Related papers: Matching Observations to Distributions: Efficient …
Maximum Likelihood Estimation (MLE) and Likelihood Ratio Test (LRT) are widely used methods for estimating the transition probability matrix in Markov chains and identifying significant relationships between transitions, such as equality.…
In this paper we further investigate the well-studied problem of finding a perfect matching in a regular bipartite graph. The first non-trivial algorithm, with running time $O(mn)$, dates back to K\"{o}nig's work in 1916 (here $m=nd$ is the…
In the online bipartite matching problem with replacements, all the vertices on one side of the bipartition are given, and the vertices on the other side arrive one by one with all their incident edges. The goal is to maintain a maximum…
Maximum likelihood estimation (MLE) is a fundamental computational problem in statistics. The problem is to maximize the likelihood function with respect to given data on a statistical model. An algebraic approach to this problem is to…
We study the problem of recovering a planted matching in randomly weighted complete bipartite graphs $K_{n,n}$. For some unknown perfect matching $M^*$, the weight of an edge is drawn from one distribution $P$ if $e \in M^*$ and another…
Towards understanding the fundamental limits of estimation from data of varied quality, we study the problem of estimating a mean parameter from heteroskedastic Gaussian observations where the variances are unknown and may vary arbitrarily…
As the maximum likelihood method is the most commonly used method for parameters estimation being unbiased, consistent, efficient, and asymptotically normal, MLE is used to fit the new distribution (MBUW). But in small to moderate sample…
A striking result of [Acharya et al. 2017] showed that to estimate symmetric properties of discrete distributions, plugging in the distribution that maximizes the likelihood of observed multiset of frequencies, also known as the profile…
This paper proposes a novel exact maximum likelihood (ML) estimation method for general Gaussian processes, where all parameters are estimated jointly. The exact ML estimator (MLE) is consistent and asymptotically normally distributed. We…
Maximum likelihood estimation of linear functionals in the inverse problem of deconvolution is considered. Given observations of a random sample from a distribution $P_0\equiv P_{F_0}$ indexed by a (potentially infinite-dimensional)…
A major line of contemporary research on complex networks is based on the development of statistical models that specify the local motifs associated with macro-structural properties observed in actual networks. This statistical approach…
As the size of modern data sets exceeds the disk and memory capacities of a single computer, machine learning practitioners have resorted to parallel and distributed computing. Given that optimization is one of the pillars of machine…
We consider the system identification problem of estimating a dynamical parameter of a Markovian quantum open system (the atom maser), by performing continuous time measurements in the system's output (outgoing atoms). Two estimation…
We present new results for consistency of maximum likelihood estimators with a focus on multivariate mixed models. Our theory builds on the idea of using subsets of the full data to establish consistency of estimators based on the full…
Capturing aleatoric uncertainty is a critical part of many machine learning systems. In deep learning, a common approach to this end is to train a neural network to estimate the parameters of a heteroscedastic Gaussian distribution by…
In this paper we consider the well-studied problem of finding a perfect matching in a d-regular bipartite graph on 2n nodes with m=nd edges. The best-known algorithm for general bipartite graphs (due to Hopcroft and Karp) takes time…
This paper considers the nonparametric maximum likelihood estimator (MLE) for the joint distribution function of an interval censored survival time and a continuous mark variable. We provide a new explicit formula for the MLE in this…
Causal mediation analysis with random interventions has become an area of significant interest for understanding time-varying effects with longitudinal and survival outcomes. To tackle causal and statistical challenges due to the complex…
A new maximum approximate likelihood (ML) estimation algorithm for the mixture of Kent distribution is proposed. The new algorithm is constructed via the BSLM (block successive lower-bound maximization) framework and incorporates manifold…
Maximum likelihood estimation (MLE) is a fundamental problem in statistics. Characteristics of the MLE problem for discrete algebraic statistical models are reflected in the geometry of the $\textit{likelihood correspondence}$, a variety…