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.
We establish conditions for maximum likelihood consistency in time series models.
problem Invertibility conditions often fail in empirical observation-driven models.
method Derive weaker conditions for maximum likelihood consistency.
result Consistency of maximum likelihood estimator holds for various models.
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.
The paper improves risk bounds for maximum likelihood estimation with arbitrary penalties.
problem Improving risk bounds for maximum likelihood estimation with arbitrary penalties.
method Developed a more general inequality for arbitrary penalties, leading to exact risk bounds of order 1/n.
result Derived exact risk bounds of order 1/n for iid parametric models, improving on previous bounds.
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.
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 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.
Efficiently approximates profile maximum likelihood for better estimation performance.
problem Computing the exact profile maximum likelihood is difficult and time-consuming.
method Proposes an algorithm that clumps symbols into one symbol to approximate PML.
result Empirical performance of the approximate solution is competitive and often superior.
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 . 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.
Quantum annealing improves EM algorithm's performance in nonconvex optimization.
problem EM algorithm's tendency to get stuck in local optima for nonconvex problems.
method Integrates quantum fluctuations into EM algorithm to induce tunnel effect and avoid local optima.
result Quantum annealing EM algorithm converges and performs better in nonconvex optimization problems.
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.
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.
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 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.
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.
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.
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…
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.
Paper proposes a new method for better super-resolution images.
problem Improving realism in super-resolution images.
method Extension of Implicit Maximum Likelihood Estimation (IMLE).
result More realistic super-resolved images with reduced artifacts.
The paper analyzes a recursive ML estimation method for non-linear state-space models.
problem Estimating maxima of the log-likelihood function in non-linear state-space models.
method Recursive maximum likelihood estimation using particle approximation to the optimal filter derivative.
result The algorithm accurately estimates maxima of the log-likelihood when the number of particles is sufficiently large.
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.
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.
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.
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. 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 …
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 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. 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.
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.
New estimators improve efficiency in two-phase designs with coarsened data.
problem Efficient estimation in two-phase designs with incomplete data.
method Developed new estimators within the TMLE framework.
result New estimators are asymptotically equivalent and more efficient.
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.
Regularized MLE for MoE models tackles high-dimensional heterogeneous data.
problem Fitting and feature selection in Mixtures-of-Experts models for high-dimensional data.
method Proposes a regularized maximum likelihood estimation approach with hybrid EM/MM algorithms.
result Automatic recovery of sparse solutions without thresholding and matrix inversion.
We propose a new method for estimating the intrinsic dimension of a dataset by applying the principle of regularized maximum likelihood to the distances between close neighbors. We propose a regularization scheme which is motivated by divergence minimization principles. We derive the estimator by a Poisson process appr…
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 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.
Transformer learns to estimate negative binomial parameters efficiently.
problem Parameter estimation for over-dispersed count data in large screens.
method Pre-trained transformer trained on synthetic data generation to invert parameter to count transformation.
result Method of moments provides faster, more efficient, and better-calibrated estimates.
A new path gradient estimator speeds up normalizing flows without sacrificing accuracy.
problem High computational cost and limited scalability of path gradient estimators for normalizing flows.
method Proposed a fast path gradient estimator that improves computational efficiency and scalability.
result The new estimator achieves superior performance and reduced variance across various applications.
New estimators outperform maximum likelihood without hyper-parameter estimation.
problem Improving system identification performance without hyper-parameter estimation.
method Developed generalized Bayes and closed-form biased estimators using excess MSE.
result New estimators have comparable performance to empirical-Bayes-based regularized estimator.
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.
Study on MLE growth rate for stable CIR process, proving consistency and normality.
problem Estimating the growth rate of a stable CIR process from continuous observations.
method Maximum likelihood estimation for a specific type of process.
result Strong consistency and asymptotic normality in subcritical and supercritical cases, asymptotic mixed normality in supercritical, open in critical case.
ARIMLE optimizes classifier fusion for brain-computer interface.
problem Improving ensemble classifier aggregation performance.
method ARIMLE uses agreement rate to estimate classifier accuracy, then refines a maximum likelihood estimator.
result ARIMLE outperforms majority voting and other methods in brain-computer interface applications.
Paper proposes a simple estimator for DPP correlation kernels.
problem Estimating the correlation kernel matrix of DPPs.
method Closed-form estimator for correlation kernel, easy to implement.
result Consistency and asymptotic normality of the estimator proved.
GeoMLE improves intrinsic dimension estimation for nonlinearly embedded data.
problem Inaccurate estimation of intrinsic dimension for nonlinearly embedded data.
method GeoMLE uses geometric properties to correct the standard MLE for flat manifolds.
result GeoMLE achieves state-of-the-art performance and is computationally efficient.
We study asymptotic properties of maximum likelihood estimators for Heston models based on continuous time observations of the log-price process. We distinguish three cases: subcritical (also called ergodic), critical and supercritical. In the subcritical case, asymptotic normality is proved for all the parameters, whi…
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.
DQAEM uses quantum annealing to improve MLE.
problem EM algorithm's dependence on initial configurations and inability to find global optimum.
method Quantum annealing extension of EM (DQAEM).
result DQAEM outperforms EM in MLE.
Deep neural networks improve angle of arrival estimation with lower complexity.
problem Estimating the number of sources and their angles of arrival from a single antenna array observation.
method Apply a deep neural network (DNN) approach to the problem.
result Deep neural networks can attain maximum likelihood performance with feasible complexity and outperform other methods.