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.
New method estimates marginal likelihood for deep learning models using training data alone.
We consider estimating the marginal likelihood in settings with independent and identically distributed (i.i.d.) data. We propose estimating the predictive distributions in a sequential factorization of the marginal likelihood in such settings by using stochastic gradient Markov Chain Monte Carlo techniques. This appro…
SUMO provides unbiased log marginal likelihood estimation for latent variable models.
In this short note we provide an unbiased multilevel Monte Carlo estimator of the log marginal likelihood and discuss its application to variational Bayes.
We consider the combined use of resampling and partial rejection control in sequential Monte Carlo methods, also known as particle filters. While the variance reducing properties of rejection control are known, there has not been (to the best of our knowledge) any work on unbiased estimation of the marginal likelihood …
New algorithm improves latent variable model estimation.
We consider two connected aspects of maximum likelihood estimation of the parameter for high-dimensional discrete graphical models: the existence of the maximum likelihood estimate (mle) and its computation. When the data is sparse, there are many zeros in the contingency table and the maximum likelihood estimate of th…
We consider discrete graphical models Markov with respect to a graph and propose two distributed marginal methods to estimate the maximum likelihood estimate of the canonical parameter of the model. Both methods are based on a relaxation of the marginal likelihood obtained by considering the density of the variable…
New method resolves nonidentifiability in mixture models.
Optimizes AIS hyperparameters for efficient marginal likelihood estimation.
Improves Gaussian process regression without bias.
Graphical models with bi-directed edges (<->) represent marginal independence: the absence of an edge between two vertices indicates that the corresponding variables are marginally independent. In this paper, we consider maximum likelihood estimation in the case of continuous variables with a Gaussian joint distributio…
Method estimates noise variance in Gaussian process regression.
Supervised topic models utilize document's side information for discovering predictive low dimensional representations of documents. Existing models apply the likelihood-based estimation. In this paper, we present a general framework of max-margin supervised topic models for both continuous and categorical response var…
A new method estimates marginal likelihood using normalizing flows.
Computing the marginal likelihood (ML) of a model requires marginalizing out all of the parameters and latent variables, a difficult high-dimensional summation or integration problem. To make matters worse, it is often hard to measure the accuracy of one's ML estimates. We present bidirectional Monte Carlo, a technique…
Improved likelihood-free inference by localizing and refining low-dimensional approximations.
AIS uses a suboptimal extended target distribution, which this paper improves using SGM.
A fast method estimates group-adaptive elastic net penalties using co-data.
We present novel understandings of the Gamma-Poisson (GaP) model, a probabilistic matrix factorization model for count data. We show that GaP can be rewritten free of the score/activation matrix. This gives us new insights about the estimation of the topic/dictionary matrix by maximum marginal likelihood estimation. In…
Identifies interpretable generative model for multivariate data.
Efficiently estimates marginal posteriors for complex simulations.
DAIS improves AIS for differentiable marginal likelihood estimation.
The paper discusses the impact of prior densities on Bayesian model selection.
The paper analyzes SBL pruning criteria under weakened assumptions.
New method optimizes hyperparameters in deep learning models efficiently.
Generalising well in supervised learning tasks relies on correctly extrapolating the training data to a large region of the input space. One way to achieve this is to constrain the predictions to be invariant to transformations on the input that are known to be irrelevant (e.g. translation). Commonly, this is done thro…
We consider distributed estimation of the inverse covariance matrix, also called the concentration or precision matrix, in Gaussian graphical models. Traditional centralized estimation often requires global inference of the covariance matrix, which can be computationally intensive in large dimensions. Approximate infer…
Speeding up Markov Chain Monte Carlo (MCMC) for datasets with many observations by data subsampling has recently received considerable attention. A pseudo-marginal MCMC method is proposed that estimates the likelihood by data subsampling using a block-Poisson estimator. The estimator is a product of Poisson estimators,…
Black box variational inference (BBVI) with reparameterization gradients triggered the exploration of divergence measures other than the Kullback-Leibler (KL) divergence, such as alpha divergences. In this paper, we view BBVI with generalized divergences as a form of estimating the marginal likelihood via biased import…
Bayesian evidence helps compare models but can overfit.
In decision-making systems, it is important to have classifiers that have calibrated uncertainties, with an optimisation objective that can be used for automated model selection and training. Gaussian processes (GPs) provide uncertainty estimates and a marginal likelihood objective, but their weak inductive biases lead…
ITF improves DSR but inflates curvature, while marginal likelihood reduces it, affecting QoIs.
A widely applicable Bayesian information criterion (Watanabe, 2013) is applicable for both regular and singular models in the model selection problem. This criterion tends to overestimate the log marginal likelihood. We identify an overestimating term of a widely applicable Bayesian information criterion. Adjustment of…
Monotonic improvement in uncertainty estimation with Gaussian processes as dimension increases.
New insights into using IPF for inferring dynamic networks from marginals.
Develops a new algorithm for estimating model parameters using interacting particle systems.
Bayesian approach learns invariances from data alone, but last layer approximation is not always sufficient.
Due to the intractable partition function, the exact likelihood function for a Markov random field (MRF), in many situations, can only be approximated. Major approximation approaches include pseudolikelihood and Laplace approximation. In this paper, we propose a novel way of approximating the likelihood function throug…
Evaluation of the marginal likelihood plays an important role in model selection problems. The widely applicable Bayesian information criterion (WBIC) and singular Bayesian information criterion (sBIC) give approximations to the log marginal likelihood, which can be applied to both regular and singular models. When the…
Empirical Bayes method improves Gaussian sequence model inference.
We show that unconverged stochastic gradient descent can be interpreted as a procedure that samples from a nonparametric variational approximate posterior distribution. This distribution is implicitly defined as the transformation of an initial distribution by a sequence of optimization updates. By tracking the change …
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 MCMC method for GPs tackles computational burden and intractable likelihoods.
Several studies explore inferences based on stochastic volatility (SV) models, taking into account the stylized facts of return data. The common problem is that the latent parameters of many volatility models are high-dimensional and analytically intractable, which means inferences require approximations using, for exa…
Kernel methods have revolutionized the fields of pattern recognition and machine learning. Their success, however, critically depends on the choice of kernel parameters. Using Gaussian process (GP) classification as a working example, this paper focuses on Bayesian inference of covariance (kernel) parameters using Mark…
Proposes a method to optimize neural network initialization using marginal likelihood maximization.
We consider an on-line system identification setting, in which new data become available at given time steps. In order to meet real-time estimation requirements, we propose a tailored Bayesian system identification procedure, in which the hyper-parameters are still updated through Marginal Likelihood maximization, but …