arXiv research

Paper establishes MLE consistency for market microstructure models.

New study shows MLE can avoid model collapse with gradual synthetic data addition.

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…

Paper explores Elliptical Wishart distributions in signal processing and machine learning.

This paper explores the preference-based top-$K$ 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-$K$ ranked items, based on partially revealed preferences. We focus on the Bradley-Terry-Luce (BTL) model…

DMLE improves active learning by correcting MLE for sample dependencies.

A new ranking model with dynamic covariates improves statistical analysis.

The paper strengthens the classical result of MLE convergence to a Gaussian distribution.

Estimates log-concave densities in graphical models using tent functions.

Develops new Markov processes with switching rates and past dependence.

We consider a jump-type Cox--Ingersoll--Ross (CIR) process driven by a standard Wiener process and a subordinator, and we study asymptotic properties of the maximum likelihood estimator (MLE) for its growth rate. We distinguish three cases: subcritical, critical and supercritical. In the subcritical case we prove weak …

The paper develops methods for high-dimensional inference in Markov random fields.

Score matching fails for general point processes, a new estimator improves accuracy.

New algorithm improves hypergraph clustering for unbalanced communities.

Maximum Likelihood Estimators (MLE) has many good properties. For example, the asymptotic variance of MLE solution attains equality of the asymptotic Cram{é}r-Rao lower bound (efficiency bound), which is the minimum possible variance for an unbiased estimator. However, obtaining such MLE solution requires calculating t…

New approach resolves ambiguity in PPCA model's maximum likelihood estimation.

MLE and CVE are equivalent under exponential families, leading to faster and more stable EM algorithms.

Paper proposes MWDE for estimating finite location-scale mixtures.

We describe $k$-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…

The paper analyzes RLHF with human feedback and provides convergence results for MLE and pessimistic MLE.

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 $h_{\text{MLE}}$, parameterized by two scalars measuring the overall magnitu…

This paper improves topic model estimation for sparse distributions and applies it to Wasserstein distances.

We explore the performance of sample average approximation in comparison with several other methods for stochastic optimization when there is information available on the underlying true probability distribution. The methods we evaluate are (a) bagging; (b) kernel smoothing; (c) maximum likelihood estimation (MLE); and…

EBR improves NMT by re-ranking samples drawn from MLE-trained models.

Improved MLE for Hawkes Processes stabilizes unstable optimization.

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 …

The Schwartz-Smith model parameters are estimated using Kalman Filter with additional constraints.

In this paper, we present a novel framework incorporating a combination of sparse models in different domains. We posit the observed data as generated from a linear combination of a sparse Gaussian Markov model (with a sparse precision matrix) and a sparse Gaussian independence model (with a sparse covariance matrix). …

Distance-based hierarchical clustering (HC) methods are widely used in unsupervised data analysis but few authors take account of uncertainty in the distance data. We incorporate a statistical model of the uncertainty through corruption or noise in the pairwise distances and investigate the problem of estimating the HC…

SpinSVAR estimates SVAR models with sparse input, improving accuracy and scalability.

The parameter estimation of unnormalized models is a challenging problem. The maximum likelihood estimation (MLE) is computationally infeasible for these models since normalizing constants are not explicitly calculated. Although some consistent estimators have been proposed earlier, the problem of statistical efficienc…

New anomaly estimator reduces bias in MLE for normally distributed data.

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…

Paper extends RUMs with features to handle incomplete preferences and proves identifiability.

The stochastic block model (SBM) is a popular tool for community detection in networks, but fitting it by maximum likelihood (MLE) involves a computationally infeasible optimization problem. We propose a new semidefinite programming (SDP) solution to the problem of fitting the SBM, derived as a relaxation of the MLE. W…

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.

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…

Advocates for MLE in regression and forecasting for better inductive biases and post-hoc optimization.

This paper uses Bayesian optimization to efficiently identify stochastic dynamical systems.

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.

Paper learns Cartesian product graphs with Laplacian constraints.

MLE works best for covariate shift without modifications.

Improved convergence rates for MLE in mixture models using penalized log-likelihood.

Unified detector calibration and simulation using MLE from generative models.

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 fast method for estimating radar amplitude density parameters.