Related papers: Estimation Error: Distribution and Pointwise Limit…
Distributional regression aims at estimating the conditional distribution of a targetvariable given explanatory co-variates. It is a crucial tool for forecasting whena precise uncertainty quantification is required. A popular methodology…
This paper studies a family of estimators based on noise-contrastive estimation (NCE) for learning unnormalized distributions. The main contribution of this work is to provide a unified perspective on various methods for learning…
This paper considers the problem of estimating probabilities of the form $\mathbb{P}(Y \leq w)$, for a given value of $w$, in the situation that a sample of i.i.d.\ observations $X_1, \ldots, X_n$ of $X$ is available, and where we…
The normal-inverse-Wishart (NIW) distribution is commonly used as a prior distribution for the mean and covariance parameters of a multivariate normal distribution. The family of NIW distributions is also a minimal exponential family. In…
The Expected Calibration Error (ece), the dominant calibration metric in machine learning, compares predicted probabilities against empirical frequencies of binary outcomes. This is appropriate when labels are binary events. However, many…
Bayesian approach to inverse problems is studied in the case where the forward map is a linear hypoelliptic pseudodifferential operator and measurement error is additive white Gaussian noise. The measurement model for an unknown Gaussian…
In this article we recover the distribution function (and possible density) of an arbitrary random variable that is subject to an additive measurement error. This problem is also known as deconvolution and has a long tradition in…
Let $X_{1}=(W_{1},Y_{1}),\ldots,X_{n}=(W_{n},Y_{n})$ be $n$ pairs of independent random variables. We assume that, for each $i\in\{1,\ldots,n\}$, the conditional distribution of $Y_{i}$ given $W_{i}$ belongs to a one-parameter exponential…
We consider the problem of modulating the value of a parameter onto a band-limited signal to be transmitted over a continuous-time, additive white Gaussian noise (AWGN) channel, and estimating this parameter at the receiver. The performance…
Consider the nonparametric regression model Y=m(X)+E, where the function m is smooth but unknown, and E is independent of X. An estimator of the density of the error term E is proposed and its weak consistency is obtained. The contribution…
Consider a nonparametric regression model with one-sided errors and regression function in a general H\"older class. We estimate the regression function via minimization of the local integral of a polynomial approximation. We show uniform…
For enhancement of noisy speech, a method of threshold determination based on modeling of Teager energy (TE) operated perceptual wavelet packet (PWP) coefficients of the noisy speech by exponential distribution is presented. A custom…
The convergence of expectation-maximization (EM)-based algorithms typically requires continuity of the likelihood function with respect to all the unknown parameters (optimization variables). The requirement is not met when parameters…
Estimation of the mean vector and covariance matrix is of central importance in the analysis of multivariate data. In the framework of generalized linear models, usually the variances are certain functions of the means with the normal…
We consider the problem of estimating the mean of a symmetric log-concave distribution under the constraint that only a single bit per sample from this distribution is available to the estimator. We study the mean squared error as a…
Distinguishing the cause and effect from bivariate observational data is the foundational problem that finds applications in many scientific disciplines. One solution to this problem is assuming that cause and effect are generated from a…
Many statistical estimators are defined as the fixed point of a data-dependent operator, with estimators based on minimizing a cost function being an important special case. The limiting performance of such estimators depends on the…
In numerous instances, the generalized exponential distribution can be used as an alternative to the most widely used non-regular family of distributions: Weibull, gamma, lognormal with three-parameters when analyzing lifetime or any skewed…
Random feature neural network approximations of the potential in Hamiltonian systems yield approximations of molecular dynamics correlation observables that have the expected error $\mathcal{O}\big((K^{-1}+J^{-1/2})^{\frac{1}{2}}\big)$, for…
We propose flexible Gaussian representations for conditional cumulative distribution functions and give a concave likelihood criterion for their estimation. Optimal representations satisfy the monotonicity property of conditional cumulative…