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.
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 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 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…
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.
Paper presents a method for estimating Hawkes process parameters.
problem Estimating parameters of Hawkes processes with self-excitation or inhibition.
method Maximum likelihood estimation for Hawkes processes with self-excitation or inhibition.
result The proposed estimator provides more accurate estimations in the inhibition context.
Invertibility conditions for observation-driven time series models often fail to be guaranteed in empirical applications. As a result, the asymptotic theory of maximum likelihood and quasi-maximum likelihood estimators may be compromised. We derive considerably weaker conditions that can be used in practice to ensure t…
A boosting method improves nonparametric density estimation without smoothing assumptions.
problem Overfitting in nonparametric data fitting.
method Introduces a boosting algorithm for univariate nonparametric maximum likelihood estimation.
result Demonstrates the effectiveness of the boosting approach through simulations and real data experiments.
Machine learning should incorporate maximum likelihood for better estimation.
problem Lack of rigorous foundational theory in machine learning.
method Integrate maximum likelihood estimation into machine learning models.
result Foundationally rigorous machine learning models have greater practical impact.
A new method improves text generation quality and diversity.
problem Exposure bias in Maximum Likelihood Estimation for text generation.
method ψ-MLE, a new training scheme based on density ratio estimation.
result ψ-MLE outperforms Maximum Likelihood Estimation and other models in text generation quality and diversity.
New approach resolves ambiguity in PPCA model's maximum likelihood estimation.
problem Ambiguity in maximum likelihood estimation of PPCA model due to rotational symmetry.
method Using quotient topological spaces, the approach resolves ambiguity and shows consistency of the maximum likelihood solution.
result Maximum likelihood solution is consistent in an appropriate quotient Euclidean space.
Paper quantifies label shift robustly.
problem Quantifying label shift in datasets.
method Robust estimators of label distribution.
result Maximum Likelihood Estimator is a robust estimator.
Geometric approach solves maximum likelihood for Cauchy-like distributions.
problem Estimating center and scatter robustly from heavy-tailed data.
method Geodesic convexity and symmetry spaces of noncompact type.
result Efficient numerical solution for robust estimates of location and spread.
We improve maximum likelihood for location estimation in finite samples.
problem Estimating a parameter from samples with unknown or varying distribution.
method Use smoothed Fisher information for finite sample size and varying distributions.
result Recover optimal estimation theory for finite n n n and arbitrary f f f . Investigates numerical issues in GP interpolation parameter estimation.
problem Numerical issues in maximum likelihood parameter estimation for Gaussian process interpolation.
method Investigates and proposes strategies to improve open-source software implementations.
result Improves reliability and reproducibility of studies relying on GP implementations.
We present a new statistical learning paradigm for Boltzmann machines based on a new inference principle we have proposed: the latent maximum entropy principle (LME). LME is different both from Jaynes maximum entropy principle and from standard maximum likelihood estimation.We demonstrate the LME principle BY deriving …
We develop a maximum penalized quasi-likelihood estimator for estimating in a nonparametric way the diffusion function of a diffusion process, as an alternative to more traditional kernel-based estimators. After developing a numerical scheme for computing the maximizer of the penalized maximum quasi-likelihood function…
Estimates GLMs robustly against label corruptions.
problem Learning GLMs under adversarial label corruptions.
method Iterative trimmed maximum likelihood estimator.
result Achieves minimax near-optimal risk.
A new method speeds up quantum state estimation.
problem Exponential growth in sample size and dimension for quantum state tomography.
method Stochastic mirror descent with Burg entropy.
result Optimization error vanishes at a O ( ( 1 / t ) d log t ) O (\sqrt{ ( 1 / t ) d \log t }) O ( ( 1/ t ) d log t ) rate. Geodesic descent optimizes likelihood in dually flat spaces.
problem Maximum likelihood estimation in exponential families.
method m-geodesic and e-geodesic updates on dually flat spaces.
result Geodesic updates can reach maximum likelihood estimator in one step.
New particle algorithms optimize latent variable models.
problem Optimizing latent variable models for maximum likelihood estimation.
method Identify gradient flows associated with free energy functional and discretize them to create particle-based algorithms.
result Novel particle algorithms scale to high-dimensional settings and perform well in experiments.
New method estimates latent gene expression factors without overlap with known confounders.
problem Estimating latent variance components in gene expression data with known confounders.
method Restricted maximum-likelihood method maximizing likelihood on orthogonal subspace.
result Method reduces runtime and attains greater likelihood values than gradient-based optimizers.
Efficiently estimates GEV distribution parameters using neural networks.
problem Computational intensity of maximum likelihood estimation for GEV distribution.
method Neural network-based likelihood-free estimation method.
result Comparable accuracy to maximum likelihood method with significant speedup.
Proposes a guaranteed regularization method for maximum likelihood estimation using gauge symmetry in Kullback-Leibler divergence.
problem Overfitting in maximum likelihood estimation.
method Introduces a regularization approach based on gauge symmetry in Kullback-Leibler divergence.
result The method provides a theoretically guaranteed optimal model without frequent hyperparameter tuning.
Paper proposes a method to estimate true positive proportion without knowing it.
problem Bias in binary classifier performance due to different positive item proportions.
method Maximum likelihood estimator for true proportion of positives.
result Method accurately estimates true positive proportion in data sets.
This paper addresses the estimation of parameters of a Bayesian network from incomplete data. The task is usually tackled by running the Expectation-Maximization (EM) algorithm several times in order to obtain a high log-likelihood estimate. We argue that choosing the maximum log-likelihood estimate (as well as the max…
The maximum likelihood approach is adapted to the problem of estimation of drift and diffusion functions of stochastic processes from measured time series. We reconcile a previously devised iterative procedure [Kleinhans et al., Physics Letters A (346), 2005] and put the application of the method on a firm theoretical …
New estimator for tensor weights with improved bias.
problem Estimating tensor weights from noisy data.
method Random matrix theory and KKT conditions.
result Asymptotically unbiased estimator for tensor rank.
Unified plug-in approach for estimating symmetric properties of distributions efficiently.
problem Estimating symmetric properties of distributions with high accuracy and efficiency.
method Profile-maximum-likelihood (PML) based estimator.
result Achieves theoretical limit for universal symmetric property estimation.
The paper analyzes how to estimate Gaussian process parameters accurately.
problem Estimating parameters of Gaussian process kernels from noisy data.
method Maximum likelihood estimation of the scale parameter of a Sobolev kernel.
result Maximum likelihood estimation provides significant adaptation against misspecification.
Improved MMD estimator for likelihood-free inference.
problem Computational challenges in estimating MMD for likelihood-free inference.
method Optimally-weighted MMD estimator with improved sample complexity.
result Significantly improved sample complexity for accurate MMD estimation.
The EM algorithm is a novel numerical method to obtain maximum likelihood estimates and is often used for practical calculations. However, many of maximum likelihood estimation problems are nonconvex, and it is known that the EM algorithm fails to give the optimal estimate by being trapped by local optima. In order to …
Unified view of KL-divergence and IPMs via DRE, with new DRM metrics.
problem Unified understanding of KL-divergence and IPMs.
method Unified representation via maximum likelihood density-ratio estimation (DRE).
result Unified form of IPMs and novel DRM metrics.
New method for efficient maximum likelihood estimation of p p p -generalized probit regression.
problem Efficient estimation of p p p -generalized probit regression models. method Combining sketching techniques with importance subsampling to obtain a coreset.
result Maximum likelihood estimator can be approximated efficiently up to a factor of ( 1 + ε ) (1+\varepsilon) ( 1 + ε ) on large data. 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.
Using stochastic gradient search and the optimal filter derivative, it is possible to perform recursive (i.e., online) maximum likelihood estimation in a non-linear state-space model. As the optimal filter and its derivative are analytically intractable for such a model, they need to be approximated numerically. In [Po…
We consider the problem of sparse estimation in a factor analysis model. A traditional estimation procedure in use is the following two-step approach: the model is estimated by maximum likelihood method and then a rotation technique is utilized to find sparse factor loadings. However, the maximum likelihood estimates c…
A new method normalizes EBM training by introducing a learnable parameter.
problem Training energy-based models with maximum likelihood is challenging due to intractable normalisation constants.
method Proposes a self-normalised log-likelihood (SNL) objective that introduces a learnable parameter representing the normalisation constant.
result The SNL objective is a lower bound of the log-likelihood and can be directly optimised using stochastic gradient techniques.
The paper proposes a mixture model with segmentation for heterogeneous functional data.
problem Heterogeneity in time and population for functional data.
method Mixture model with segmentation of time, maximum likelihood estimator, EM algorithm with dynamic programming.
result The method is consistent and identifiable, and illustrated on simulated and real datasets.
Estimates log-likelihood of interacting particle systems using virtual particles.
problem Inconsistent estimation of finite-particle log-likelihood in large particle systems.
method Stochastic gradient estimate using continuous trajectory and virtual particle systems.
result Convergence to stationary points of limiting mean-field system's log-likelihood.
Consistent estimator for mixtures of nonparametric elliptical distributions helps cluster analysis.
problem Consistency of maximum likelihood estimator for mixtures of nonparametric elliptical distributions.
method Maximum likelihood estimation for mixtures of elliptically-symmetric distributions under nonparametric P P P . result Components of the estimator correspond to well-separated components of the underlying distribution P P P . New method estimates Schrödinger bridges using ML techniques.
problem Finding most likely stochastic evolution between two distributions.
method Equivalence with maximum likelihood estimation, numerical Gaussian process approach.
result Direct application of ML techniques for SBP estimation.
CMLE reduces spurious correlations in deep models.
problem Spurious correlations in deep learning models.
method Counterfactual Maximum Likelihood Estimation (CMLE) on interventional distribution.
result CMLE outperforms regular MLE in out-of-domain generalization and spurious correlation reduction.
Improved autoregressive models generate higher quality images and are more robust to noise.
problem Generating high-quality images from autoregressive models.
method Noise conditional maximum likelihood estimation (MLE) with score-based sampling.
result Models trained with noise conditional MLE achieve better test likelihoods and generate higher quality images.
MAXENT method outperforms ML in sparse data with specific prior correlations.
problem Evaluating MAXENT method's validity limits and comparing it with ML.
method Bayesian decision theory, Dirichlet density, KL distance, regularized maximum likelihood.
result MAXENT can outperform ML in sparse data with specific prior correlations.
The MDL two-part coding index of resolvability \textit{index of resolvability} index of resolvability provides a finite-sample upper bound on the statistical risk of penalized likelihood estimators over countable models. However, the bound does not apply to unpenalized maximum likelihood estimation or procedures with exceedingly small penalties. In this paper,…
Graphical lasso may fail to fit models when data points are insufficient.
problem When does graphical lasso fail to select and fit a graphical model?
method Computational experiments with graphical lasso.
result Graphical lasso may fail when the number of data points is less than the maximum likelihood threshold.
Study uniform rates for estimating Gaussian mixtures without separation assumption.
problem Estimating parameters in two-component Gaussian mixtures without separation.
method Uniform convergence rates derived using minimax lower bounds and careful analysis of polynomial equalities.
result Phase transition in optimal estimation rate based on mixture balance.