Related papers: Noise contrastive estimation: asymptotics, compari…
Ordinary Differential Equations (ODEs) have recently gained a lot of attention in machine learning. However, the theoretical aspects, e.g., identifiability and asymptotic properties of statistical estimation are still obscure. This paper…
We introduce a general Monte Carlo method based on Nested Sampling (NS), for sampling complex probability distributions and estimating the normalising constant. The method uses one or more particles, which explore a mixture of nested…
Principal stratification is a widely used framework for addressing post-randomization complications. After using principal stratification to define causal effects of interest, researchers are increasingly turning to finite mixture models to…
Noise ubiquitously exists in signals due to numerous factors including physical, electronic, and environmental effects. Traditional methods of symbolic regression, such as genetic programming or deep learning models, aim to find the most…
Sequential Monte Carlo Samplers are a class of stochastic algorithms for Monte Carlo integral estimation w.r.t. probability distributions, which combine elements of Markov chain Monte Carlo methods and importance sampling/resampling…
In this paper, we propose an estimator of the generalized maximum mean discrepancy between several distributions, constructed by modifying a naive estimator. Asymptotic normality is obtained for this estimator both under equality of these…
This paper develops a quasi-maximum likelihood estimator for genuinely unbalanced dynamic network panel data models with individual fixed effects. We propose a model that accommodates contemporaneous and lagged network spillovers, temporal…
This paper investigates asymptotic properties of algorithms that can be viewed as robust analogues of the classical empirical risk minimization. These strategies are based on replacing the usual empirical average by a robust proxy of the…
In this paper non-asymptotic exact exponential estimates are derived (under minimal conditions) for the tail of deviation of the MLE distribution in the so-called natural terms: natural function, natural distance, metric entropy, Banach…
Maximum likelihood estimation in nonlinear models can exhibit substantial instability in finite samples when the data provide limited information about certain parameters. Such instability is driven by rare but extreme realizations of the…
In compressed sensing, measurements are typically contaminated by additive noise, and therefore, information about the noise variance is often needed to design algorithms. In this paper, we propose a method for estimating the unknown noise…
We study nonparametric maximum likelihood estimation of a log-concave density function $f_0$ which is known to satisfy further constraints, where either (a) the mode $m$ of $f_0$ is known, or (b) $f_0$ is known to be symmetric about a fixed…
Determinantal Point Processes (DPPs) have attracted significant interest from the machine-learning community due to their ability to elegantly and tractably model the delicate balance between quality and diversity of sets. DPPs are commonly…
This paper investigates the asymptotic properties of parameter estimation for the Ewens--Pitman partition with parameters $0<\alpha<1$ and $\theta>-\alpha$. Especially, we show that the maximum likelihood estimator (MLE) of $\alpha$ is…
Maximum pseudolikelihood (MPL) estimators are useful alternatives to maximum likelihood (ML) estimators when likelihood functions are more difficult to manipulate than their marginal and conditional components. Furthermore, MPL estimators…
There are a number of hypotheses underlying the existence of adversarial examples for classification problems. These include the high-dimensionality of the data, high codimension in the ambient space of the data manifolds of interest, and…
Nested sampling is a simulation method for approximating marginal likelihoods proposed by Skilling (2006). We establish that nested sampling has an approximation error that vanishes at the standard Monte Carlo rate and that this error is…
We consider quantile estimation using Markov chain Monte Carlo and establish conditions under which the sampling distribution of the Monte Carlo error is approximately Normal. Further, we investigate techniques to estimate the associated…
The sampling of probability distributions specified up to a normalization constant is an important problem in both machine learning and statistical mechanics. While classical stochastic sampling methods such as Markov Chain Monte Carlo…
This work establishes regularity conditions for consistency and asymptotic normality of the multiple parameter maximum likelihood estimator(MLE) from censored data, where the censoring mechanism is in the form of $1$-bit measurements. The…