Related papers: Likelihood landscape of binary latent model on a t…

In many statistical learning problems, the target functions to be optimized are highly non-convex in various model spaces and thus are difficult to analyze. In this paper, we compute \emph{Energy Landscape Maps} (ELMs) which characterize…

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…

We consider the nonparametric maximum likelihood estimation for the underlying event time based on mixed-case interval-censored data, under a log-concavity assumption on its distribution function. This generalized framework relaxes the…

A fundamental question in the field of molecular computation is what computational tasks a biochemical system can carry out. In this work, we focus on the problem of finding the maximum likelihood estimate (MLE) for log-affine models. We…

A Maximum Likelihood recursive state estimator is derived for non-linear and non-Gaussian state-space models. The estimator combines a particle filter to generate the conditional density and the Expectation Maximization algorithm to compute…

Empirical Bayes provides a powerful approach to learning and adapting to latent structure in data. Theory and algorithms for empirical Bayes have a rich literature for sequence models, but are less understood in settings where latent…

We propose a topological learning algorithm for the estimation of the conditional dependency structure of large sets of random variables from sparse and noisy data. The algorithm, named Maximally Filtered Clique Forest (MFCF), produces a…

Conventional methods for computing maximum-likelihood estimators (MLE) often converge slowly in practical situations, leading to a search for simplifying methods that rely on additional assumptions for their validity. In this work, we…

A Brownian motion tree (BMT) model is a Gaussian model whose associated set of covariance matrices is linearly constrained according to common ancestry in a phylogenetic tree. We study the complexity of inferring the maximum likelihood (ML)…

The matrix normal model, i.e., the family of Gaussian matrix-variate distributions whose covariance matrices are the Kronecker product of two lower dimensional factors, is frequently used to model matrix-variate data. The tensor normal…

Estimating the unconstrained mean and covariance matrix is a popular topic in statistics. However, estimation of the parameters of $N_p(\mu,\Sigma)$ under joint constraints such as $\Sigma\mu = \mu$ has not received much attention. It can…

Consider a setting with $N$ independent individuals, each with an unknown parameter, $p_i \in [0, 1]$ drawn from some unknown distribution $P^\star$. After observing the outcomes of $t$ independent Bernoulli trials, i.e., $X_i \sim…

Maximum likelihood estimators (MLE) and control variate estimators (CVE) have been used in conjunction with known information across sketching algorithms and applications in machine learning. We prove that under certain conditions in an…

We provide a polyhedral description of the conditions for the existence of the maximum likelihood estimate (MLE) for a hierarchical log-linear model. The MLE exists if and only if the observed margins lie in the relative interior of the…

This work characterizes the effect of depth on the optimization landscape of linear regression, showing that, despite their nonconvexity, deeper models have more desirable optimization landscape. We consider a robust and over-parameterized…

A central task in the study of molecular sequence data from present-day species is the reconstruction of the ancestral relationships. The most established approach to tree reconstruction is the maximum likelihood (ML) method. In this…

We solve the problem of estimating the distribution of presumed i.i.d. observations for the total variation loss. Our approach is based on density models and is versatile enough to cope with many different ones, including some density…

Temporal Point Processes (TPP) with partial likelihoods involving a latent structure often entail an intractable marginalization, thus making inference hard. We propose a novel approach to Maximum Likelihood Estimation (MLE) involving…

Likelihood-based methods are widely considered the best approaches for reconstructing ancestral states. Although much effort has been made to study properties of these methods, previous works often assume that both the tree topology and…

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)…