.
The paper studies multi-view representation learning with generalization guarantees and a new regularizer.
Study optimizes insurance liability cash flows with regulatory capital requirements.
Bottlenecks of binary classification from positive and unlabeled data (PU classification) are the requirements that given unlabeled patterns are drawn from the test marginal distribution, and the penalty of the false positive error is identical to the false negative error. However, such requirements are often not fulfi…
Boltzmann machines (BMs) are appealing candidates for powerful priors in variational autoencoders (VAEs), as they are capable of capturing nontrivial and multi-modal distributions over discrete variables. However, non-differentiability of the discrete units prohibits using the reparameterization trick, essential for lo…
A new framework improves tensor completion accuracy by considering numerical priors.
Bayesian deep learning improves neural network accuracy and generalization.
We consider the problem of learning Bayesian network classifiers that maximize the marginover a set of classification variables. We find that this problem is harder for Bayesian networks than for undirected graphical models like maximum margin Markov networks. The main difficulty is that the parameters in a Bayesian ne…
Gradient-based methods can be biased by distributional asymmetries in bivariate categorical data.
Study proposes learning optimal priors from data for better Bayesian inference.