Related papers: Ensemble Estimation of Distributional Functionals …
In this paper, we consider nonparametric multidimensional finite mixture models and we are interested in the semiparametric estimation of the population weights. Here, the i.i.d. observations are assumed to have at least three components…
Estimating the score, i.e., the gradient of log density function, from a set of samples generated by an unknown distribution is a fundamental task in inference and learning of probabilistic models that involve flexible yet intractable…
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 revisit the classical problem of estimating an unknown distribution from its samples by fitting a mixture model that minimizes cross-entropy loss. Framing the task as a stochastic convex optimization problem over the space of $ M…
We provide general adaptive upper bounds for estimating nonparametric functionals based on second order U-statistics arising from finite dimensional approximation of the infinite dimensional models. We then provide examples of functionals…
We consider a multi-process remote estimation system observing $K$ independent Ornstein-Uhlenbeck processes. In this system, a shared sensor samples the $K$ processes in such a way that the long-term average sum mean square error (MSE) is…
Nearest neighbor (NN) algorithms have been extensively used for missing data problems in recommender systems and sequential decision-making systems. Prior theoretical analysis has established favorable guarantees for NN when the underlying…
We consider the problem of clustering noisy finite-length observations of stationary ergodic random processes according to their nonparametric generative models without prior knowledge of the model statistics and the number of generative…
Many statistical procedures, including goodness-of-fit tests and methods for independent component analysis, rely critically on the estimation of the entropy of a distribution. In this paper, we seek entropy estimators that are efficient…
A combinatorial analysis of the false alarm (FA) and misdetection (MD) probabilities of non-adaptive group testing with sparse pooling graphs is developed. The analysis targets the combinatorial orthogonal matching pursuit and definite…
We develop and analyze $M$-estimation methods for divergence functionals and the likelihood ratios of two probability distributions. Our method is based on a non-asymptotic variational characterization of $f$-divergences, which allows the…
While deep neural networks (DNNs) are used for prediction, inference on DNN-estimated subject-specific means for categorical or exponential family outcomes remains underexplored. We address this by proposing a DNN estimator under…
This letter presents an improved version of diffusion least mean ppower (LMP) algorithm for distributed estimation. Instead of sum of mean square errors, a weighted sum of mean square error is defined as the cost function for global and…
We introduce a novel \textit{k}-nearest neighbor (\textit{k}-NN) regression method for joint estimation of the conditional mean and variance. The proposed algorithm preserves the computational efficiency and manifold-learning capabilities…
This paper investigates the large sample properties of local regression distribution estimators, which include a class of boundary adaptive density estimators as a prime example. First, we establish a pointwise Gaussian large sample…
We analyze the $\ell_1$ and $\ell_\infty$ convergence rates of k nearest neighbor density estimation method. Our analysis includes two different cases depending on whether the support set is bounded or not. In the first case, the…
This paper deals with nonparametric maximum likelihood estimation for Gaussian locally stationary processes. Our nonparametric MLE is constructed by minimizing a frequency domain likelihood over a class of functions. The asymptotic behavior…
Demands for minimum parameter setup in machine learning models are desirable to avoid time-consuming optimization processes. The $k$-Nearest Neighbors is one of the most effective and straightforward models employed in numerous problems.…
Statistical divergences (SDs), which quantify the dissimilarity between probability distributions, are a basic constituent of statistical inference and machine learning. A modern method for estimating those divergences relies on…
The advent of data science has spurred interest in estimating properties of distributions over large alphabets. Fundamental symmetric properties such as support size, support coverage, entropy, and proximity to uniformity, received most…