We describe -MLE, a fast and efficient local search algorithm for learning finite statistical mixtures of exponential families such as Gaussian mixture models. Mixture models are traditionally learned using the expectation-maximization (EM) soft clustering technique that monotonically increases the incomplete (expec…
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48 results for “weighted MLE”
MLE and CVE are equivalent under exponential families, leading to faster and more stable EM algorithms.
problem Finding maximum likelihood estimators (MLE) efficiently and stably.
method Proved equivalence between MLE and CVE under exponential families, leading to an EM algorithm.
result EM algorithm achieves the same asymptotic variance as MLE and is faster and more stable.
Improved convergence rates for MLE in mixture models using penalized log-likelihood.
problem Convergence rates for MLE in finite mixture models.
method Penalizing log-likelihood to discourage vanishing mixing weights, using Wasserstein distance and new loss functions.
result Improved convergence rates for some mixture components, faster than traditional methods.
Maximum Likelihood Estimation (MLE) is the bread and butter of system inference for stochastic systems. In some generality, MLE will converge to the correct model in the infinite data limit. In the context of physical approaches to system inference, such as Boltzmann machines, MLE requires the arduous computation of pa…
Paper tackles ranking items with a semi-random comparison graph and a monotone adversary.
problem Ranking items based on pairwise comparisons from a semi-random comparison graph with a monotone adversary.
method Developed a weighted maximum likelihood estimator (MLE) and an SDP-based approach to reweight the semi-random graph.
result Achieves near-optimal sample complexity, up to a log^2(n) factor, for identifying the top-K preferred items.
MLE works best for covariate shift without modifications.
problem OOD generalization under covariate shift.
method Maximum Likelihood Estimation (MLE) without modifications.
result MLE achieves minimax optimality for covariate shift under well-specified setting.
This study tackles adversarial corruption in model-based reinforcement learning.
problem Adversarial corruption in model-based reinforcement learning.
method Maximum likelihood estimation (MLE) approach for learning transition model in both online and offline settings.
result Proves a regret of for CR-OMLE and a suboptimality of for CR-PMLE.
This paper improves topic model estimation for sparse distributions and applies it to Wasserstein distances.
problem Estimating sparse topic distributions in topic models with high-dimensional data.
method MLE for topic weights when is known, plug-in estimator for unknown .
result MLE can be exactly sparse and contain true zero pattern of topic weights.
New algorithm improves hypergraph clustering for unbalanced communities.
problem Hypergraph clustering with unbalanced community sizes and outliers.
method CRTMLE algorithm using convex relaxation of truncated MLE.
result Achieves optimal recovery guarantees for unbalanced community sizes.
The paper analyzes RLHF with human feedback and provides convergence results for MLE and pessimistic MLE.
problem Improving RLHF with human feedback from pairwise or -wise comparisons.
method Theoretical framework for RLHF with convergence analysis of MLE and pessimistic MLE.
result MLE fails but pessimistic MLE provides improved policies under certain coverage assumptions.
This paper rigorously establishes that the existence of the maximum likelihood estimate (MLE) in high-dimensional logistic regression models with Gaussian covariates undergoes a sharp `phase transition'. We introduce an explicit boundary curve , parameterized by two scalars measuring the overall magnitu…
Improved MLE for Hawkes Processes stabilizes unstable optimization.
problem Unstable Maximum Likelihood Estimation (MLE) for Hawkes Processes.
method Simple stabilization procedure to improve MLE without restrictive assumptions.
result Stabilized MLE outperforms traditional methods over various sequence lengths.
Mixtures-of-Experts models and their maximum likelihood estimation (MLE) via the EM algorithm have been thoroughly studied in the statistics and machine learning literature. They are subject of a growing investigation in the context of modeling with high-dimensional predictors with regularized MLE. We examine MoE with …
Unified framework SVAM learns GLMs robustly to adversarial label corruption.
problem Learning GLMs under adversarial label corruption.
method SVAM framework based on variance reduction technique.
result Provable model recovery guarantees superior to state-of-the-art.
New anomaly estimator reduces bias in MLE for normally distributed data.
problem Bias in Maximum Likelihood Estimation of structured anomalies.
method Derive a new anomaly estimator using a mixture model.
result New estimator is asymptotically unbiased regardless of anomaly family size.
Paper establishes MLE consistency for market microstructure models.
problem Estimating parameters in partially observed diffusion models.
method Tractable sufficient condition for MLE consistency based on stationary distribution.
result Maximum likelihood estimators are consistent for market microstructure parameters.
Ensemble learning is a powerful approach to construct a strong learner from multiple base learners. The most popular way to aggregate an ensemble of classifiers is majority voting, which assigns a sample to the class that most base classifiers vote for. However, improved performance can be obtained by assigning weights…
The Chirikov standard map and the 2D Froeschlé map are investigated. A few thousand values of the Hurst exponent (HE) and the maximal Lyapunov exponent (mLE) are plotted in a mixed space of the nonlinear parameter versus the initial condition. Both characteristic exponents reveal remarkably similar structures in this s…
Score matching fails for general point processes, a new estimator improves accuracy.
problem Score matching estimators fail for general point processes.
method Introduced a weighted score matching estimator for point processes.
result The weighted score matching estimator accurately estimates model parameters on synthetic and real data.
We conduct non-asymptotic analysis on the mean-field variational inference for approximating posterior distributions in complex Bayesian models that may involve latent variables. We show that the mean-field approximation to the posterior can be well-approximated relative to the Kullback-Leibler divergence discrepancy m…
A new method for sampling on manifolds reduces density estimation errors.
problem Sampling on implicitly defined manifolds in various applications.
method Polynomial-Maximization Moment (PMM) estimator replacing local k-nearest-neighbour density estimate.
result Reduces density estimation errors by 22--36% on asymmetric gamma and boundary-spacing regimes.
We have observed an interesting, yet unexplained, phenomenon: Semidefinite programming (SDP) based relaxations of maximum likelihood estimators (MLE) tend to be tight in recovery problems with noisy data, even when MLE cannot exactly recover the ground truth. Several results establish tightness of SDP based relaxations…
New estimators improve Rasch model item parameter estimation for sparse data.
problem Estimating item parameters in sparse Rasch model data.
method Random pairing maximum likelihood estimator (RP-MLE) and its bootstrapped variant (MRP-MLE).
result RP-MLE and MRP-MLE are minimax optimal and provide precise item parameter estimates.
Operational risk models commonly employ maximum likelihood estimation (MLE) to fit loss data to heavy-tailed distributions. Yet several desirable properties of MLE (e.g. asymptotic normality) are generally valid only for large sample-sizes, a situation rarely encountered in operational risk. In this paper, we study how…
Paper tackles exposure bias in recommender systems using contrastive learning.
problem Exposure bias in large-scale recommender systems.
method Contrastive learning to reduce exposure bias via inverse propensity weighting.
result Contrastive learning effectively reduces exposure bias in recommender systems.
This paper explores the preference-based top- rank aggregation problem. Suppose that a collection of items is repeatedly compared in pairs, and one wishes to recover a consistent ordering that emphasizes the top- ranked items, based on partially revealed preferences. We focus on the Bradley-Terry-Luce (BTL) model…
Advocates for MLE in regression and forecasting for better inductive biases and post-hoc optimization.
problem Designing effective loss functions for regression and forecasting.
method Maximum Likelihood Estimation (MLE) approach for regression and forecasting.
result MLE approach outperforms direct empirical risk minimization under certain conditions and for various datasets.
This letter proposes a low-computational Bayesian algorithm for noisy sparse recovery in the context of one bit compressed sensing with sensing matrix perturbation. The proposed algorithm which is called BHT-MLE comprises a sparse support detector and an amplitude estimator. The support detector utilizes Bayesian hypot…
Proposes MLEs for MMJDM with EM-algorithm.
problem Estimating stock prices with varying drift and volatility.
method EM-algorithm for MLEs of MMJDM.
result Validated with simulated data and fitted to Amazon and Netflix stock prices.
Develops new Markov processes with switching rates and past dependence.
problem Modeling processes with dynamic switching rates and path dependence.
method Introduces a new class of Markov jump processes with regime switching and path dependence. Derives distributional properties and maximum likelihood estimates.
result Maximum likelihood estimates of the process parameters are derived in closed form and have asymptotic normality.
DMLE improves active learning by correcting MLE for sample dependencies.
problem Dependencies among samples in active learning affect model parameter estimation.
method Dependency-aware Maximum Likelihood Estimation (DMLE).
result DMLE achieves superior performance across multiple benchmark datasets.
The paper improves spectral ranking methods for diverse comparison graphs.
problem Estimating preference scores from multiway comparisons with heterogeneous sizes.
method Develops a two-step spectral method for estimating preference scores and their uncertainties.
result The two-step spectral method achieves the same asymptotic efficiency as the Maximum Likelihood Estimator (MLE).
Paper explores Elliptical Wishart distributions in signal processing and machine learning.
problem Estimating parameters of Elliptical Wishart distributions.
method Proposes fixed point and Riemannian optimization algorithms for maximum likelihood estimation.
result Characterizes existence, uniqueness, and convergence of the MLE.
We consider a stable Cox--Ingersoll--Ross process driven by a standard Wiener process and a spectrally positive strictly stable Lévy process, and we study asymptotic properties of the maximum likelihood estimator (MLE) for its growth rate based on continuous time observations. We distinguish three cases: subcritical, c…
Unified detector calibration and simulation using MLE from generative models.
problem Combining detector calibration and simulation using traditional methods.
method Maximum likelihood estimation from conditional generative models.
result Prior-independent and non-Gaussian resolutions possible.
Distributed learning of probabilistic models from multiple data repositories with minimum communication is increasingly important. We study a simple communication-efficient learning framework that first calculates the local maximum likelihood estimates (MLE) based on the data subsets, and then combines the local MLEs t…
A new ranking model with dynamic covariates improves statistical analysis.
problem Statistical ranking with varying covariates across comparisons.
method Introduced a Plackett--Luce framework for covariate-assisted ranking, providing conditions for model identifiability and MLE existence, and developing an alternating maximization algorithm.
result Uniform consistency of the Maximum Likelihood Estimation (MLE) under suitable assumptions on graph design and covariates.
New study shows MLE can avoid model collapse with gradual synthetic data addition.
problem Model collapse in generative models trained on synthetic data.
method Theoretical study of maximum likelihood estimation (MLE) under iterative training with accumulating synthetic data.
result Non-asymptotic bounds show MLE can avoid model collapse even as real data fraction vanishes.
A fast method for estimating radar amplitude density parameters.
problem Accurate estimation of amplitude density function parameters in radar applications.
method Projecting amplitude data onto horizontal and vertical axes, then using MLE for -stale distribution parameters.
result The average of computed MLEs based on two projections is a fast and accurate estimator for amplitude distribution parameters.
A number of applications (e.g., AI bot tournaments, sports, peer grading, crowdsourcing) use pairwise comparison data and the Bradley-Terry-Luce (BTL) model to evaluate a given collection of items (e.g., bots, teams, students, search results). Past work has shown that under the BTL model, the widely-used maximum-likeli…
A Gradient Analysis Framework for Rewarding Good and Penalizing Bad Examples in Language Modelscs.CL
This paper introduces a gradient analysis framework to improve language model performance by rewarding good examples and penalizing bad ones.
problem Improving language model output quality by penalizing bad examples.
method Gradient analysis of loss functions to reward good examples and penalize bad ones.
result ExMATE is superior to MLE and combining DPO with ExMATE enhances performance.
The paper strengthens the classical result of MLE convergence to a Gaussian distribution.
problem The classical result of MLE convergence to a Gaussian distribution.
method Sub-Gaussian concentration and entropic normality of the normalized MLE.
result Entropic central limit theorem for a smoothed version of the estimator.
Transformers can simulate MLE for Bayesian network sequences.
problem Understanding transformers' capabilities in Bayesian network sequence generation.
method In-context maximum likelihood estimation (MLE) for autoregressive sequence generation.
result A simple transformer model can estimate Bayesian network probabilities and generate new samples.
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.
Estimates log-concave densities in graphical models using tent functions.
problem Maximum likelihood estimation of log-concave densities in undirected graphs.
method MLE as product of tent functions corresponding to maximal cliques.
result MLE can be found via convex optimization.
New Riemannian radial distributions help estimate parameters on symmetric spaces.
problem Challenges in manifold data analysis due to lack of parametric distributions.
method Introduced Riemannian radial distributions on symmetric spaces, utilized symmetry, and developed M-estimators.
result MLE achieves root-n convergence rate up to logarithmic terms, demonstrating optimality.
C-SURE improves complex-valued deep learning models by shrinking estimates, outperforming MLE and SurReal.
problem Improving accuracy and robustness of complex-valued deep learning models.
method Proposes a Stein's unbiased risk estimate (SURE) for complex-valued data and integrates it into a prototype CNN classifier.
result C-SURE outperforms SurReal and MLE in accuracy and robustness on complex-valued datasets.
This paper uses Bayesian optimization to efficiently identify stochastic dynamical systems.
problem Efficiently identifying linear stochastic dynamical systems with unknown coefficients and noise variances.
method Adaptive Bayesian optimization with ensemble Gaussian processes (EGP) and Kalman filter recursion.
result BO-based estimator achieves RMSE below the Cramer-Rao bound, improving robustness and consistency.