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…
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48 results for “Maximum Marginal Likelihood Estimation”
New algorithm improves latent variable model estimation.
problem Estimating parameters in latent variable models.
method Jarzynski-adjusted Langevin algorithm (JALA) for SMC methods.
result JALA-EM provides maximum marginal likelihood estimate.
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…
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…
We study the parameter estimation problem in mixture models with observational nonidentifiability: the full model (also containing hidden variables) is identifiable, but the marginal (observed) model is not. Hence global maxima of the marginal likelihood are (infinitely) degenerate and predictions of the marginal likel…
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…
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…
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…
We give polynomial-time algorithms for the exact computation of lowest-energy (ground) states, worst margin violators, log partition functions, and marginal edge probabilities in certain binary undirected graphical models. Our approach provides an interesting alternative to the well-known graph cut paradigm in that it …
Develops a new algorithm for estimating model parameters using interacting particle systems.
problem Estimating parameters of latent variable models.
method Interacting Particle Langevin Algorithm (IPLA) based on Langevin diffusion.
result Nonasymptotic optimisation error bounds for the estimator.
A scalable method for estimating spatial data using VREML.
problem Costly computation of REML for large, sparse precision matrices in spatial data.
method Proposes VREML framework approximating marginal likelihood with Gaussian variational distribution and deriving a coordinate-ascent algorithm.
result Empirically shows VREML outperforms MLE and INLA.
New CTRL algorithm adapts to varying problem difficulty.
problem Adapting to varying levels of problem difficulty in CTRL.
method MLE with a general function approximator, estimating state marginal density.
result Regret bound scales with reward variance and measurement resolution, independent of measurement strategy.
New algorithms learn latent variable models without tuning, outperforming existing methods.
problem Learning latent variable models without manual tuning.
method Two particle-based algorithms using free energy minimization and coin betting.
result Learning algorithms are entirely tuning-free and competitive with existing methods.
New insights into using IPF for inferring dynamic networks from marginals.
problem Inferring dynamic networks from time-aggregated adjacency matrices and time-varying marginals.
method Identifying a generative network model and establishing its maximum likelihood estimates via IPF, with convergence guarantees for sparse data.
result IPF provides principled estimation of dynamic networks from marginals under certain conditions, with structure-dependent error bounds and guaranteed convergence for sparse data.
Maximum likelihood estimator performance in logistic regression analyzed.
problem Performance of maximum likelihood estimator in logistic regression.
method Sharp non-asymptotic guarantees for existence and excess logistic risk.
result Sharp guarantees for the existence and excess risk of MLE in logistic regression.
New method learns latent energy models using particle algorithms.
problem Learning latent variable models with energy priors.
method Continuous-time SDEs for MMLE, particle-based discretization.
result Practical algorithm converges to solve MMLE problem.
Unbiased gradient estimation improves VAE performance.
problem Training VAEs via maximum likelihood is difficult due to intractable integrals.
method Introduced unbiased estimators of the log-likelihood gradient using coupled Markov chains.
result Unbiased estimators lead to better predictive performance in VAEs.
New SMC samplers improve stochastic optimisation efficiency.
problem Optimizing functions with intractable gradients in machine learning and statistics.
method Sequential Monte Carlo (SMC) samplers for stochastic optimisation.
result Significant computational gains achieved with SMC approximations.
Ultrahigh-dimensional variable selection plays an increasingly important role in contemporary scientific discoveries and statistical research. Among others, Fan and Lv [J. R. Stat. Soc. Ser. B Stat. Methodol. 70 (2008) 849-911] propose an independent screening framework by ranking the marginal correlations. They showed…
The normalized maximized likelihood (NML) provides the minimax regret solution in universal data compression, gambling, and prediction, and it plays an essential role in the minimum description length (MDL) method of statistical modeling and estimation. Here we show that the normalized maximum likelihood has a Bayes-li…
A new method estimates marginal likelihood using normalizing flows.
problem Estimating marginal likelihood in Bayesian model selection.
method Learned harmonic mean estimator using normalizing flows.
result Normalizing flows avoid the exploding variance problem.
Accelerates MMLE using SVGD with Nesterov acceleration.
problem Maximum Marginal Likelihood Estimation optimization.
method Stein variational gradient descent with Nesterov acceleration.
result Consistently accelerates convergence across various tasks.
The paper analyzes SBL pruning criteria under weakened assumptions.
problem Sparse Bayesian learning hyperparameter divergence and pruning.
method Analyzing marginal likelihood function under weakened Gaussian assumptions.
result Conditions for finite vs infinite hyperparameters lead to F-SBL pruning.
Identifies interpretable generative model for multivariate data.
problem Black-box architectures of deep generative models are often unidentified and difficult to interpret.
method Introduces Deep Discrete Encoder (DDE) Copula, a hierarchical binary latent variable model inside a copula framework.
result Establishes conditions for identification of DDE copula parameters and proves posterior consistency.
A new copula estimation method using classification.
problem Estimating copula density from joint and marginal distributions.
method Train a classifier to distinguish joint density from product of marginals.
result Empirically outperforms existing copula estimators.
Proposes a new method for high-dimensional density estimation.
problem Estimating high-dimensional probability density functions efficiently.
method Tensorizing flow method combining tensor-train and flow-based generative modeling.
result Efficiently constructs an approximate density in tensor-train form and trains a flow model to match empirical distribution.
New method estimates marginal likelihood for deep learning models using training data alone.
problem Estimation difficulties in marginal likelihood for model selection in deep learning.
method Scalable marginal likelihood estimation based on Laplace's method and Gauss-Newton approximations.
result Estimate outperforms cross-validation and manual tuning on various datasets.
Stochastic Gradient Annealed Importance Sampling for Efficient Online Marginal Likelihood Estimationstat.ML
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…
Maximum likelihood estimation fails to be well-posed in Gaussian process regression.
problem Establishing well-posedness of maximum likelihood estimation in Gaussian process regression.
method Analyzing the conditions under which maximum likelihood estimation is not Lipschitz in the data with respect to the Hellinger distance.
result Maximum likelihood estimation is not well-posed in the noiseless data setting for any Gaussian process with a stationary covariance function whose lengthscale parameter is estimated using maximum likelihood.
When used as a surrogate objective for maximum likelihood estimation in latent variable models, the evidence lower bound (ELBO) produces state-of-the-art results. Inspired by this, we consider the extension of the ELBO to a family of lower bounds defined by a particle filter's estimator of the marginal likelihood, the …
We define a generalized likelihood function based on uncertainty measures and show that maximizing such a likelihood function for different measures induces different types of classifiers. In the probabilistic framework, we obtain classifiers that optimize the cross-entropy function. In the possibilistic framework, we …
New method uses unlabeled data to estimate intercept in case-control logistic regression.
problem Estimating intercept in case-control logistic regression.
method Construct likelihood function, use iterative algorithm to find maximum likelihood estimator.
result Proposed method identifies intercept and improves estimation efficiency.
SUMO provides unbiased log marginal likelihood estimation for latent variable models.
problem Biased estimates of log marginal likelihood in latent variable models.
method Randomized truncation of infinite series for unbiased estimation.
result Models trained with SUMO give better test-set likelihoods than standard methods.
Bayesian networks with latent variables are characterized and their likelihoods compared.
problem Characterizing and comparing likelihoods of Bayesian networks with latent variables.
method Characterized likelihood function and empirical Bayesian network. Proved dominance of global maximum likelihood from empirical model.
result The global maximum likelihood of the original Bayesian network is attained if and only if parameters are consistent with empirical model.
Temporal Point Processes (TPP) with partial likelihoods involving a latent structure often entail an intractable marginalization, thus making inference hard. We propose a novel approach to Maximum Likelihood Estimation (MLE) involving approximate inference over the latent variables by minimizing a tight upper bound on …
Improved Gaussian process regression with tighter log marginal likelihood bounds.
problem Improving predictive performance in Gaussian process regression models.
method Lower bound on log marginal likelihood using conjugate gradients.
result Improved predictive performance compared to other conjugate gradient based approaches.
In this short note we provide an unbiased multilevel Monte Carlo estimator of the log marginal likelihood and discuss its application to variational Bayes.
Empirical Bayes method improves Gaussian sequence model inference.
problem Estimating parameters in correlated Gaussian sequence models.
method Maximum Composite Marginal Likelihood (CML) estimator, leveraging geometric Brascamp-Lieb inequality.
result CML estimator converges at rate \( n_*^{-1/2} \) in weighted Hellinger distance.
Efficiently marginalizes over Gaussian Process kernels for better model flexibility and uncertainty.
problem Inefficient marginalization over Gaussian Process kernels for large datasets.
method Bayesian Quadrature scheme with maximum mean discrepancies and invariances between Spectral Mixture kernels.
result Achieves more accurate predictions and better calibrated uncertainty than state-of-the-art baselines.
GCMM improves clustering and fits un-synchronized data.
problem Improving clustering performance with copulas.
method Mathematical definition, copula concepts, Expectation Maximum algorithms, nonparametric estimation.
result GCMM outperforms GMM in goodness-of-fit and data analysis.
Combinatorial and algebraic perspectives on the marginal independence structure of Bayesian networksstat.ME
Estimates marginal independence structure of Bayesian networks from data.
problem Learning the marginal independence structure of Bayesian networks from observational data.
method Using Gröbner basis and MCMC method (GrUES) to connect and recover the true structure.
result GrUES recovers the true marginal independence structure at a higher rate than simple independence tests.
Corrects pseudo log-likelihood method issues in various applications.
problem Log-likelihood function unbounded issues in pseudo log-likelihood methods.
method Provided a counterexample and corrected algorithms in previous literature.
result Ensured well-definedness of maximum pseudo log-likelihood estimation.
We study the connections between spectral clustering and the problems of maximum margin clustering, and estimation of the components of level sets of a density function. Specifically, we obtain bounds on the eigenvectors of graph Laplacian matrices in terms of the between cluster separation, and within cluster connecti…
Unified view of label shift estimation methods.
problem Label distribution changes but class-conditional distributions remain the same.
method Unified view of two approaches: BBSE and MLLS.
result Unified framework and theoretical characterization of MLLS.
We propose a robust estimator to improve maximum likelihood in probabilistic models.
problem Overfitting and sensitivity to noise in maximum likelihood estimation.
method Distributionally robust maximum likelihood estimator that minimizes worst-case expected log-loss.
result The robust estimator is statistically consistent and performs well in regression and classification tasks.
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 …
Proposes a new approach to approximate maximum likelihood for complex models.
problem Intractable likelihood functions in complex parametric models.
method Simulation-based constrained approximation to the structural model.
result Estimators nearly as efficient as maximum likelihood, feasible in many cases.
A simple graphical model for correlated defaults is proposed, with explicit formulas for the loss distribution. Algebraic geometry techniques are employed to show that this model is well posed for default dependence: it represents any given marginal distribution for single firms and pairwise correlation matrix. These t…